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IB Chemistry/Stoichiometry

1.1.1: Apply the mole concept to substances.
A mole is equivalent to 6.022 x 1023 (Avogadro's constant) units. Chemists refer to a mole of something much as we refer to a dozen eggs; it is a convenient unit for counting. The periodic table provides molar masses, i.e. the number of grams of an element equivalent to one mole of atoms of that specific element. This can be extrapolated to molecules of known molecular formula.

1.1.2: Determine the number of particles and the amount of substance (in moles).
Number of moles = mass / molar mass (Usually found on periodic table). The coefficients in chemical equations give the molar ratios of reactants and products i.e. 2A + 3B → C. There is 2/3 as much A as B, and 3 times more B than C involved in the reaction. Assuming the reaction goes to completion, there must be 3/2 times as much B as A for neither to remain. If this ratio is not followed, one will be a limiting reactant, and so the reaction will have some of the other reactant left over when it completes.

1.2.1: Define the term molar mass (M) and calculate the mass of one mole of a species.
The molar mass (M) is the mass of one mole's worth of a substance. To find the atomic/molecular mass, multiply the amount of moles by the molar mass.

1.2.2: Atomic mass, Molecular Mass, Formula Mass
The molar mass can be found in the periodic table, and will give the mass for 1 mol of the species (or rather the average accounting for different isotopes and their relative abundance).

1.2.3: Define the terms relative molecular mass (Mr) and relative atomic mass (Ar)
Mr is the ratio between the molar masses of two species. Ar is the ratio of the number of atoms between two species.

1.2.4: The difference between moles and mass
The number of moles refers to the amount of the substance, every mol being 6.02 x 1023 individual elements. Mass is the property which results in 'weight' in the presence of gravity. Given a molar mass, M a mass m and a number of mols n then n = m / M.

1.2.5: The difference between the molecular formula and the empirical formula
An 'empirical formula' is the formula describing the different atoms present in a molecules, and their ratios, but not the actual number present. For example, could be an empirical formula if x, y, and z are in lowest common terms. The molar mass can then be used to calculate the actual numbers of each atom present per molecule. The empirical formula can be determined by percentage composition, or anything else which gives the ratios of atoms present. A 'molecular formula', on the other hand, has the actual number of atoms present in each molecule. It will be an integer multiple of the empirical formula. For example,.

 * Example:
 * If you are given the empirical formula with an equation, and a mass of 30.08 g mol-1. What is the molecular formula of this compound?
 * We will compare the molecular mass of the molecular formula, 30.08 g mol-1, to that of the empirical formula, found to be 15.04 g mol-1. By dividing, we find the ratio to be 2, meaning that the molecular formula must be 2 times as large as the empirical formula.  The molecular formula is therefore.

1.3 Chemical Equations
Chemical equations are a convenient, standardised system for describing chemical reactions. They contain the following information.

 * The type of reactants consumed and products formed
 * The relative amounts of reactants and products
 * The electrical charges on ions
 * The physical state of each species (e.g. solid, liquid, gas)
 * The reaction conditions (e.g. temperature, catalysts)

The final two points are optional and sometimes omitted.

Anatomy of an Equation
$$\hbox{H}_{2 (g)} + \hbox{Cl}_{2 (g)} \to 2\hbox{HCl}_{(g)}$$

Hydrogen gas and chlorine gas will react vigorously to produce hydrogen chloride gas. The equation above illustrates this reaction. The reactants, hydrogen and chlorine, are written on the left and the products (hydrogen chloride) on the right. The large number 2 in front of HCl indicates that two molecules of HCl are produced for each 1 molecule of hydrogen and chlorine gas consumed. The 2 in subscript below H indicates that there are two hydrogen atoms in each molecule of hydrogen gas. Finally, the (g) symbols subscript to each species indicates that they are gases.

Reacting Species
Species in a chemical reaction is a general term used to mean atoms, molecules or ions. A species can contain more than one chemical element (HCl, for example, contains hydrogen and chlorine). Each species in a chemical equation is written:

$$\hbox{E}_{x}^y$$

E is the chemical symbol for the element, x is the number of atoms of that element in the species and y is the charge (if it is an ion).

For example, ethanol would be written $$\hbox{C}_2\hbox{H}_6\hbox{O}_{}$$ because each molecule contains 2 carbon, 6 hydrogen and 1 oxygen atom. A magnesium ion would be written $$\hbox{Mg}^{2+}$$ because it has a double positive charge. Finally, an ammonium ion would be written $$[\hbox{NH}_4]^+$$ because each molecule contains 1 nitrogen and 4 hydrogen atoms and has a charge of 1+.

Coefficients
The numbers in front of each species have a very important meaning - they indicate the relative amounts of the atoms that react. The number infront of each species is called a coefficient. In the above equation, for example, one H2 molecule reacts with one Cl2 molecule to produce two molecules of HCl. This can also be interpreted as moles (i.e. 1 mol H2 and 1 mol Cl2 produces 2 mol HCl).

Other Information
Occasionally, other information about a chemical reaction will be supplied in an equation (such as temperature or other reaction conditions). This information is often written above the reaction arrow. We will ignore this for now, as it only complicates matters (and it's hard to draw in TeX).

1.3.1 : The mole ratio of two species in a chemical equation is the ratio of their coefficients...ie aX + bY → cZ : The ratio of X/Y is a/b, Y/Z = b/c etc.

Chemical equations are useful because they give the relative amounts of the substances that react in a chemical equation. For example, from the chemical equation for the formation of ammonia, we can see that one mole of nitrogen gas will combine with three moles of hydrogen gas to form two moles of ammonia gas.

$$\hbox{N}_{2 (g)} + 3\hbox{H}_{2 (g)} \to 2\hbox{NH}_{3 (g)}$$

1.3.2 : Balancing equations...change only the coefficients, not the subscripts to make sure all atoms, and charge is conserved (half equations can be balanced by addition of electrons to either side...2 half equations can be added by making the number of electrons equal in each, then vertically adding.)

In some cases, however, we may not know the relative amounts of each substance that reacts. Fortunately, we can always find the correct coefficients of an equation (the relative amounts of each reactant and product) by applying the law of conservation of matter. Because matter can neither be created nor destroyed, the total number of each atom on one side of the equation must be the same as the total on the other. This process of finding the coefficients is known as balancing the equation.

For example, assume in the above equation that we do not know how many moles of ammonia gas will be produced:

$$\hbox{N}_{2 (g)} + 3\hbox{H}_{2 (g)} \to ?\hbox{NH}_{3 (g)}$$

From the left side of this equation, we see that there are 2 atoms of nitrogen gas in the molecule N2 (2 atoms per molecule x 1 molecule), and 6 atoms of hydrogen gas in the 3 H2 molecules (2 atoms per molecule x 3 molecules). Because of the law of conservation of matter, there must also be 2 atoms nitrogen gas and 6 atoms of hydrogen gas on the right side. Since each molecule of the resultant ammonia gas (NH3) contains 1 atom of nitrogen and 3 atoms of hydrogen, 2 molecules are needed to obtain 2 atoms of nitrogen and 6 atoms of hydrogen.

In a similar manner, you can use the law of conservation of matter to solve equations containing a greater number of unknown coefficients (the relative amounts of each reactant and product), or even subscripts (the number of each element in a molecule) on either side of the equation:

$$\hbox{N}_{2 (g)} + 3\hbox{H}_{2 (g)} \to ?\hbox{NH}_{3 (g)}$$

1.3.3 : State symbols -- (s)-Solid, (l)-liquid, (g)-gas, (aq)-aqueous solution...i.e. something dissolved in water. Should be included in all chemical reactions (but won't be penalized).

$$\hbox{E}_{(state)} \,$$

E is the chemical symbol for the element and (state) is the physical state.

Examples
$$\hbox{CH}_{4} + 2\hbox{O}_{2} \to \hbox{CO}_{2} + 2\hbox{H}_{2}\hbox{O}$$

Above is the equation for burning methane gas (CH4) in the presence of oxygen (O2) to form carbon dioxide and water: CO2 and H2O respectively.

$$\hbox{Pb}^{+2}_{(aq)} + 2\hbox{I}^{-}_{(aq)} \to \hbox{PbI}_{2 (s)}$$

This is a precipitation reaction in which dissolved lead cations and iodide anions combine to form a solid yellow precipitate of lead iodide (an ionic solid).

Simple Formulas
Moles to Particles: number of moles x (6.02 x 1023/1 mole)= number of Particles

ex: 2.50 mol Zn x (6.02*1023 atoms of Zn/1 mol Zn)= 1.51 x 1024 atoms of Zn

Particles to Moles: number of Particles * (1 mole/6.02 x 1023)= number of moles

ex: 1.204 x 1024 atoms Ag * (1 mol/6.02 x 1023 atoms Ag)= 2 moles of Ag

Moles to Mass: number of moles x (molar mass/ 1 mole)= number of grams (or other unit of measurement)

ex: 3.57 mol Al x (26.982 g Al/ 1 mol Al)= 96.3 g

Mass to Moles: number of grams * (1 mole/ molar mass)= number of moles

ex: 25.5 g Ag * (1 mol Ag/ 107.868 g Ag)= 0.236 mol

ex: Na2CO3 = 2(mass of Na)+ mass of C + 3(mass of O)
 * to find molar mass

=2(22.990)+12.011+3(15.999)

=45.98+12.001+47.997

=105.99 g Na2CO3

1.4 Mass relationships in chemical reactions
1.4.1 : Mass is conserved throughout reactions. This fact allows masses to be calculated based on other masses in the reaction eg burning Mg in air to produce MgO and so to find the mass or Mg present in the original sample (ie purity)...can be extended to concentrations...ie titration.

1.4.2 : When a reaction contains several reactants, some may be in excess...is more is present that can be used in the reaction. The first reactant to run out is the limiting reagent (or reactant). Knowing the number of mols of the limiting reagent allows all other species to be calculated, and so the yield, and remaining quantities of other reactants.

1.5 Solutions
1.5.1
 * Solvent - the fluid you're dissolving in e.g. water.
 * Solute - something which has been dissolved to form a solution e.g. an ionic compound such as sodium hydroxide.
 * Solution - a mixture of solvent and solute where the solute has dissolved into the solvent to form an indistinguishable liquid.
 * Concentration - the amount of solute per volume of solution. Measured in moles per dm3 (i.e. moles per liter) or grams per liter.

1.5.2 : Apply the equation concentration = moles/volume...rather obvious from the units of concentration, but remember to convert everything into the same units.

1.5.3 : Use chemical equations to relate the amount of one species to the amounts of others.

TOPIC 1: QUANTITATIVE CHEMISTRY (12.5 HOURS)
Notes below are based on the specification for exams in 2009

SOME COMMON CATIONS
N.B. Many metals, including some of those above, show more than one valency. The valency is then always given with the name of the compound. It is written in Roman Numerals after the name of the metal.

e.g. Iron may be Fe+2 or  Fe+3

Iron II Chloride is Fe+2(Cl-)2

Iron III Chloride is Fe+3(Cl-)3

Other examples which you may meet are

Chromium II or Chromium III	Cr+2 or Cr+3

Manganese II or Manganese IV	Mn+2 or Mn+4

Tin II or Tin IV	Sn+2 or Sn+4

Lead II or Lead IV	Pb+2 or Pb+4

Some Common Anions
Rules of thumb: Anions consisting of just one element have names ending -ide.

 * Anions consisting of an element plus oxygen have names ending in -ate.

 * Notable exception: OH- is hydroxide, not 'hydrate'.

EXERCISE 1
 * If an element has two anions whose names should end in -ate, the one with fewer oxygens ends in -ite.

