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E-Commerce and E-Business/Concepts and Definitions

What is e-commerce?
Electronic commerce or e-commerce refers to a wide range of online business activities for products and services. It also pertains to “any form of business transaction in which the parties interact electronically rather than by physical exchanges or direct physical contact.”

E-commerce is usually associated with buying and selling over the Internet, or conducting any transaction involving the transfer of ownership or rights to use goods or services through a computer-mediated network. Though popular, this definition is not comprehensive enough to capture recent developments in this new and revolutionary business phenomenon. A more complete definition is: E-commerce is the use of electronic communications and digital information processing technology in business transactions to create, transform, and redefine relationships for value creation between or among organizations, and between organizations and individuals.

International Data Corp (IDC) estimates the value of global e-commerce in 2000 at US$350.38 billion. This is projected to climb to as high as US$3.14 trillion by 2004. IDC also predicts an increase in Asia’s percentage share in worldwide e-commerce revenue from 5% in 2000 to 10% in 2004 (See Figure 1).

Figure 1: Worldwide E-Commerce Revenue, 2000 and 2004 (as a % share of each country/region)

Asia-Pacific e-commerce revenues are projected to increase from $76.8 billion at year-end of 2001 to $338.5 billion by the end of 2004.

Is e-commerce the same as e-business?

While some use e-commerce and e-business interchangeably, they are distinct concepts. In e-commerce, information and communications technology (ICT) is used in inter-business or inter-organizational transactions (transactions between and among firms/organizations) and in business-to-consumer transactions (transactions between firms/organizations and individuals).

In e-business, on the other hand, ICT is used to enhance one’s business. It includes any process that a business organization (either a for-profit, governmental or non-profit entity) conducts over a computer-mediated network. A more comprehensive definition of e-business is:

 * “The transformation of an organization’s processes to deliver additional customer value through the application of technologies, philosophies and computing paradigm of the new economy.”

Three primary processes are enhanced in e-business:

1. Production processes, which include procurement, ordering and replenishment of stocks; processing of payments; electronic links with suppliers; and production control processes, among others;

2. Customer-focused processes, which include promotional and marketing efforts, selling over the Internet, processing of customers’ purchase orders and payments, and customer support, among others; and

3. Internal management processes, which include employee services, training, internal information-sharing, video-conferencing, and recruiting. Electronic applications enhance information flow between production and sales forces to improve sales force productivity. Workgroup communications and electronic publishing of internal business information are likewise made more efficient.

Is the Internet economy synonymous with e-commerce and e-business?
The Internet economy is a broader concept than e-commerce and e-business. It includes e-commerce and e-business.

The CREC (Center for Research in Electronic Commerce) at the University of Texas has developed a conceptual framework for how the Internet economy works. The framework shows four layers of the Internet economy-the three mentioned above and a fourth called intermediaries (see Table 1).

'''Figure 2. Table 1. Internet Economy Conceptual Frame'''

Based on Center for Research in Electronic Commerce, University of Texas, "Measuring the Internet Economy," 6 June 2000; available from http://www.internetindicators.com

This image is available under the terms of GNU Free Documentation License and Creative Commons Attribution License 2.5

The major different kinds of e-commerce are: business-to-business (B2B); business-to-consumer (B2C); business-to-government (B2G); consumer-to-consumer (C2C); and mobile commerce (m-commerce).
What is B2B e-commerce?

B2B e-commerce is simply defined as e-commerce between companies. This is the type of e-commerce that deals with relationships between and among businesses. About 80% of e-commerce is of this type, and most experts predict that B2B e-commerce will continue to grow faster than the B2C segment. The B2B market has two primary components: e-frastructure and e-markets. E-frastructure is the architecture of B2B, primarily consisting of the following:

 * logistics - transportation, warehousing and distribution (e.g., Procter and Gamble);
 * application service providers - deployment, hosting and management of packaged software from a central facility (e.g., Oracle and Linkshare);
 * outsourcing of functions in the process of e-commerce, such as Web-hosting, security and customer care solutions (e.g., outsourcing providers such as eShare, NetSales, iXL Enterprises and Universal Access);
 * auction solutions software for the operation and maintenance of real-time auctions in the Internet (e.g., Moai Technologies and OpenSite Technologies);
 * content management software for the facilitation of Web site content management and delivery (e.g., Interwoven and ProcureNet); and
 * Web-based commerce enablers (e.g., Commerce One, a browser-based, XML-enabled purchasing automation software).