Work out the formula for the following ionic chemicals

 * 1) 	Zinc Chloride ZnCl2
 * 2) 	Sodium Oxide Na2O
 * 3) 	Aluminium Fluoride AlF3
 * 4) 	Iron III Chloride FeCl3
 * 5) 	Aluminium Oxide	 Al2O3
 * 6) 	Zinc Hydroxide Zn(OH)2
 * 7) 	Copper (II) Nitrate Cu(NO3)2
 * 8) 	Barium Sulphate BaSO4
 * 9) 	Sodium Carbonate Na2SO4
 * 10) 	Calcium Hydrogencarbonate Ca(HCO3)2
 * 11) 	Lead Iodide	 PbI2
 * 12) 	Nickel (II) Sulphate NiSO4
 * 13) 	Ammonium Carbonate (NH4)2CO3
 * 14) 	Manganese IV Oxide MnO2
 * 15) 	Sodium Bromide NaBr
 * 16) 	Magnesium Ethanoate Mg(CH3COO)2
 * 17) 	Silver Nitrate AgNO3
 * 18) 	Mercury II Chloride HgCl2
 * 19) 	Magnesium Nitride Mg3N2
 * 20) 	Potassium Phosphate K3PO4

What are the names of the following chemicals?

 * 1) 	CuBr2 Copper II Bromide
 * 2) 	K2O Potassium Oxide
 * 3) 	K2Cr2O7 Potassium DiChromate (VI)
 * 4) 	KNO3 Potasium Nitrate
 * 5) 	AlCl3 Aluminium Chloride
 * 6) 	FeCl2 Iron II Chloride
 * 7) 	FeS	 Iron II Sulphide
 * 8) 	Na2S2O3 Sodium ThioSulphate
 * 9) 	Al2(SO4)3 Aluminium Sulphate
 * 10) 	Mg(OH)2 Magnesium Hydroxide
 * 11) 	Pb(CH3CO2)2 Lead (II) Ethanoate
 * 12) 	Na2Zn(OH)4 Sodium Zincate
 * 13) 	Pb(NO3)2 Lead (II) Nitrate
 * 14) 	KMnO4 Potassium Manganate (VII)
 * 15) 	PbO2	 Lead (IV) Oxide
 * 16) 	Ni(NO3)2 Nickel Nitrate
 * 17) 	Na2SO3 Sodium Sulphite/Sodium Sulphate (IV)
 * 18) 	Ca(HCO3)2	 Calcium HydrogenCarbonate
 * 19) 	CuO	 Copper II Oxide
 * 20) 	MgCO3 Magnesium Carbonate

Relative molecular mass (Mr) and relative atomic mass (Ar).
Definition: The relative isotopic mass of 12C = 12

All other relative isotopic masses are measured relative to this standard and are not whole numbers e.g.

13C 13.003	19F 18.998	35Cl 34.97	37Cl 36.97

The IB requires you to use whole numbers as an approximation to the relative isotopic mass of every isotope.

The relative atomic mass (Ar) is the average value of an element’s relative isotopic masses e.g. Ar (C) = 12 * 0.9889 + 13.0033 * 0.011 = 12.0098

What is Ar (Cl) if 75.77 % is 35Cl and the rest is 37Cl?

Relative atomic masses are in your data booklet, written beneath each element’s symbol in Table 5. e.g.

The relative molecular mass (Mr) is the sum of a compound’s relative atomic masses e.g.

Mr (CO) = 12.01 + 16.00

What is Mr (CO2)?

What is Mr (Al2(CO3)3)?

Calculating the mass of one mole of a species from its formula.
Another way of saying the same thing is to use the term ‘Molar mass’

The molar mass (M) of carbon-12 atoms is 12 g mol-1

NB Molar mass has units (it is not ‘relative’)

You must specify if it refers to atoms, isotopes, molecules, etc.

EXERCISE 2:

Calculate the Relative Molecular Mass, Mr, of the following

1.	Sodium Chloride

2.	Copper Sulphate

3.	Lead Nitrate

4.	Magnesium Oxide

5.	Potassium Hydroxide

6.	Sulphuric Acid

7.	Carbon Dioxide

8.	Calcium Carbonate

9.	Aluminium Sulphate

10.	Sulphur Trioxide

11.	Ammonium Nitrate

12.	Zinc Chloride

13.	Iron II Bromide

14.	Iron III Iodide

15.	Oxygen

16.	Aluminium Zincate

17.	Nitric Acid

18.	Dilead II lead IV Oxide Pb3O4.

19.	Magnesium Sulphate - 7 – water MgSO4.7H2O

20.	Ammonium Iron II Sulphate - 6 – water (NH4)2SO4.FeSO4.6H2O

Calculate M for :-

1.	Copper Carbonate

2.	Potassium Dichromate

3.	Magnesium Hydroxide

4.	Sodium Phosphate

5.	Calcium Hydrogencarbonate

6.	Potassium Oxalate

7.	Sodium Cyanide

8.	Nitrogen Dioxide

9.	Ethanol

10.	Lead Chromate

11.	Potassium Permanganate

12.	Tin IV Chloride

13.	Ethane

14.	Lithium Carbonate

15.	Ammonia

16.	Butane

17.	Sodium Chromate

18.	Hydrochloric Acid

Applying the mole concept to substances.
Definition: A mole of particles contains the same number of particles as there are atoms in 12 g of carbon-12.

It turns out that there are 6.02 x 1023 particles per mole.

6.02 x 1023 mol-1 is Avogadro’s constant

Solving problems involving amount, mass and molar mass.
Maths (learn this thoroughly):

Mass = Amount x Molar mass

or

m = nM

or

Grams = Moles x Grams per mole

EXERCISE 3

1.	What is the mass of 0.5 moles of calcium carbonate (CaCO3)?

2.	What is the amount of 27 g of water?

3.	What is the relative molecular mass of fullerene if 2/3 mole has a mass of 480 g?

4.	What mass of magnesium contains the same number of atoms as there are in 4 grams of calcium?

5.	Calculate the mass of iron which contains the same number of atoms as there are molecules in 16 grams of oxygen.

6.	What is the mass of copper sulphate (CuSO4 ) which contains the same number of copper atoms as there are atoms in 6.5 grams of zinc?

7.	How much nitrogen contains the same number of atoms as there are sulphur atoms in 3.96 grams of ammonium sulphate ([NH4]2SO4)?

8.	What mass of manganese contains twice the number of atoms that there in 0.6 grams of carbon?

Empirical formula and molecular formula.
Empirical formula: the simplest expression of the proportions of the elements in a compound. The empirical formula can be obtained from the proportions of masses of each element.

Molecular formula: the numbers of atoms of each element in a molecule of a compound.

Sometimes the two formulae are the same: H2O, for example, is both the molecular and empirical formula.

Hydrogen peroxide has an empirical formula of HO but its molar mass is 34 g mol-1. Its molecular formula is H2O2

EXERCISE 4 1.	Analysis of two compounds showed that they contained the following proportions of elements: A: Carbon 26.1%	Oxygen 69.6%	Hydrogen 4.3% B: Carbon 52.2%	Oxygen 34.8%	Hydrogen 13.0% Calculate the empirical formula of each compound

2. If the empirical formula of methane is CH4, and its relative molecular mass is 16, what is the molecular formula?

3. If the empirical formula of ethane is CH3, and its relative molecular mass is 30, what is the molecular formula?

4. What is the mass of carbon dioxide that is produced when 50 g of calcium carbonate decomposes?

CaCO3 → CaO + CO2

5. If 12 g of magnesium react with oxygen to produce 20 g of magnesium oxide: a. What is the formula of magnesium oxide? b. What is the equation for the reaction?

6.	Determine the empirical formula and the molecular formula of the following compounds from the given information. a.	0.36 mol S are combined with 0.72 mol oxygen atoms. Mr of this compound is measured to be 64. b.	0.193 mol Fe combined with 0.2895 mol O and its molar mass is 160 g mol-1 c.	0.3285 mol Pb combined with 0.438 mol O. Mr = 685 d.	0.309 mol carbon combined with 0.618 mol H. Molar mass is 42 g mol-1 e.	0.379 mol H combined with 0.379 mol O. Mr = 34

7.	A compound was shown by qualitative analysis to contain nitrogen and hydrogen as the only elements. It was found by quantitative analysis that 0.02 mol of nitrogen are combined with 0.04 mol of hydrogen. Its relative molecular mass is approximately 30. Determine its empirical formula and its molecular formula.

8.	The relative molecular mass of a compound of boron and hydrogen was measured as just under 28. Every 0.25 mol of boron are combined with 0.75 mol hydrogen atoms. Find its empirical and its molecular formula.

9.	Calculate the empirical formulae of the following substances whose compositions are given below: a.	5g of an oxide of magnesium which contains 3g magnesium b.	7g nitrogen combined with 16g oxygen c.	0.6g magnesium combined with 1.2g oxygen and 0.3g of carbon d.	3.5g nitrogen combined with 2g oxygen e.	4.8 g oxygen combined with 3.2 g copper and 1.4 g nitrogen f.	28.2 g of an oxide of potassium which contains 23.4 g potassium g.	0.08 mol uranium combined with 3.413 g oxygen h.	1 mol zinc combined with 32 g oxygen and 2 g hydrogen i.	A chloride of lead in which 1.302 g of the compound contains 0.530 g chlorine j.	Aluminium bromide which contains 2.4 g bromine in every 2.67 g of bromide

10.	Determine the molecular formula of the following from the given information: a. 	8 g carbon are combined with 2 g hydrogen and the molar mass is 30 g mol-1. b. 	1.56 g of a hydrocarbon contains 1.44 g carbon and its relative molecular mass is 78 c. 	0.2 mol nitrogen atoms are combined with every 6.4 g oxygen and the molar mass of this compound is 92 g mol-1. e. 	3.55 g of an oxide of phosphorus contain 1.55 g phosphorus. Its relative molecular mass is estimated to be a little below 300.

Find the formula for each of the following substances whose percentage composition is given

11.	40% calcium, 12% carbon & 48% oxygen

12.	40% copper, 40% oxygen & sulphur

13.	the oxide of copper which contains 88.9% Cu by mass

14.	the hydrocarbon which contains 85.7% carbon and has a relative molecular mass of 96

15.	the carbohydrate which has a molar mass of 180 g mol-1 and contains 53.33% oxygen and 6.67% hydrogen.

Balancing chemical equations
Once you know the formulae of the chemicals in a reaction, you need to make a balanced chemical equation.

You cannot change the formulae of the chemicals.

You can only add coefficients to indicate how many molecules of each chemical react.

Example 1

 * C10H16 + Cl2 → C + HCl

This is unbalanced. Let’s balance the carbons first:

 * 1 C10H16 + Cl2 → 10 C + HCl

Now let’s try the hydrogens:

 * 1 C10H16 + Cl2 → 10 C + 16 HCl

Finally, time for the chlorines:

 * C10H16 + 8 Cl2 → 10 C + 16 HCl

Example 2

 * Si2H3 + O2 → SiO2 + H2O

This is unbalanced. Let’s balance the silicon first:

 * 1 Si2H3 + O2 → 2 SiO2 + H2O

Now let’s try the hydrogens:

 * 2 Si2H3 + O2 → 4 SiO2 + 3 H2O

Finally, time for the oxygens:

 * 4 Si2H3 + 11 O2 → 8 SiO2 + 6 H2O

Here is a trick you can use to guide you in steps 2 and 3:

 * 1 Si2H3 + O2 → 2 SiO2 + 3/2 H2O

Example 3

 * Ca10F2(PO4)6 + H2SO4 → Ca(H2PO4)2 + CaSO4 + HF

I don’t like the calcium. It appears in more than two compounds here. Next in line is fluorine:

 * 1 Ca10F2(PO4)6 + H2SO4 → Ca(H2PO4)2 + CaSO4 + 2 HF

The phosphate and sulphate can be treated as units:

 * 1 Ca10F2(PO4)6 + H2SO4 → 3 Ca(H2PO4)2 + CaSO4 + 2 HF

 * 1 Ca10F2(PO4)6 + 1 H2SO4 → 3 Ca(H2PO4)2 + 1 CaSO4 + 2 HF

Note that although we have coefficients for every substance, the coefficients 1, 3 and 2 are not balanced with the coefficients 1 and 1 – so I write them in two different colours.