E-markets are simply defined as Web sites where buyers and sellers interact with each other and conduct transactions.10

The more common B2B examples and best practice models are IBM, Hewlett Packard (HP), Cisco and Dell. Cisco, for instance, receives over 90% of its product orders over the Internet.

Most B2B applications are in the areas of supplier management (especially purchase order processing), inventory management (i.e., managing order-ship-bill cycles), distribution management (especially in the transmission of shipping documents), channel management (i.e., information dissemination on changes in operational conditions), and payment management (e.g., electronic payment systems or EPS).11

eMarketer projects an increase in the share of B2B e-commerce in total global e-commerce from 79.2% in 2000 to 87% in 2004 and a consequent decrease in the share of B2C e-commerce from 20.8% in 2000 to only 13% in 2004 (Figure 3).

'''Figure 3. Share of B2B and B2C E-Commerce in Total Global E-Commerce (2000 and 2004)'''

This image is available under the terms of GNU Free Documentation License and Creative Commons Attribution License 2.5

Likewise B2B growth is way ahead of B2C growth in the Asia-Pacific region. According to a 2001 eMarketer estimate, B2B revenues in the region are expected to exceed $300 billion by 2004.

Table 2 shows the projected size of B2B e-commerce by region for the years 2000-2004.

'''Figure 4. Projected B2B E-Commerce by Region, 2000-2004 ($billions)'''

This image is available under the terms of GNU Free Documentation License and Creative Commons Attribution License 2.5

 * Box 1. Benefits of B2B E-Commerce in Developing Markets

What is B2C e-commerce?

Business-to-consumer e-commerce, or commerce between companies and consumers, involves customers gathering information; purchasing physical goods (i.e., tangibles such as books or consumer products) or information goods (or goods of electronic material or digitized content, such as software, or e-books); and, for information goods, receiving products over an electronic network.12

It is the second largest and the earliest form of e-commerce. Its origins can be traced to online retailing (or e-tailing).13 Thus, the more common B2C business models are the online retailing companies such as Amazon.com, Drugstore.com, Beyond.com, Barnes and Noble and ToysRus. Other B2C examples involving information goods are E-Trade and Travelocity.

The more common applications of this type of e-commerce are in the areas of purchasing products and information, and personal finance management, which pertains to the management of personal investments and finances with the use of online banking tools (e.g., Quicken).14

eMarketer estimates that worldwide B2C e-commerce revenues will increase from US$59.7 billion in 2000 to US$428.1 billion by 2004. Online retailing transactions make up a significant share of this market. eMarketer also estimates that in the Asia-Pacific region, B2C revenues, while registering a modest figure compared to B2B, nonetheless went up to $8.2 billion by the end of 2001, with that figure doubling at the end of 2002-at total worldwide B2C sales below 10%.

B2C e-commerce reduces transactions costs (particularly search costs) by increasing consumer access to information and allowing consumers to find the most competitive price for a product or service. B2C e-commerce also reduces market entry barriers since the cost of putting up and maintaining a Web site is much cheaper than installing a “brick-and-mortar” structure for a firm. In the case of information goods, B2C e-commerce is even more attractive because it saves firms from factoring in the additional cost of a physical distribution network. Moreover, for countries with a growing and robust Internet population, delivering information goods becomes increasingly feasible.

What is B2G e-commerce?

Business-to-government e-commerce or B2G is generally defined as commerce between companies and the public sector. It refers to the use of the Internet for public procurement, licensing procedures, and other government-related operations. This kind of e-commerce has two features: first, the public sector assumes a pilot/leading role in establishing e-commerce; and second, it is assumed that the public sector has the greatest need for making its procurement system more effective.15

Web-based purchasing policies increase the transparency of the procurement process (and reduces the risk of irregularities). To date, however, the size of the B2G e-commerce market as a component of total e-commerce is insignificant, as government e-procurement systems remain undeveloped.