The hydrogens look tricky too, but it’s either them or the calcium now:

1 Ca10F2(PO4)6 + 7 H2SO4 → 3 Ca(H2PO4)2 + 7 CaSO4 + 2 HF

Better do the calcium now…

Ca10F2(PO4)6 + 7 H2SO4 → 3 Ca(H2PO4)2 + 7 CaSO4 + 2 HF

EXERCISE 5 Balance these equations: 1.	   Cu +     O2 →     CuO 2.	   Fe +     O2 →     Fe3O4 3.	   Mg +     HCl →    MgCl2 +     H2 4.	    Al +     HCl →     AlCl3 +     H2 5.	    P +     O2 →     P2O5 6.	   NaHCO3 →     Na2CO3 +     CO2 +     H2O 7.	   KClO3 →     KCl +     O2 8.	    NaNO3 →     NaNO2 +     O2 9.	    Cu(NO3)2 →     CuO +     NO2 +     O2 10. PbO +    C →     Pb +     CO2 11.	   C4H8 +     O2 →     CO2 +     H2O 12.	   C4H10 +     O2 →     CO2 +     H2O 13.	   Na2CO3 +     HCl →     NaCl +     H2O +     CO2 14.	   KOH +     H2SO4 →    K2SO 4 +     H2O 15.	    (NH4)2SO4 +     NaOH →     NH3 +     Na2SO4 +     H2O 16.	   Mg +     H2O →    MgO +     H2 17. Na +    H2O →    NaOH +     H2 18. Pb3O 4 +    H2 →     Pb +     H2O 19.	   Fe2O3 +     CO →     Fe +     CO2 20.	   Fe(OH)3 →    Fe2O 3 +     H2O 21.	   CuO +     H2 →    Cu +     H2O 22.	   Zn +     HCl →     ZnCl2 +     H2 23. KClO3 →    KCl +     O2 24. S8 +    F2 →     SF6 25.	   Fe +     O2 →     Fe2O3 26.	   C2H6 +     O2 →     CO2 +     H2O

The mole ratios of any species in a chemical equation.
EXERCISE 6

1.	What is the amount (unit : mole) of hydrochloric acid needed to react with 1 mol Mg and how much magnesium chloride is formed?

2.	What is the amount of chlorine which will react with 4 mol Fe? How much iron III chloride is formed?

3.	How much carbon dioxide can be produced by reacting 0.1 mol CuCO3 with hydrochloric acid? What is the minimum amount of acid required?

4.	What is the amount of sodium hydrogencarbonate which should be heated to produce 0.2 mol Na2CO3?

5.	What amount of barium sulphate can be precipitated from a solution containing 0.01 mol barium chloride? What amount of potassium sulphate will be required to react with this barium chloride? What would be the effect of adding twice the amount of potassium sulphate?

The state symbols (s), (l), (g) and (aq).
EXERCISE 7 Can you add state symbols to the equations above? Aqueous solutions and Ionic equations Many substances dissolve in water to form aqueous solutions. Ionic substances are usually soluble, separating into their component ions: Al2(SO4)3 (s)  2 Al+3(aq) + 3 SO4-2(aq) The mobility of the ions in solution means that these solutions will conduct electricity (though the solid substance will not). Covalent substances do not usually dissolve in water. If they do dissolve, the molecules remain intact: C6H12O6(s)  C6H12O6(aq) When no more solute can be dissolved in a solvent, the solution is said to be saturated.

Ionic equations describe only the ions that react, omitting other (‘spectator’) ions. AgNO3 (aq) + NaCl(aq) ® AgCl(s) + NaNO3 (aq) Each aqueous compound can be treated as a pair of ions: Ag+(aq) + NO-3 (aq) + Na+(aq) + Cl-(aq) ® AgCl(s) + Na+(aq) + NO-3 (aq) The sodium and nitrate ions do not take part in the reaction Ag+(aq) + Cl-(aq) ® AgCl(s) This treatment simplifies the equation and makes it more generally applicable. E.g. What if silver fluoride and potassium chloride solutions were mixed? When an acid and an alkali react, ionic equations can be very useful: Sodium hydroxide (NaOH) and hydrochloric acid (HCl) react to form sodium chloride and water Magnesium hydroxide (Mg(OH)2) and sulphuric acid (H2SO4) react to form magnesium sulphate (MgSO4) and water Treating Na+, Mg2+, Cl- and SO42- as spectator ions, what is the common ionic equation when a hydroxide reacts with an acid? EXERCISE 8 Write balanced equations for the following reactions. Put in the physical states in the appropriate manner and write the ionic equation as well where this is appropriate (numbers 1, 2, 5, 11, & 15). Occasionally, oxygen appears as reactant but is not in any of the named products. In these cases, assume it is converted into water. 1. Iron filings reacting with dilute hydrochloric acid to give hydrogen plus iron II chloride solution. 2. Zinc oxide powder dissolves in dilute hydrochloric acid to give zinc chloride and water. 3. In the Contact process, sulphur dioxide and oxygen combine to form sulphur trioxide in the presence of vanadium V oxide catalyst and at a temperature of 450°C. 4. When crystalline potassium nitrate [nitrate (V)] is heated, oxygen is given off and a residue of potassium nitrite [nitrate (III)] remains. 5. When chlorine is bubbled into aqueous potassium iodide, a ppt. of iodine is formed along with a solution of potassium chloride. 6. The effect of heat on dilead II lead IV oxide (Pb3O4) is to produce oxygen, leaving lead II oxide behind. 7. Baking soda, sodium hydrogen carbonate, is used in cooking and when heated it decomposes to form sodium carbonate, carbon dioxide and steam. 8. When carbon dioxide is bubbled through lime water (calcium hydroxide solution), milkiness is observed due to the formation of a ppt of calcium carbonate. 9. If carbon dioxide is allowed to continue to bubble through the solution from (8) for a long time, the ppt redissolves, forming calcium hydrogencarbonate. 10. In the blast furnace, carbon monoxide reduces iron III oxide to molten iron while being oxidised itself into carbon dioxide. 11. The chemical test for a sulphate is to add barium chloride solution to a solution of the test sample. A white ppt. of barium sulphate indicates a positive result. 12. Magnesium burns in an extremely exothermic reaction in which magnesium oxide is the product. 13. When conc. sulphuric acid (a liquid) is poured onto common salt, fumes of hydrogen chloride are observed, while sodium hydrogensulphate remains in the test tube. 14. A solution of hydrogen peroxide will decompose spontaneously, in the presence of manganese IV oxide catalyst, to liberate oxygen. 15. When solutions of ammonium chloride and sodium hydroxide were heated together, the smell of ammonia was observed. Sodium chloride was one of the other products.

Calculating theoretical yields from chemical equations.
EXERCISE 9

1	What is the amount of sodium nitrate (nitrate V) (NaNO3) in 17.0g ? What mass of sodium nitrite (nitrate III) will be obtained by heating this if it decomposes according to the equation :- 2 NaNO3  2 NaNO2 + O2

2.	What mass of zinc oxide remains after heating 9.45g zinc nitrate? 2 Zn(NO3)2  2 ZnO + 4 NO2 + O2

3.	What mass of sodium carbonate remains after heating 4.2g sodium hydrogencarbonate?

4.	What mass of powdered zinc would react with 0.96 g of sulphur? What is the expected yield of zinc sulphide?

5.	What will be the loss in mass on heating 6.2g copper carbonate until no further reaction takes place? CuCO3 (s)  CuO (s) + CO2 (g)

6.	A solution contained 6.62g of lead nitrate. A solution of sodium chloride was added in order to precipitate lead chloride. What is the expected yield of lead chloride?

7.	What is the amount of Mg contained in 4.8g magnesium? If this reacts with hydrochloric acid, what is the amount of hydrogen gas which will be produced?

8.	An aqueous solution contains 12.6 g HNO3. What amount of HNO3 is this? Find the amount and the mass of potassium hydroxide which will just neutralise this. What mass of potassium nitrate could you expect as product?

9.	5.05 g of copper nitrate decomposes according to the following equation when it is heated 2 Cu(NO3)2  2 CuO + 4 NO2 + O2 (a)	What mass of copper oxide is produced? (b)	What amount of nitrogen dioxide is formed?

The limiting reactant and the reactant in excess: Theoretical, experimental and percentage yield.
EXERCISE 10

1.	What mass of zinc will be required to react completely with 5g of copper sulphate and what mass of copper will be formed?

2.	How much iron II sulphate will be required to react with 4g sodium hydroxide and what mass of iron II hydroxide will be formed?

3.	8g of calcium are dissolved in excess hydrochloric acid. How many molar masses of acid will actually react? What amount of calcium chloride can you expect? If this crystallises out of solution as CaCl2.6H2O, what is the maximum mass of crystals that can be produced?

4.	A technician used 2.4g of magnesium ribbon to produce crystals of magnesium sulphate - 7 - water by reaction with dil. sulphuric acid. What should his yield (in grams) have been? If he managed to make only 16.4 g, calculate his percentage yield.

5.	A portable gas stove burns butane at the rate of 116 g per hour. What mass of water will be produced after one hour? In what physical state will this water first appear? What will eventually happen to it? If the appliance is used in a confined space, state what problems or dangers might result.

6.	8.0 g of copper oxide were dissolved in dilute sulphuric acid and after suitable treatment 20 g copper II sulphate - 5 - water were obtained. What is the percentage yield?

7.	Ethanol (20 cm3) was heated with an equal volume of ethanoic acid in the presence of concentrated sulphuric acid catalyst. The yield of ethyl ethanoate was 8 cm3. (a)	Calculate the mass and the amount of each reagent. (b)	Which of the two reagents, ethanol or ethanoic acid is the limiting reagent i.e. which is not in excess? (c)	Calculate the percentage yield of ester. [ densities in g cm-3 :- ethanol 0.79; ethanoic acid 1.05; ethyl ethanoate 0.9]

8.	8.4g of sodium hydrogen carbonate are mixed with 15g of hydrochloric acid. Explain which reagent is in excess. Find the amount of carbon dioxide produced in the reaction. Would more or less carbon dioxide have been produced by heating the hydrogencarbonate?

9.	On heating 4.2g of a metal carbonate, XCO 3, 0.05 mol carbon dioxide was produced. Calculate the relative atomic mass, A r, of the metal X. XCO 3  XO + CO 3

10.	Bath salts (sodium carbonate crystals) (9.53g) were gently heated in a crucible in order to drive off all their water of crystallisation. 3.53g of anhydrous salt remained. Calculate the number of molecules of water of crystallisation in the sodium carbonate and hence its formula. However when 12 g of the crystals were left in a hot room, the loss in mass was only 6.80g. What can you deduce about the formula of the sodium carbonate after it had undergone efflorescense in these conditions?

Avogadro’s law of volumes of gases.
Avogadro’s law: Equal volumes of gases, at the same pressure and temperature, contain equal amounts of molecules. The law can be used to find the volumes of gases in a reaction: e.g. 1 dm3 of hydrogen will react with 1 dm3 of chlorine to give 2 dm3 of hydrogen chloride. EXERCISE 11 What volume of CO2 will be produced when 1 dm3 of methane (CH4) combines with 3 dm3 of oxygen? What volume of CO2 will be produced when 1 dm3 of ethene (C2H4) combines with 3 dm3 of oxygen?

Graphs relating to the ideal gas equation.
This section meets many criteria for Topic 11.3 Graphical techniques EXERCISE 12

1. A sample of gas was heated while the pressure was kept constant. The changes in volume were recorded. Graph the following data:

Use a scale which starts at -300 °C and 0 dm3.

Estimate the temperature required for the gas to have a zero volume.

2. Another gas sample was pressurized and the effect on its volume was recorded. The temperature was kept constant. Graph the following data:

What is the relationship between pressure and volume? 3. A gas was gradually introduced to a rigid, constant temperature, vacuum-filled container, and the pressure recorded as more gas was added. Graph the following data:

What is the relationship between pressure and amount?

4. One mole of a gas was kept in a 1 m3 (1000 dm3) container as the temperature was varied. The effect on the pressure was recorded:

What is the relationship between pressure and temperature?

What is the gradient of the graph?

Use the gradient to estimate the temperature required for the pressure to be 101325 Pa (1 atm).

Molar volume of a gas
A mole of any gas at 298 K and 1 atmosphere pressure occupies 24 dm3. At 273 K the volume is 22.4 dm3. E.g. 2 moles of argon atoms occupy 48 dm3 0.5 moles of oxygen molecules occupy 12 dm3 What is the volume of carbon dioxide that is produced when 50 g of calcium carbonate decomposes? CaCO3 ® CaO + CO2

The relationship between temperature, pressure and volume for a fixed mass of an ideal gas.
We can summarize the behavior of an ideal gas with this equation:

PV = nRT

P is the pressure (in Pa or N m-2)

V is the volume (m3)

n is the number of moles of the gas

R is the ideal gas constant (=8.31 J K-1 mol-1)

T is the absolute temperature (K)

You can see from this that if pressure increase, either the volume must decrease or the temperature increases. Similarly, increasing temperature causes increased volume and/or pressure. EXERCISE 12

Use PV = nRT to calculate: a)	The volume occupied by 1 mol of a gas at 25 oC (298 K) and 100000 Pa (1 bar) pressure.

b)	The pressure required to make 5 mol of gas occupy 50 dm3 (50 x 10-3 m3) at 35 oC.

c)	The number of moles of gas which occupy 25 dm3 at 85 oC and 1.05 bar.

d)	The temperature of a 3 mol gas sample which has a volume of 18 dm3 at 1 atm (1.013 bar) pressure.

If we change the conditions for a given sample of gas, we can simplify the equation considerably. Call the initial pressure, temperature and volume P1, T1 and V1, and the values after the conditions have changed are called P2, T2 and V2. The amount of gas, n, and the constant, R, are the same in both cases. This gives us the formula: = P1*V1 / T1 = P2*V2 / T2 The ‘1’ and ‘2’ refer to the volume (V) of the gas under different conditions of Pressure (P) and Absolute Temperature (T - measured in kelvins) Helpfully, the pressure and volume do not now have to measured in Pa and m3. Any units are suitable, so long as the same units are used for P1and P2, and for T1 and T2.

EXERCISE 13

1. Use the simplified equation (and answers to the previous exercise) to calculate:

a)	The volume occupied by 1 mol of a gas at 0 oC and 100000 Pa (1 bar) pressure.

b)	The pressure required to make 5 mol of gas occupy 40 dm3 (50 x 10-3 m3) at 35 oC.

c)	The temperature of a 3 mol gas sample which has a volume of 25 dm3 at 1 atm (1.013 bar) pressure.

d)	If a sample of gas which occupies 26.25 dm3 at 120.8 oC and 1.10 bar could be the same as a sample which occupies 25 dm3 at 85 oC and 1.05 bar.

2. If 1 dm3 of gas is warmed from 298 to 745 K, while the pressure is kept constant at 1 atm, what is its new volume?

3. What pressure is now required to pressurize the hot gas until it reaches its original volume?

Solute, solvent, solution and concentration
Concentration (c) is measured as the quantity of solute per unit volume (usually per dm3 i.e. dm-3) of solution (not solvent). Remember that 1 dm3 = 1000 cm3 The solute quantity can be measured as mass, so the units are g dm-3. cm = m/v	mass concentration = mass / volume The solute quantity can be measured as amount, so the units are mol dm-3. cn = n/v	molar concentration = amount / volume The molar concentration of a substance is often written in the shorthand form [substance]. E.g. Instead of writing ‘The molar concentration of NaCl’ we can write [NaCl].

EXERCISE 14

1)	Write down all the possible mathematical expressions which might be needed when doing calculations based on volumetric analysis (titrations).

2)	What is the mass concentration if 5 g of NaCl are dissolved in 500 cm3 of solution?

3)	What is the amount of 5 g of NaCl?

4)	What is the molar concentration if 5 g of NaCl are dissolved in 500 cm3 of solution?

5)	25 cm3 of hydrochloric acid (0.12 mol dm-3) were just neutralized by 28.4 cm3 of sodium hydroxide solution. Calculate the concentration of the base.

6)	23.2 cm3 of hydrochloric acid were required to cause the formation of the very pale grey colour - almost colourless - of screened methyl orange indicator in 25.0 cm3 of potassium hydroxide solution. Determine the concentration of the acid given that the potassium hydroxide was made by dissolving 1.372 g in 250.0 cm3 of solution.

7)	A sample of lithium hydroxide was weighed as 0.62 g. It was dissolved in water & made up to 250.0 cm3. 25.00 cm3 aliquots were titrated and 21.25 cm3 of standard hydrochloric acid (0.100 mol dm-3) were required. The lithium hydroxide is thought to be contaminated with lithium chloride. Calculate the mass of lithium hydroxide in the sample and hence its percentage purity.

8)	Butanedioic acid is a dibasic acid (diprotic acid) of molecular formula C4H6O4. 1.0073 g were weighed, dissolved in water and the solution made up to 250 cm3. 25 cm3 portions required 23.95 cm3 of potassium hydroxide solution to cause the colour change of a suitable indicator. Calculate the concentration of the alkali.

 * a)	What amount of butanedioic acid was used (how many moles)?

 * b)	What amount was used in each titration?

 * c)	What amount (mol) of potassium hydroxide was present in each titration?

 * d)	What is the concentration of potassium hydroxide?

9)	A technician was asked to analyse a solution of commercial caustic soda for its sodium hydroxide & sodium carbonate content. She did this by titrating a 25.00 cm3 portion with hydrochloric acid solution (0.100 mol dm-3.) using firstly phenolphthalein and then, as part of the same titration, by adding methyl orange.

Results obtained were 16.90 cm3 of acid to bring about the colour change of the phenolphthalein and a total end point of 24.55 cm3.

At the first colour change (phenolphthalein goes pink to colourless), the reactions taking place are:

OH- + H+  H2O & also CO3-2 + H+  HCO3-2.

At the second colour change (methyl orange turns green to red), the reaction taking place is

HCO3-2 + H+  CO2 + H2O

Thus the first part of the titration relates to the concentration of hydroxide plus carbonate. The second part refers to the concentration of the carbonate (in its hydrogencarbonate form) only.

 * a)	Calculate the number of moles of acid used in the first part and thus the total number of moles of hydroxide plus carbonate in the 25.00 cm3 portion.

 * b)	Calculate the volume and hence the number of moles of acid used in the second part of the titration and thus the number of moles of hydrogencarbonate (and thus carbonate).

 * c)	From a) & b) calculate the number of moles of hydroxide and of carbonate in the 25.00 cm3 portion. From these results calculate the concentrations of the sodium hydroxide & sodium carbonate in the solution. Give your answer in each case in mol dm-3 & also in g dm-3.

10)	1.483 g of the mineral Dolomite were added to excess hydrochloric acid (50 cm3, 1.0 mol dm-3). After reaction was complete, the solution was filtered and made up to 250 cm3. 25 cm3 portions of this solution containing unreacted acid were titrated against 0.1 mol dm-3 KOH when a mean titre of 26.3 cm3 was obtained. Assuming that Dolomite is essentially magnesium carbonate plus insoluble silica, calculate its percentage composition.

 * a)	What amount of potassium hydroxide was in the 26.3 cm3?

 * b)	What amount of hydrochloric acid would have reacted with this?

 * c)	What amount of hydrocloric acid was in the 250 cm3 solution?

 * d)	What amount of acid was taken at the start?

 * e)	What amount of acid reacted with the Dolomite?

 * f)	Calculate the amount and hence the mass of magnesium carbonate which would have reacted with the hydrochloric acid.

 * g)	Calculate the percentage by mass of magnesium carbonate in Dolomite.

title: IB Chemistry/Stoichiometry


text:
IB Chemistry/Atomic Theory

Atomic Theory Revision Notes
2.1 The Nuclear Atom

2.1.1 : Protons and Neutrons form the nucleus of the atom, electrons orbit the nucleus in electron shells.

2.1.2 : Protons -- Mass = 1 amu, charge = +1 .. Neutrons -- Mass = 1 amu, charge = 0 .. Electron -- Mass = 1/1840 amu (usually insignificant), charge = -1

Atoms are made up of a nucleus and electrons that orbit the nucleus.

The nucleus
The nucleus is made up of positively charged protons, and neutrons, which have no charge but about the same mass as a proton.

Electrons
Electrons are negatively charged and move around the nucleus of an atom very quickly. So far, they do not appear to be made up of anything smaller: they are fundamental particles. They are extremely tiny, so small in fact that no one has managed to detect any size whatsoever. They are also very light, much much lighter than either a proton or a neutron. Hence, the weight of the electron is not included in the atomic number.

An atom in its natural, uncharged state has the same number of electrons as protons. If it gains or loses electrons, the atom acquires a charge and is then referred to as an ion. The number of protons in an atom defines its chemical identity (e.g. hydrogen, gold, argon, etc). Protons are not gained or lost through chemical reactions, but only through high energy nuclear processes.

2.1.3 : Mass number (A) -- Number of protons + neutrons. Atomic number (Z) -- number of proton. Isotope -- atoms with same atomic number but different mass number (i.e. different numbers of neutrons)

2.1.4 : X Az... A = mass number, Z = atomic number, X = atomic symbol.

2.1.5 : Isotopes may differ in physical properties (mass/density) and radioactivity but not generally in chemical properties.

2.1.6 : Atomic masses are the average of the atomic mass of each isotope (isotopic mass) times the isotope's relative abundance. results in non integer atomic masses

2.1.7 : Atomic number = number of protons (or number of electrons - ionic charge), mass number - atomic number = number of neutrons.

2.2 Electron Arrangement

2.2.1 : Continuous spectrum goes continuously through red, orange, yellow, green, blue, indigo, violet. A line spectrum contains only some individual lines from this spectrum.

2.2.2 : Electrons are excited (usually by running an electric current through them). This causes electrons to 'jump' into higher electron shells ( X -> X* ) this state is only temporary, however, and the electron falls back to its ground state. This change (When the electron falls back from the higher shell to a lower one) decreases the energy of the electron, and this energy is emitted in the form of a photon. If this photon falls into the visible spectrum of light, then it produces a visible spectrum. As electrons move further away from the nucleus, the electron shells become closer together in terms of space and energy, and so lines converge towards the end of the spectrum.

Wave nature of electrons
Electrons behave as particles but also as waves.

One of the results of this observation is that electrons can not orbit with any energy they like. Think of a standing wave on a guitar string. Only a whole number of half wavelengths will fit in the string to form a standing wave, likewise for an atomic shell. Since the energy is dependent on the wavelength this means that the energy of an electron in an atom (a bound electron) is quantized. This means that the energy is limited to certain distinct values, one for each shell with no middle values allowed.

2.2.3 : The main electron levels go : 2, 8, 18 etc...2n + 2 for n0, n1 and n2...

2.2.4 : Electrons are added from the left...after each shell is filled, move to the next...2, 8, 18...only up to Z = 20 is required.

=HL Material=

Topic 12 is the additional HL material for Topic 2.