What is C2C e-commerce?

Consumer-to-consumer e-commerce or C2C is simply commerce between private individuals or consumers.

This type of e-commerce is characterized by the growth of electronic marketplaces and online auctions, particularly in vertical industries where firms/businesses can bid for what they want from among multiple suppliers.16 It perhaps has the greatest potential for developing new markets.

This type of e-commerce comes in at least three forms:

 * auctions facilitated at a portal, such as eBay, which allows online real-time bidding on items being sold in the Web;
 * peer-to-peer systems, such as the Napster model (a protocol for sharing files between users used by chat forums similar to IRC) and other file exchange and later money exchange models; and
 * classified ads at portal sites such as Excite Classifieds and eWanted, Pakwheels.com (an interactive, online marketplace where buyers and sellers can negotiate and which features “Buyer Leads & Want Ads”).

Consumer-to-business (C2B) transactions involve reverse auctions, which empower the consumer to drive transactions. A concrete example of this when competing airlines gives a traveler best travel and ticket offers in response to the traveler’s post that she wants to fly from New York to San Francisco.

There is little information on the relative size of global C2C e-commerce. However, C2C figures of popular C2C sites such as eBay and Napster indicate that this market is quite large. These sites produce millions of dollars in sales every day.

Advantages of C2C sites

Consumer to consumer e-commerce has many benefits. The primary benefit to consumers is reduction in cost. Buying ad space on other e-commerce sites is expensive. Sellers can post their items for free or with minimal charge depending on the C2C website. C2C websites form a perfect platform for buyers and sellers who wish to buy and sell related products. The ability to find related products leads to an increase in the visitor to customer conversion ratio. Business owners can cheaply maintain C2C websites and increase profits without the additional costs of distribution locations. A good example of a C2C e-commerce website is Esty, a site that allows consumers to buy and sell handmade or vintage items and supplies including art, photography, clothing, jewelry, food, bath and beauty products, quilts, knick-knacks, and toys.

Disadvantages of C2C sites

There are a couple of disadvantages to these type of sites as well.Doing transaction on these type of websites requires co-operation between the buyer and seller.It has been noted many times that these two do not co-operate with each other after a transaction has been made.They do not share the transaction information which may be via credit or debit card or internet banking.This can result in online fraud since the buyer and seller are not very well versed with each other.This can lead to lawsuit being imposed on either ends or also on the site if it has not mentioned the disclaimer in its terms and conditions.This may also hamper the c2c website's reputation.Companies which handle consumer to consumer ecommerce websites seem to have becoming very cautious to prevent online scams.

What is m-commerce?

M-commerce (mobile commerce) is the buying and selling of goods and services through wireless technology-i.e., handheld devices such as cellular telephones and personal digital assistants (PDAs). Japan is seen as a global leader in m-commerce.

As content delivery over wireless devices becomes faster, more secure, and scalable, some believe that m-commerce will surpass wireline e-commerce as the method of choice for digital commerce transactions. This may well be true for the Asia-Pacific where there are more mobile phone users than there are Internet users.

Industries affected by m-commerce include:

 * Financial services, including mobile banking (when customers use their handheld devices to access their accounts and pay their bills), as well as brokerage services (in which stock quotes can be displayed and trading conducted from the same handheld device);
 * Telecommunications, in which service changes, bill payment and account reviews can all be conducted from the same handheld device;
 * Service/retail, as consumers are given the ability to place and pay for orders on-the-fly; and
 * Information services, which include the delivery of entertainment, financial news, sports figures and traffic updates to a single mobile device.17

Forrester Research predicts US$3.4 billion sales closed using PDA and cell phones by 2005 (See Table 3).

'''Figure 5. Table 3. Forrester’s M-Commerce Sales Predictions, 2001-2005'''

This image is available under the terms of GNU Free Documentation License and Creative Commons Attribution License 2.5

What forces are fueling e-commerce?
There are at least three major forces fueling e-commerce: economic forces, marketing and customer interaction forces, and technology, particularly multimedia convergence.18

Economic forces.One of the most evident benefits of e-commerce is economic efficiency resulting from the reduction in communications costs, low-cost technological infrastructure, speedier and more economic electronic transactions with suppliers, lower global information sharing and advertising costs, and cheaper customer service alternatives.