It's not just the energy that is quantized, other properties that an electron can posess are also split into distinct units with no in betweens. The angular momentum is quantised, the spin is quantised, the component of the angular moment in any direction that you care to choose is quantised. There are in fact a whole host of rules determining the values that each of these properties can take.

Electron shells
Each different shell is subdivided into one or more orbitals, each of which  has a different angular momentum. Each shell in an orbital has a characteristic shape, and are named by a letter. They are: s, p, d, and f.

In a one electron atom (e.g H, He+, Li++ etc.) the energy of each of the orbitals within a particular shell are all identical. However when there is more than one electron, they interact with one another and split the orbitals into slightly different energies. Within any particular shell, the energy of the orbitals depends on the angular momentum, with the s orbital having the lowest energy, then p, then d, etc.

The s Orbital
The simplest orbital in the atom is the 1s orbital. The 1s orbital is simply a sphere of electron density.

There is only one s orbital per shell. The s orbital can hold two electrons, as long as they have different spin quantum numbers.

The "P" Orbitals
Stylised image of all the 2p atomic orbitals. Starting from the 2nd shell, there is a set of p orbitals. The angular momentum quantum number of the electrons confined to p orbitals is 1, so each orbital has one angular node. There are 3 choices for the magnetic quantum number, which indicates 3 differently orientated p orbitals. Finally, each orbital can accommodate two electrons (with opposite spins), giving the p orbitals a total capacity of 6 electrons.

The p orbitals all have two lobes of electron density pointing along each of the axes. Each one is symmetrical along its axis. The notation for the p orbitals indicate which axis it points down, i.e. px points along the x axis, py on the y axis and pz up and down the z axis. The p orbitals are degenerate, they all have the same energy. P orbitals are very often involved in bonding.

The "D" Orbitals
The first set of d orbitals is the 3d set. There are 5 choices for the magnetic quantum number, which gives rise to 5 different d orbitals. Each orbital can hold two electrons (with opposite spins), giving the d orbitals a total capacity of 10 electrons.

Note that you are only required to know the shapes of s and p orbitals for the IB.

In most cases, the d orbitals are degenerate, but sometimes, they can split, with the eg and t2g subsets having different energy. Crystal Field Theory predicts and accounts for this. D orbitals are sometimes involved in bonding, especially in inorganic chemistry.

=Material for new syllabus=

SL TOPIC 2.1 THE ATOM (1H).
SEE NEUSS, P6-7 TOK: What is the significance of the model of the atom in the different areas of knowledge? Are the models and theories that scientists create accurate descriptions of the natural world, or are they primarily useful interpretations for prediction, explanation and control of the natural world?

The position of protons, neutrons and electrons in the atom.
Here is a typical atom, helium:

TOK: None of these particles can be (or will be) directly observed. Which ways of knowing do we use to interpret indirect evidence gained through the use of technology? Do we believe or know of their existence?

the relative mass and relative charge of protons, electrons and neutrons.
The accepted values are:

The mass of the atom is due to its nucleons (which is protons and neutrons).

An atom is electrically neutral because it has equal numbers of protons and electrons. electrons and protons.

Chemistry (basically every single chemical reaction) is solely because of the behavior of electrons.

The terms mass number (A), atomic number (Z) and isotopes of an element.
The atomic number of an atom is the number of protons.

The mass number of an atom is the number of nucleons (the number of protons + the number of neutrons).

The atomic number defines which element we are talking about. The element with 16 protons would be ‘sulfur’.

The symbols for isotopes
The following notation should be used AZX, for example 126C

Give the symbols for the following isotopes:

The properties of the isotopes of an element.
Isotopes have the same chemical properties but different physical properties.

‘Heavy water’ (21H2O or D2O) has the following properties:

Boiling point: 101.42 °C at standard pressure.

Freezing point: 3.81 °C at standard pressure.

Relative density: 1107 g dm-3 at STP.

Hydrogen-3 (‘Tritium’, T) is radioactive with a half-life of 12.32 years.

Carbon-14 is radioactive with a half-life of 5730 years.

CO2 normally has a density of 1.83 g dm-3 but if made with carbon-14 it would have a density of 1.92 g dm-3

The density of chlorine-35 gas is 2.92 g dm-3 under standard conditions, but chlorine-37 gas is 3.08 g dm-3.

14C in radiocarbon dating
Living things constantly accumulate carbon-14 but the isotope decays with a half-life of 5730 y.

After death, accumulation stops but the decay continues, so the ratio of carbon-14 to carbon-12 can be used to calculate how long ago death occurred.

This can be used to date organic material from archaeological sites.

60Co in radiotherapy
Cobalt-60 emits gamma radiation which can be directed onto tumours in an attempt to kill their cancerous cells. Whole-body irradiation can be used to destroy bone marrow before a transplant is attempted.

131I and 125I as medical tracers
The thyroid is the only organ of the body which accumulates iodine, so isotopes of iodine can be used to study thyroid disorders. Iodine-131 or iodine-125 are given to patients in very low doses, and the pattern of radiation can reveal tumours or other abnormal growths. Larger doses of iodine radioisotopes can be used as therapy for thyroid cancer.

The number of protons, electrons and neutrons in atoms and ions
Complete the following table:

The operation of a mass spectrometer.

Schematic diagram of a mass spectrometer.

How the mass spectrometer may be used to determine relative atomic mass
By varying the strength of the magnetic field, ions of different masses can be brought to focus on the detector. In this way the relative abundances of ions of different masses produced from the sample can be determined. This is known as a mass spectrum. Usually the electron bombardment is adjusted to produce ions with only a single charge. Any doubly charged ions will be deflected more than the singly charged ions and will in fact behave in the same way as a singly charged ion of half the mass. That is why the x-axis is labeled m/z, where m is the relative mass of the species and z its relative charge. For example, Sulfur-32 (2+) will be observed at m/z=16.

Calculation of non-integer relative atomic masses and abundance of isotopes
The relative atomic masses of many elements are not whole numbers. This is because they are mixtures of isotopes. Each isotope has a molar mass which is (almost) an integer e.g. the molar mass of chlorine-35 is 35.0 g mol-1 and chlorine-37 is 37.0 g mol-1.

Chlorine is a mixture of 24 % chlorine-37 and 76 % chlorine-35.

The molar mass is therefore: 37 x 0.24 + 35 x 0.76 = 35.48

Secret information: Carbon-12 is the only isotope with an exact integer for its molar mass. Other isotopes have molar masses which are almost, but not quite, whole numbers. The IB don’t require you to know this – but it explains why the values you calculate don’t always match the values in your data booklet.

This is the mass spectrum of mercury. There are two types of information we can find from this spectrum:

Mercury has six isotopes

Mercury-202 is the most common isotope The molar mass of mercury is actually the average of the molar masses of its isotopes. From the table we can read these values:

Note that ‘%’ does not mean ‘percent of the total mercury ions’. It means ‘percent of the most intense signal’. The total ‘percentage’ is 335 %.

To find the average, we treat ‘%’ as moles:

33.8 moles of mercury-198 have a mass of 6692.4 g

So we have a molar mass for the average mercury atom:  = 200.6 g mol-1

Classwork 1.	Copper has two stable isotopes:

Isotope	Abundance (%) 63Cu	69.1 65Cu	30.9 Calculate the molar mass of copper.

2.	Bromine has two isotopes, 79Br and 81Br. Look up the molar mass of bromine. What is the proportion of the two isotopes?

3.	Boron has two isotopes, 10B and 11B. What is the proportion?

4.	Lead has four stable isotopes:

Isotope	Abundance (%) 204Pb	1.5 206Pb	23.6 207Pb	22.6 208Pb	52.3 Calculate the molar mass of lead.

1 An experiment was performed to determine the density of gold. The following measurements were recorded. Mass of sample of gold = 30.923 g (to 5 sig fig), Volume of sample of gold = 1.6 cm3 (to 2 sig fig). Which of the following is the most accurate value for the density of gold (in g cm-3) which can be justified by these measurements? A. 19.327 (to 5 sig fig) B. 19.33 (to 4 sig fig) C. 19.3 (to 3 sig fig) D. 19 (to 2 sig fig)

2 The nucleus of a radon atom 22286Rn, contains A. 222 protons and 86 neutrons. B. 86 protons and 136 neutrons. C. 86 protons and 222 neutrons. D. 86 protons, 136 neutrons and 86 electrons.

3 Which of the following statements is/are true according to our current picture of the atom?

I More than 90 % of the mass of a given atom is found in its nucleus.

II Different atoms of an element may have different masses.

III The chemical properties of an element are due mainly to its electrons.

A. I only B. I and II only C. II and III only D. I, II and III

4. In which pair do the species contain the same number of neutrons? A. 10846Pd and 11048Cd B. 11850Sn and 12050Sn C. 19678Pt and 19878Pt+2 D. 22688Ra+2 and 22286Rn

5	Which pairing of electrons and protons could represent a Sr+2 ion? Protons	Electrons A.	38	36 B.	38	38 C.	38	40 D.	40	38

6	All isotopes of tin have the same I.	number of protons; II. number of neutrons; III. mass number. A.	I only B.	II only C.	III only D.	I and III only

The electromagnetic spectrum.
The electromagnetic spectrum unifies a vast range of ‘waves’, ‘rays’ and ‘radiation’.

All electromagnetic radiation travels at 299776 ms-1 in a vacuum.

Parts of the spectrum can be specified by their wavelength, frequency, or energy.

''The electromagnetic spectrum. The red line indicates the room temperature thermal energy.'' ''(Opensource Handbook of Nanoscience and Nanotechnology). The energies are quoted in eV: 1 eV is 96.5 kJ mol-1.''

The frequency is directly proportional to the energy, and inversely proportional to the wavelength.

When transferring energy, electromagnetic radiation behaves as ‘packets’ of energy known as ‘photons’.

Visible light has wavelengths of 400 (blue) to 700 (red) nm, which corresponds to energies of 299 (blue) to 171 (red) kJ mol-1. This is too small to interact with electrons in most bonds, but too large to set bonds resonating.

Infrared light has wavelengths of 0.7 to 1000 um, and carries energies (less than 171 kJ mol-1) which can set bonds vibrating. In this way, infrared efficiently carries thermal energy.

Ultraviolet light has wavelengths of 1-400 nm, which gives the waves enough energy (300+ kJ mol-1) to disrupt most chemical bonds.

It tells us the number of energy levels that the electron of a specific element can occupy.

A continuous spectrum and a line spectrum.
A continuous emission spectrum shows emission over a wide range of wavelengths of electromagnetic radiation:

A line emission spectrum only shows emissions at certain wavelengths, with no emission at intermediate wavelengths.

The diagram below shows the line emission spectrum of hydrogen, and the continuous emission spectrum of a black body at 10000 K.

How the lines in the emission spectrum of hydrogen are related to electron energy levels.
When hydrogen gas is stimulated, it emits a characteristic set of spectral lines. The gas is usually stimulated by passing a current through a sample of the gas at low pressure, but the same effect occurs if hydrogen gas is heated strongly.

The spectral lines have the following characteristics:

There are several series of lines, which become more closely packed at higher frequencies (lower wavelengths) until finally the series ends.

The highest frequency series, discovered by Lyman, is in the ultraviolet. Lower frequency series are in the visible and infrared:

Spectral lines of the hydrogen atom.

The lines are emitted by electrons in the hydrogen atoms. The electrons are ‘excited’ by the energy input to the hydrogen sample (usually electrical current).

‘Excitation’ means that the electron leaves its usual low energy orbit (its ‘ground state’) and enters a higher-energy orbit. The orbits of electrons are often called ‘shells’.

Excited electrons eventually ‘relax’ to lower-energy orbits. They emit the excess energy in the form of photons.