Economic integration is either external or internal. External integration refers to the electronic networking of corporations, suppliers, customers/clients, and independent contractors into one community communicating in a virtual environment (with the Internet as medium). Internal integration, on the other hand, is the networking of the various departments within a corporation, and of business operations and processes. This allows critical business information to be stored in a digital form that can be retrieved instantly and transmitted electronically. Internal integration is best exemplified by corporate intranets. Among the companies with efficient corporate intranets are Procter and Gamble, IBM, Nestle and Intel.

 * Box 2. SESAMi.NET.: Linking Asian Markets through B2B Hubs

 Market forces. Corporations are encouraged to use e-commerce in marketing and promotion to capture international markets, both big and small. The Internet is likewise used as a medium for enhanced customer service and support. It is a lot easier for companies to provide their target consumers with more detailed product and service information using the Internet.

 * Box 3. Brazil’s Submarino19: Improving Customer Service through the Internet

Technology forces. The development of ICT is a key factor in the growth of e-commerce. For instance, technological advances in digitizing content, compression and the promotion of open systems technology have paved the way for the convergence of communication services into one single platform. This in turn has made communication more efficient, faster, easier, and more economical as the need to set up separate networks for telephone services, television broadcast, cable television, and Internet access is eliminated. From the standpoint of firms/businesses and consumers, having only one information provider means lower communications costs.20

Moreover, the principle of universal access can be made more achievable with convergence. At present the high costs of installing landlines in sparsely populated rural areas is a disincentive to telecommunications companies to install telephones in these areas. Installing landlines in rural areas can become more attractive to the private sector if revenues from these landlines are not limited to local and long distance telephone charges, but also include cable TV and Internet charges. This development will ensure affordable access to information even by those in rural areas and will spare the government the trouble and cost of installing expensive landlines.21

What are the components of a typical successful e-commerce transaction loop?
E-commerce does not refer merely to a firm putting up a Web site for the purpose of selling goods to buyers over the Internet. For e-commerce to be a competitive alternative to traditional commercial transactions and for a firm to maximize the benefits of e-commerce, a number of technical as well as enabling issues have to be considered. A typical e-commerce transaction loop involves the following major players and corresponding requisites:

The Seller should have the following components:

 * A corporate Web site with e-commerce capabilities (e.g., a secure transaction server);
 * A corporate intranet so that orders are processed in an efficient manner; and
 * IT-literate employees to manage the information flows and maintain the e-commerce system.

Transaction partners include:

 * Banking institutions that offer transaction clearing services (e.g., processing credit card payments and electronic fund transfers);
 * National and international freight companies to enable the movement of physical goods within, around and out of the country. For business-to-consumer transactions, the system must offer a means for cost-efficient transport of small packages (such that purchasing books over the Internet, for example, is not prohibitively more expensive than buying from a local store); and
 * Authentication authority that serves as a trusted third party to ensure the integrity and security of transactions.

Consumers (in a business-to-consumer transaction) who:

 * Form a critical mass of the population with access to the Internet and disposable income enabling widespread use of credit cards; and
 * Possess a mindset for purchasing goods over the Internet rather than by physically inspecting items.

Firms/Businesses (in a business-to-business transaction) that together form a critical mass of companies (especially within supply chains) with Internet access and the capability to place and take orders over the Internet.

Government, to establish:

 * A legal framework governing e-commerce transactions (including electronic documents, signatures, and the like); and
 * Legal institutions that would enforce the legal framework (i.e., laws and regulations) and protect consumers and businesses from fraud, among others.

And finally, the Internet, the successful use of which depends on the following:

 * A robust and reliable Internet infrastructure; and
 * A pricing structure that doesn’t penalize consumers for spending time on and buying goods over the Internet (e.g., a flat monthly charge for both ISP access and local phone calls).