From the emission spectrum patterns we can deduce two things:

a) Because we observe a line spectrum, we know that there are only a limited number of higher-energy orbits for excited electrons.

b) The energy of each successive orbit/shell converges to a maximum value, because each series of lines converges at higher energy.

The Lyman series is caused by electrons relaxing directly to the ground state.

Ionisation energy:

The first ionisation energy is the energy required to remove an electron from each atom in a mole of gaseous atoms.

e.g. Ca (g) → Ca+(g) + e-

The convergence limit of the Lyman series is related to the ionisation energy of the hydrogen atom: The maximum energy photon emitted in the Lyman series is the highest energy an electron can have while still remaining part of the hydrogen atom.

The lower-energy series are caused by electrons relaxing, but not to the ground state. The Balmer series, for example, is due to photons emitted as electrons relax to the orbit with the second-lowest energy (to ‘the second shell’).

Homework

1.	The spectral line that corresponds to the electronic transition n = 3 → n = 2 in the hydrogen atom is red in colour. What type of radiation is released during the transition n = 2 → n = 1 ?

A.	Ultraviolet

B.	Red light

C.	Infrared

D.	Radiowaves

2.	The electron transition between which two levels releases the most energy?

A.	First to third

B.	Fourth to ninth

C.	Sixth to third

D.	Second to first

3. (a) The diagram below (not to scale) represents some of the electron energy levels in the hydrogen atom.

(i) Draw an arrow on this diagram to represent the electron transition for the ionisation of hydrogen. Label this arrow A	[2]

(ii) Draw an arrow on this diagram to represent the lowest energy transition in the visible emission spectrum. Label this arrow B	[2]

The electron arrangement up to Z = 20.
Give the ground state electron arrangements for: Sulphur atom: Potassium atom: Chloride ion: Magnesium ion: HIGHER LEVEL

How ionization energy data is related to the electron configuration.
Studying the ionisation energies of an element such as calcium allows us to count the number of electrons which can occupy each shell.

Classwork:

Plot a graph of the log10(IE) against the ionisation.

Why does the ionisation energy always increase?

What causes the sudden jumps between the 2nd and 3rd, the 10th and 11th, and the 18th and 19th ionisations?

What is the electronic configuration of calcium?

Draw your prediction for the equivalent graph for sodium: Homework

Which element would produce a graph like this?

Explain the shape of the graph.

Evidence from first ionization energies and sub-levels.
Use your data booklet to plot a graph of the first ionisation energies of the elements Li to Ne. Why do the ionisation energies generally increase from Li to Ne?

The charge on the nucleus increases from Li to Ne. If we subtract the charge of the inner shell of electrons we can calculate the charge exerted on the outer electron shell: The effective nuclear charge. Because each element in the period has the same number of inner-shell electrons, the effective nuclear charge increases from 1 (Li) to 8 (Ne). The increased charge holding the outer electrons in place increases the energy required to remove one of these electrons. (It also reduces the size of the atom: Li is larger than Ne).

Why do the ionisation energies of boron and oxygen break the general trend?

The s2 arrangement is stable (like 'noble gas configurations' are stable).

Boron has a [He] 2s2 2px1 arrangement. Losing the px1 electron returns boron to this stable state, so losing this electron is suprisingly easy.

Similarly, the s2 px1 py1 pz1 arrangement is stable.

Oxygen has a [He] 2s2 2px2 2py1 2pz1 arrangement. Losing a px electron returns oxygen to this stable state, so losing this electron is surprisingly easy.

The maximum number of orbitals in a given energy level.
Each energy level (‘shell’) is made of orbitals (‘sub-shells’).

Each orbital can hold two electrons.

The number of orbital types is equal to the shell number e.g. shell 3 has three types of orbital, s p and d.

Shell 1	 1s

Shell 2	 2s 2p

Shell 3	 3s 3p 3d

Shell 4	 4s 4p 4d 4f

Shell 5 has, in theory, five types of orbital. No known element uses its g orbitals, however.

The orbitals in each shell have increasing energy. s is least energetic, then p, d, f, etc. There is only one s orbital per shell. There are three p orbitals, five d orbitals, etc.

The shapes of s, px, py and pz orbitals.
s orbitals are simple spheres: The three p orbitals are aligned along the x y and z axes:

The orbitals of shells 1 and 2 shown as (top) a cloud of possible electron positions and (bottom) surfaces containing most of the electron character.

The Aufbau principle, Hund’s rule and the Pauli exclusion principle
The aufbau principle: To find the electron configuration of an element, we build up the electrons one by one, putting each electron into the orbital with the lowest available energy. An easy way to remember which is the lowest available orbital is to use the following diagram:

1s

2s	2p

3s	3p	3d

4s	4p	4d	4f

5s	5p	5d	5f	…

6s	6p	6d	…

7s	7p	…

Hund’s rule: If there is more than one orbital to choose from e.g. the 2p orbitals, then the orbitals are filled with one electron each, and then with pairs of electrons.

The electron configuration of nitrogen is:

1s		2s		2px	2py	2pz

↑↓		↑↓		↑	↑	↑

And not:

1s		2s		2px	2py	2pz

↑↓		↑↓		↑↓	↑

The simplest way to write the full electronic configuration is to note the last noble gas and then to add any extra electrons like so:

Vanadium: 1s2 2s2 2p6 3s2 3p6 4s2 3d3

Vanadium: [Ar] 4s2 3d3

It does not matter if you write the orbitals in the order they are filled (as in the example above) or in order of their shells:

Vanadium: [Ar] 3d3 4s2

Elements 24 and 29 are special cases. The 3d5 and 3d10 configurations are so stable that an electron is taken from the 4s orbital to create 3d5 and 3d10 configurations.

e.g. Chromium is not: [Ar] 4s2 3d4 Chromium is: [Ar] 4s1 3d5 Complete the following table: 1s H He 2s			2p Li	[He] 2s^1 Be	[He] 2s^2 B	[He] 2s^2 2p^1 C	[He] 2s^2 2p^2 N	[He] O	[He] F	[He] Ne	[He] 3s			3p Na	[Ne] Mg	[Ne] Al	[Ne] Si	[Ne] P	[Ne] S	[Ne] Cl	[Ne] Ar	[Ne] 3d				4s			4p K	[Ar] Ca	[Ar] Sc	[Ar] Ti	[Ar] V	[Ar] Cr	[Ar] Mn	[Ar] Fe	[Ar] Co	[Ar] Ni	[Ar] Cu	[Ar] Zn	[Ar] Ga	[Ar] Ge	[Ar] As	[Ar] Se	[Ar] Br	[Ar] Kr	[Ar] 4d				5s			5p Rb	[Kr] Sr	[Kr] Y	[Kr] Zr	[Kr] Nb	[Kr] Mo	[Kr] Tc	[Kr] Ru	[Kr] Rh	[Kr] Pd	[Kr] Ag	[Kr] Cd	[Kr] In	[Kr] Sn	[Kr] Sb	[Kr] Te	[Kr] I	[Kr] Xe	[Kr]

The four blocks of the periodic table are named after the highest-energy occupied orbital:

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title: IB Chemistry/Atomic Theory


text:
IB Chemistry/Periodicity

3.1 The Periodic Table
3.1.1 : Elements increase in atomic number across each period, and down each group.

3.1.2 : Group - the columns proceeding vertically. Period - the rows proceeding horizontally.

3.1.3 : Group = number of valence electrons in the atom. Period = number of main electron shells...s, p, d and f blocks as described above.

3.2 Physical Properties
3.2.1 : Electron structure
 * As a period is crossed, valency electrons increase
 * As a group is descended, a shell is added (with the same number of valence electrons)

Atomic radii
 * Across a period, radii decreases due to an increasing nuclear charge and reduced screening (more electrons and protons in the outer shell)
 * Down a group, radii increases due to additional shells blocking nuclear charge and increased screening (shielding)

Ionic radii Ionisation energy Ionization energy is the energy required to remove 1MOLE of electrons from 1MOLE of gaseous atoms (e.g. M ‡ M+ + e-)
 * Positive ions (Na ‡ Na+ + e-) have smaller radii due to 1 less shell and reduced screening
 * Negative ions (F + e- ‡ F-) have larger radii because the positive charge of the nucleus has less positive pulling power (PPP) due to the presence of an extra electron in this ionic state.

Successive ionization energies are 3rd > 2nd > 1st, because of smaller radii and greater charge.

Electron affinity Electron affinity is the energy change on the addition of 1 mole of electrons to 1 mole of gaseous atoms (e.g. X(g) + e- ‡ X-(g))

Electronegativity Electronegativity is the measure of the ability of an element in a bond to attract electrons. The most electronegative elements are (in decreasing) F, O, and N.
 * Across a period, electronegativity increases because the increase in nuclear charge makes the nucleus more attracted to electrons
 * Down a group, electronegativity decreases due to increased screening and less nuclear attraction

Melting Points
 * Melting point decrease down group 1 due to the elements metallic structure, which is held together by attractive forces between de-localized electrons.
 * Melting point increases down group 7 due to the strong intermolecular forces that increase in strength with more electrons.

Periodic Trends - Moving Across the Periodic Table
Because of the way in which the periodic table is organized, many trends become apparent.

Moving across the periodic table, proton and electrons are added. Because all of these electrons are added into the same shell, the ionization energy increases. The ionization energy is the amount of energy required to remove the outermost electrons. Because of the overall greater attraction between more protons and more electrons across the periodic table, it becomes more and more difficult to remove an electron. The atomic radius of the elements decreases. Also, metallic character decreases (electronegativity increases; electronegativity is the tendency of an element to gain electrons). This traces the tendency of atoms of metals to lose electrons while nonmetals gain them.

Periodic Trends - Moving Down the Periodic Table
Because elements in the same family (column) contain the same valence shell electron configuration, they tend to behave very similarly. Moving down the periodic table, electrons are added to successively higher energy levels. Because of this, atomic radius increases. Also, it is easier to remove the outermost electron of larger atoms, so ionization energy decreases as well as electro negativity.

Noble Gases 0/8A/18
helium, neon, argon, krypton, xenon, radon

Noble gases except helium all share a full valence shell electron configuration ( 8 outer electrons, 2 for helium). Because this configuration is extremely stable as well as symmetrical, the noble gases are very unreactive and will only react under extremely rigorous conditions.

Halogens 7A/17
fluorine, chlorine, bromine, iodine, astatine

Halogens have an electron configuration of 7, meaning they require only one more electron for a noble configuration. They have very negative electron affinities, are extremely reactive, and form ions with a -1 charge. They are so reactive that in their homogenous state UV light will catalyze a radical reaction.

Fluorine is the most electronegative of the elements and is so reactive that it attacks almost any other element (noble gases, oxygen, nitrogen, and gold are the exceptions) to form fluorides. Chlorine is somewhat less reactive, bromine somewhat less reactive than chlorine, and iodine even less, but even iodine is a formidable iodizer. Strong radioactivity masks the chemical properties of astatine.

All except astatine form gaseous compounds with hydrogen: hydrogen fluoride HF, hydrogen chloride HCl, hydrogen bromide HBr, and hydrogen iodide HI; these are acidic, strongly reactive substances; except for hydrogen fluoride these substances are among the strongest known acids. They free halogens and the hydrogen halides react with most metals, halides of metals being known as salts, of which sodium chloride NaCl is best known as "salt".

Electronegativity decreases in this group with increasing atomic mass, and oxygen is more electronegative than any element except fluorine; it acts much like a halogen except for its -2 oxidation state. Fluorine and oxygen oxidize these elements to the +6 oxidation state, resulting in such substances (for sulfur) as sulfur hexafluoride SF6 and sulfur trioxide SO3 and its derivative sulfuric acid H2SO4, one of the most heavily-used industrial chemicals. Fluorine, oxygen, chlorine, and bromine oxidize all of the elements of this group except oxygen to the +4 oxidation state.

Oxides of sulfur, selenium, and tellurium are acidic. Strong radioactivity largely masks the chemical properties of polonium.

Alkaline Earth Metals group 2A/2
(beryllium, magnesium, calcium, strontium, barium, radium)

These substances are all metals having two electrons in the outer shell, or the ns2 configuration. With increasing mass these elements become softer, have lower melting and boiling points, and become more reactive. None appear uncombined in nature, and all are separated from their compounds with difficulty. All react with halogens and, except for beryllium, with water and oxygen (magnesium at temperatures higher than those of living things)

All oxidize to the +2 state that represents an ion in the stable configuration of an inert gas.

Beryllium is the least reactive; it is the hardest of these elements. Its oxide is amphoteric; it reacts with both strong acids and bases.

Magnesium burns in hot air or steam to form alkaline oxides or hydroxides. Powders or thin slices of this metal can be ignited with a match. Magnesium hydroxide is a strong base, although its low solubility masks its alkalinity. At room temperature magnesium metal is light and strong, but it can be ignited in air. Halogens and acids attack magnesium violently with the formation of salts like magnesium chloride (MgCl2) or magnesium sulfate (MgSO4). Although magnesium would react with atmospheric oxygen, an oxide layer protects the metal from oxidation.

With calcium and the heavier elements of this group, the reactions are even more violent and take place at lower temperatures; they react not only with halogens and acids but also with water, oxygen, and even nitrogen. They are such strong reducing agents that they can reduce carbon dioxide to carbon as well as many metal oxides to metals.

The strong radioactivity of radium masks its chemical properties, but to the extent that its chemistry is known it fits well into the group and its pattern.

Alkali Metals group 1A/1
(lithium, sodium, potassium, rubidium, caesium (US spelling cesium), francium)

These elements are best marked by their reactivity. Physically they are soft, shiny (when freshly prepared) solids with low melting points; they conduct electricity well. They all have one outermost electron that they lose easily to almost any electronegative substance other than nitrogen (lithium reacts with nitrogen, unlike the others). None is ever found uncombined on earth, and none is ever put to use as a structural metal. They must be kept under inert liquids such as kerosene or in inert gases (nitrogen suffices for any of these elements other than lithium.

All oxidize easily to the +1 oxidation state. High reactivity masks the chemistry of francium.

They react with atmospheric oxygen to form various oxides and react violently with water, halogens, and acids. A typical reaction between one of these metals and water is as such:

Na(s) + H2O → Na+(aq) + OH-(aq) + 1/2 H2 (g)

(WARNING: this reaction generates much heat. One should not cast any alkali metal into water or acids except with the cautions that professional chemists use. The hydrogen gas from this reaction may itself ignite with atmospheric oxygen in a dangerous flame. These metals should never allowed to touch flesh because they react with any water upon them and yield corrosive hydroxides that burn flesh. Strong solutions of alkali metal hydroxides are destructive to flesh).

Hydroxides of these elements dissociate completely in water to form some of the strongest bases known. These are as strongly alkaline as any acids and react violently with acids to form halides and water in neutralization:

NaOH(s) + HCl (g) → NaCl(s) + H2O (s)

The results of any reactions of these metals and any acids are salts. Almost all salts of these elements are highly soluble in water and form conducting solutions, proving their ionic nature. The best known of these substances is sodium chloride, NaCl, a substance known as common salt. Salts of these elements and strong acids are neutral (for example, potassium nitrate KNO3); salts with weak acids such as acetic acid are alkaline (sodium carbonate, Na2CO3).

Hydrogen, an element like no other
Hydrogen is the most common element in the universe; as a gas, it is too light for the Earth's gravitation to hold. It is by far the most common constituent of the Sun and all other stars and of the gas giant planets of our solar system. It exists on or just under the surface of the Earth as a component of water and in innumerable compounds of carbon, many essential to life.

The heat and light from the sun (or any other star) arises largely from the nuclear fusion of hydrogen into helium. Nuclear reactions are outside of the normal scope of the discussion of chemistry, so that can be largely ignored here.

Hydrogen, although having one outermost electron does not fit into the alkali metals or any other group. It deserves its own treatment. It forms compounds analogous to those of the alkali metals, but such hydrogen compounds are much less alkaline (or more acidic), much less ionic, and more volatile. Sodium chloride, the stereotypical salt, is neutral and clearly ionic; hydrogen chloride is a non-ionic gas under normal conditions and is a strong acid. The hydrogen analog of sodium hydroxide is a volatile liquid under normal situations: unlike the strongly alkaline and solid sodium hydroxide, water is feebly ionic and effectively neutral.

Hydrogen is a non-metal, forming a diatomic gas which results from the sharing of the single electrons of hydrogen atoms. It can achieve a stable ionic structure (no electrons!) by losing an electron or by gaining an electron and achieving the completed shell configuration of helium. The hydrogen molecule is best described as sharing the two electrons between two hydrogen atoms. This structure is highly stable and has little inclination to form bonds between other hydrogen molecules; hydrogen is a gas down to some of the lowest temperatures known. It is also the lightest of gases, weighing less even than helium.

Hydrogen readily shares its electron with a strongly-electronegative element like any halogen, oxygen, or sulfur. The combination with fluorine is particularly violent and possible down to very low temperatures:

1/2 H2 (g) + 1/2 F 2(g) → HF(g)

Light is enough to force combustion between hydrogen and chlorine, and a spark is enough to cause combustion between hydrogen and oxygen. In view of the Hindenburg disaster of 1936, helium has long replaced hydrogen in lighter-than-air aircraft. That reaction is as such:

H2 (g) + 1/2 O2 (g) → H2O (g)

(Note that at the temperatures associated with such a combustion, water is in the gaseous state!)

Somewhat analogously (but not very well), hydrogen can act somewhat like a halogen, forming hydrides with some metals. Most of these react violently with water to form hydrogen gas and the metal hydroxide. Hydrogen compounds with non-metals are typically among the most volatile substances of those elements.

Under pressure, in aqueous solution or non-solid acids, hydrogen is a good reducing agent. Strong acids attack most metals:

Zn(s) + 2 H+(aq) → Zn 2+(aq)  + H 2 (g).

In the atmospheres of gas giants, gaseous hydrogen under great pressure reduces nitrogen to ammonia, carbon compounds to methane and other hydrocarbons, and oxides to water. Hydrogen forms more chemical compounds than any other element including carbon (almost all carbon compounds are compounds of hydrogen as well and vice-versa, but more substances containing hydrogen but not carbon exist than do compounds of carbon but not hydrogen). Hydrogen forms bonds with most non-metals, including oxygen, nitrogen, and carbon. Although a hydrogen atom can bond with only one other element, and then only in a single bond, hydrogen allows very long chains of carbon atoms to form. Most of the hydrogen compounds with carbon alone are combustible gases or volatile liquids or waxy solids that can be vaporized and burned to produce water, carbon dioxide, and much heat. Natural gas, gasoline (a mixture of liquid hydrocarbons), and waxes as found in candles make suitable fuels. With such other elements as oxygen, nitrogen, sulfur, and in some cases metals hydrogen allows the formation of substances necessary for life, including carboxylic acids, sugars, proteins, nucleic acids, hemoglobin, and chlorophyll.

Such complex compounds are ordinarily discussed in organic chemistry, a study associated more obviously with carbon.

title: IB Chemistry/Periodicity


text:
IB Chemistry/Bonding

Introduction to Bonding
Put simply, chemical bonding joins atoms together to form more complex structures (like molecules or crystals). Bonding can occur between atoms of the same element, or between atoms of different elements. There are several types of chemical bonding which have different properties and give rise to different structures.

Ionic bonding occurs between positive and negative ions (charged atoms). This type of bonding seldom occurs between just two atoms, but typically leads to the formation of an ionic solid, in which the ions arrange themselves into a rigid crystal lattice. NaCl (common salt) is an example of an ionic substance.

Covalent bonding occurs when atoms share electrons with each other. This gives rise to two types of structures: molecules and covalent network solids. Methane (CH4) is a covalent molecule and glass is a covalent network solid. In molecules we can distinguish individual covalent bonds between pairs of atoms.

Whether the interaction between two atoms has a covalent or ionic character can be predicted from the atoms' electronegativities:

Metallic bonding occur between metal atoms. In a metallically bonded substance, the atoms' outer electrons are able to freely move around - they are delocalised. In principle, all electrons can behave like delocalized waves, but in substances with covalent or ionic bonding the number of accessible energy states equals the number of electrons and that makes this wave character less apparent. In metals there are far more accessible states than electrons and that leaves the electrons free to move and conduct electrically. Aluminum, tin, lead, silver are all metallically bonded elements, but there are also compounds with metallic bonding, such as alloys and intermetallic compounds.

Chemical bonding is one of the most crucial concepts in the study of Chemistry. In fact, the properties of materials are basically defined by the type and number of atoms they contain and how they are bonded together.

4.1 Ionic Bonding
4.1.1 : Ionic bonding - +ve (cations) and -ve (anions) ions are attracted to each other and form a continuous ionic lattice.

What are ions?
Ions are atoms or molecules which are electrically charged. Cations are positively charged and anions are negatively charged. Ions form when atoms gain or lose electrons. Since electrons are negatively charged, an atom that loses an electron will become positively charged (similarly an atom that gains one or more electrons becomes negatively charged).

Description of Ionic Bonding
Ionic bonding occurs between positive and negatively charged ions. These oppositely charged ions attract each other and remain close together - they become ionically bonded. The law of electrostatic explains why this happens: opposite charges attract and like charges repel. When many ions attract each other, they form into large, orderly crystal lattices in which each ion is surrounded by ions of the opposite charge. When a metal forms an ionic bond with a non-metal, electrons are transferred from metal element to non-metal. When Ions are formed it is called Ionization

A diagram of an ionic solid should go here

Formation of Ions
Ions result when metals and non-metals chemically react. Due to its low ionization energy, a metal atom is destabilized only a little if it loses electrons to form a complete valence shell and becomes positively charged. Likewise, a non-metal is stabilized strongly by gaining electrons to complete its valence shell and become negatively charged. When a metal and a non-metal come into contact, the metal loses electrons by transferring them to the non-metal, which gains them. Consequently, ions are formed, which instantly attract each other. An ionic bond is the electrostatic attraction between cations and anions due to Coulombic forces. The process of attraction typically does not stop with two ions, but proceeds to involve a great many of them that stack in a solid lattice structure, in which individual 'bonds' or individual molecules cannot be distinguished.

4.1.2 : Group 1 metals form +1 ions, group 2 metals form +2 ions, metals in group 3 form +3 ions. Examples : Li+, Mg2+, Al3+...Greater ease of ionisation Li->Cs is due to the increased electron shielding of the nuclear attraction caused by additional inner shells of electrons. The easier atoms are to ionise, the more reactive they will be because less energy is required to ionise them, and so they react more easily.

4.1.3 : Group 6 ions will form 2- ions, Group 7 ions will form 1- ions. Examples : O2-, Cl-...

4.1.4 : The transitions metals (elements from Ti to Cu, ignore Sc and Zn) can form multiple ions (ie Fe2+, Fe3+) (due to proximity of 4s and 3d shells)

4.1.5 : The ionic or covalent nature of the bonding in a binary compound is a result in the difference between their electronegativity...NaCl(s) is ionic, HCl(g) is (polar) covalent (also, covalent molecules tend to be gases/liquids, ionic tends to be solid...except network covalent which will be solid). In general, if the difference between electronegativities is greater than 1.7, the bond will be more than 50% ionic.

4.1.6 : Take the name of the group 1,2, or 3 metal and add...fluoride, chloride, bromide, iodide etc, oxide, sulfide, nitride or phosphide...

4.2 Covalent Bond
One useful model of covalent bonding is called the Valence Bond model. It states that covalent bonds form when atoms share electrons with each other in order to complete their valence (outer) electron shells. They are mainly formed between non-metals (i.e. chlorine, sulfur, carbon etc.).

The Valence Bond Model
An example of a covalently bonded substance is hydrogen gas (H2). A hydrogen atom on its own has one electron – there is room for two to complete its valence shell. When two hydrogen atoms bond, each one shares its electron with the other, i.e. the electrons are attracted by two nuclei instead of just one and so releasing energy. Both atoms now have access to two electrons: they become a stable H2 molecule joined by a single covalent bond.

Double and Triple Bonds
Covalent bonds can also form between other non-metals, for example chlorine. A chlorine atom has 7 electrons in its valence shell — it needs 8 to complete it. Two chlorine atoms can share 1 electron each to form a single covalent bond. They become a Cl2 molecule.

Oxygen can also form covalent bonds; however, it needs a further 2 electrons to complete its valence shell (it has 6). Two oxygen atoms must share 2 electrons each to complete each other's shells, making a total of 4 shared electrons. Because twice as many electrons are shared, this is called a double covalent bond.

Furthermore, nitrogen has 5 valence electrons (it needs a further 3). Two nitrogen atoms can share 3 electrons each (6 in total) to make a N2 molecule joined by a triple covalent bond.

Electron Sharing and Orbitals
Carbon, contrary to the trend, does not share four electrons to make a quadruple bond. The reason for this is that the fourth pair of electrons in carbon cannot physically move close enough to be shared. The valence bond model explains this by considering the orbitals involved. Also more energy can be released by making 4 single bonds to 4 other carbon atoms to form a diamond structure.

Recall that electrons exist as clouds of electron density (orbitals) in atoms. The valence bond model works on the principle that orbitals on different atoms must overlap to form a bond. There are several different ways that the orbitals can overlap, forming several distinct kinds of covalent bonds.

The Sigma Bond
The first, and simplest kind of overlap is when two s orbitals come together. It is called a sigma bond (sigma, or 'σ', is the greek equivalent of 's'). Sigma bonds can also form between two p orbitals that lie pointing towards each other.

picture of sigma bonds- please press the no.1O sigma bond.jpg

The Pi Bond
The second, and equally important kind of overlap is between two parallel p orbitals. Instead of overlapping, head-to-head (as in the sigma bond), they join side-to-side, forming two areas of electron density above and below the molecule(delocalization). This type of overlap is referred to as a pi ('π', from the greek equivalent of p) bond.

4.2.1 : Covalent bonds are where two atoms each donate 1 electron to form a pair held between the two atoms...Such bonds are generally formed by atoms with little difference in electronegativity...ie C, H and O in organic chemistry.

4.2.2 : All electrons must be paired...Lewis diagrams are the element symbol with the outer (valence) shell of electrons left over and spare electrons pair up...in general C forms 4 bonds, N forms 3, O forms 2, halogens form 1, H forms 1...(Li would form 1, Be 2, and B 3 but they don't usually...metallic or ionic bonding)

4.2.3 : Electronegativity values range from 0.7 to 4...from bottom left to top right respectively (hydrogen falls B and C with a electronegativity of 2.1...

4.2.4 : When covalent molecules have a difference in electronegativity (between the two bonding atoms) then the pair will be held closer to the more electronegative atom...resulting in a small -ve charge on the more electronegative atom, and a small +ve charge on the other...results in polar bonds

4.2.5 : Shape of molecule with 4 electron pairs depends on number of lone pairs.

3 lone pairs -> linear, 2 lone pairs -> bent, 1 lone pair -> trigonal pyramid, No lone pairs -> tetrahedral

4.2.6 : The polarity of a molecule depends on both the shape and the polarity of the bonds...1) if there are no polar bonds, it's not polar. 2) if there are polar bonds, but the shape is symmetrical, it's not polar (think about it like 3D vector addition...if they add to zero, then it's not polar). 3) if there are polar bonds, and it's not symmetric, then the molecule is polar

4.3 Intermolecular forces
4.3.1 : van der Waal's forces -- Electrons will not be evenly spread around an atom/molecule at any given time, meaning the molecule will have a slight positive charge on one end, and a negative at the other. This temporary state may cause attraction between two molecules, pulling them together (also known as London Dispersion Forces). Polar molecules, when properly oriented, will attract each other as a result of Dipole-Dipole forces. Dipole-Dipole forces are stronger than van der Waal's forces. Hydrogen bonding is when hydrogen is bonded to nitrogen, oxygen or fluorine, and a very strong dipole is formed, making the hydrogen very strongly positive. This hydrogen is then attracted to the lone pairs on other similar molecules--nitrogen, oxygen and fluorine all have lone pairs--forming a hydrogen bond, which is stronger than van der Waal's or dipole-dipole forces, but weaker than covalent bonding.

4.3.2 : Structural features -- Nonpolar molecules have van der Waal's forces only. This is also present in all other molecules, though its strength is often insignificant compared to the others. Polar molecules have dipole-dipole forces, which arise from polar bonds and asymmetry in molecules. Hydrogen bonds result from strongly delta positive hydrogen. This results in molecules with hydrogen bonding exhibiting stronger intermolecular forces, i.e. higher boiling/melting points etc. For example, H2O has a higher bp then H2S due to hydrogen bonding. Neutral molecules don't conduct electricity but some polar molecules exchange protons to form ions e.g. 2H2O makes H3O+ and OH-

4.4 Metallic bonding
4.4.1 : The metal atoms lose their outer electrons which then become delocalized, and free to move throughout the entire metal. These -ve delocalized electrons hold the metal cations together strongly. Since these electrons can flow, atoms with metallic bonding exhibit high electrical conductivity. The number of valence electrons involved in the bonding and the strength of the nucleus charge determines the strength. Unlike ionic bonding, distorting the atoms does not cause repulsion so metallic substances are ductile (can be stretched into wires) and malleable (can be made into flat sheets). The free moving electrons also allow for high thermal conductivity, and the electrons can carry the heat energy rather than it being transferred slowly through atoms vibrating.

Metallic bonds occur among metal atoms. A sea of valence electrons surrounds positive metal ions. The electrons are free to move throughout the resulting crystal. The delocalized nature of the electrons explains a number of unique characteristics of metals: they are good conductors of electricity, they are ductile, meaning they can be made into wires, and they are malleable, meaning they can easily be hammered into thin sheets.

4.5 Physical Properties
Melting and Boiling point: High with Ionic, Metallic Bonding and Network Covalent. Low with Covalent Molecular Bonding.

Volatility: Covalent Molecular Substances are volatile, others are not.

Conductivity: Metallic substances conduct. Polar molecular substances conduct, non-polar ones don't. Ionic substances do conduct when molten or dissolved in water but never when solid.

Solubility: Ionic substances --> generally dissolve in polar solvents (like water). Metallic substances --> soluble in liquid metal. Non-polar molecules are generally soluble in non-polar solvents, and polar in polar. Organic molecules with a polar head --> Short chain molecules are solubility in polar solvents but long chains can eventually outweigh the polar 'head' and will dissolve in non-polar solvents.

Characteristics
$$NaCl$$. $$KNO_3$$

Ionically bonded substances typically have the following characteristics.

 * High melting point (solid at room temp)
 * Hard
 * Brittle (can shatter)
 * Some dissolve in water
 * Conduct electricity when dissolved or melted
 * Typically stronger than covalent bonds.

= HL Material =

Topic 14 is the additional HL material for Topic 4.

title: IB Chemistry/Bonding


text:
IB Chemistry/States of Matter

5.1.1 Solids
In a solid-state molecules/atoms are tightly packed. The force of attraction between molecules/atoms overcomes any translational motion of molecules (they do, however, vibrate in position).

5.1.2 Liquids
Liquids are particles that are held close together, but not as strongly as solids in that they are free to move, but not to escape the liquid (except for fast traveling particles -> evaporation).

5.1.3 Gas
Gas consists of particles that can move independently and randomly, with no significant forces between particles, and a large (comparatively) amount of space between them. An ideal gas is composed of randomly moving point masses occupying no space and with no forces between masses. The average (rms) speed of the movement of particles is proportional to temperature (in K). As a result, the kinetic energy of the particles is also proportional to temperature.

5.1.4 Transitions
Solid into liquid, the rigid structure of the solid is overcome due to increased vibration of particles (due to energy being added in the form of heat). The particles cannot escape from the liquid, but can move within it (thus dissolving in it). Liquid to gas, as energy (in the form of heat) is given to the liquid, the particles gain enough energy to escape the liquid, and become a gas, with particles widely spaced gas can take tremendous volumes. Gas into liquid, as heat (energy) is removed, the particles slow down to the point where the forces between particles are strong enough to hold them together, a liquid is formed! Liquid into solid, even more energy is removed and particles move slower. Stronger forces build a more rigid structure for the material.

5.1.5 Increasing the temperature
Causes the material to become larger in volume or higher pressure. An increase in volume (which holds the material) will translate itself in a decrease in temperature or a decrease in pressure. An increase in pressure(on the other hand) will cause a decrease in volume or increase in temperature.

5.1.6 Diffusion
Since the particles are moving at random (here: in a gas), two separated samples of gas will eventually mix causing diffusion. This will occur at a higher rate with higher temperature since the particles are moving faster.

title: IB Chemistry/States of Matter


text:
Perl Programming/Reference Cards/File Tests

< Reference cards

-r	File is readable by effective uid/gid. -w	File is writable by effective uid/gid. -x	File is executable by effective uid/gid. -o	File is owned by effective uid.

-R	File is readable by real uid/gid. -W	File is writable by real uid/gid. -X	File is executable by real uid/gid. -O	File is owned by real uid.

-e	File exists. -z	File has zero size (is empty). -s	File has nonzero size (returns size in bytes).

-f	File is a plain file. -d	File is a directory. -l	File is a symbolic link. -p	File is a named pipe (FIFO), or Filehandle is a pipe. -S	File is a socket. -b	File is a block special file. -c	File is a character special file. -t	Filehandle is opened to a tty.

-u	File has setuid bit set. -g	File has setgid bit set. -k	File has sticky bit set.

-T	File is an ASCII text file (heuristic guess). -B	File is a "binary" file (opposite of -T).

-M	Script start time minus file modification time, in days. -A	Same for access time. -C	Same for inode change time (Unix, may differ for other platforms)


text:
User:COLETTE~enwikibooks

Hi,

I am a teacher in France. I have already completed or created articles on french wikipedia.

title: User:COLETTE~enwikibooks


text:
IB Economics

IB Economics Review Guide

Syllabus section
--

/Introduction to Economics/

 * 1.1 Basic Definitions
 * 1.2 PPF and PPC
 * 1.3 Free Market vs Planned Economy

/Microeconomics/

 * 2.1 Markets
 * 2.2 Elasticities
 * 2.3 Theory of the Firm (HL)
 * 2.4 Market Failure

/Macroeconomics/

 * 3.1 Measuring National Income
 * 3.2 Introduction to Development
 * 3.3 Macroeconomic Models
 * 3.4 Demand-side and Supply-side policies
 * 3.5 Unemployment and Inflation
 * 3.6 Distribution of Income

/International Economics/

 * 4.1 Reasons for trade
 * 4.2 Free trade and protectionism
 * 4.3 Economic integration
 * 4.4 World Trade Organization (WTO)
 * 4.5 Balance of payments
 * 4.6 Exchange rates
 * 4.7 Balance of Payment problems
 * 4.8 Terms of trade

/Development Economics/

 * 5.1 Sources of Economic Growth and/or Development
 * 5.2 Consequences of Growth
 * 5.3 Barriers to Economic Growth
 * 5.4 Growth and Development Strategies
 * 5.5 Evaluation of Growth and Development Strategies

title: IB Economics