For e-commerce to grow, the above requisites and factors have to be in place. The least developed factor is an impediment to the increased uptake of e-commerce as a whole. For instance, a country with an excellent Internet infrastructure will not have high e-commerce figures if banks do not offer support and fulfillment services to e-commerce transactions. In countries that have significant e-commerce figures, a positive feedback loop reinforces each of these factors.22

How is the Internet relevant to e-commerce?
The Internet allows people from all over the world to get connected inexpensively and reliably. As a technical infrastructure, it is a global collection of networks, connected to share information using a common set of protocols. Also, as a vast network of people and information, the Internet is an enabler for e-commerce as it allows businesses to showcase and sell their products and services online and gives potential customers, prospects, and business partners access to information about these businesses and their products and services that would lead to purchase.

Before the Internet was utilized for commercial purposes, companies used private networks-such as the EDI or Electronic Data Interchange-to transact business with each other. That was the early form of e-commerce. However, installing and maintaining private networks was very expensive. With the Internet, e-commerce spread rapidly because of the lower costs involved and because the Internet is based on open standards.25

How important is an intranet for a business engaging in e-commerce?
An intranet aids in the management of internal corporate information that may be interconnected with a company’s e-commerce transactions (or transactions conducted outside the intranet). Inasmuch as the intranet allows for the instantaneous flow of internal information, vital information is simultaneously processed and matched with data flowing from external e-commerce transactions, allowing for the efficient and effective integration of the corporation’s organizational processes. In this context, corporate functions, decisions and processes involving e-commerce activities are more coherent and organized.

The proliferation of intranets has caused a shift from a hierarchical command-and-control organization to an information-based organization. This shift has implications for managerial responsibilities, communication and information flows, and workgroup structures.

Aside from reducing the cost of doing business, what are the advantages of e-commerce for businesses?
E-commerce serves as an “equalizer”. It enables start-up and small- and medium-sized enterprises to reach the global market.

 * Box 4. Leveling the Playing Field through E-commerce: The Case of Amazon.com

However, this does not discount the point that without a good e-business strategy, e-commerce may in some cases discriminate against SMEs because it reveals proprietary pricing information. A sound e-business plan does not totally disregard old economy values. The dot-com bust is proof of this.

 * Box 5. Lessons from the Dot Com Frenzy

E-commerce makes “mass customization” possible. E-commerce applications in this area include easy-to-use ordering systems that allow customers to choose and order products according to their personal and unique specifications. For instance, a car manufacturing company with an e-commerce strategy allowing for online orders can have new cars built within a few days (instead of the several weeks it currently takes to build a new vehicle) based on customer’s specifications. This can work more effectively if a company’s manufacturing process is advanced and integrated into the ordering system.

E-commerce allows “network production.” This refers to the parceling out of the production process to contractors who are geographically dispersed but who are connected to each other via computer networks. The benefits of network production include: reduction in costs, more strategic target marketing, and the facilitation of selling add-on products, services, and new systems when they are needed. With network production, a company can assign tasks within its non-core competencies to factories all over the world that specialize in such tasks (e.g., the assembly of specific components).

How is e-commerce helpful to the consumer?
In C2B transactions, customers/consumers are given more influence over what and how products are made and how services are delivered, thereby broadening consumer choices. E-commerce allows for a faster and more open process, with customers having greater control.

E-commerce makes information on products and the market as a whole readily available and accessible, and increases price transparency, which enable customers to make more appropriate purchasing decisions.

How are business relationships transformed through e-commerce?
E-commerce transforms old economy relationships (vertical/linear relationships) to new economy relationships characterized by end-to-end relationship management solutions (integrated or extended relationships).

How does e-commerce link customers, workers, suppliers, distributors and competitors?
E-commerce facilitates organization networks, wherein small firms depend on “partner” firms for supplies and product distribution to address customer demands more effectively.

To manage the chain of networks linking customers, workers, suppliers, distributors, and even competitors, an integrated or extended supply chain management solution is needed. Supply chain management (SCM) is defined as the supervision of materials, information, and finances as they move from supplier to manufacturer to wholesaler to retailer to consumer. It involves the coordination and integration of these flows both within and among companies. The goal of any effective supply chain management system is timely provision of goods or services to the next link in the chain (and ultimately, the reduction of inventory within each link).29

There are three main flows in SCM, namely:

 * The product flow, which includes the movement of goods from a supplier to a customer, as well as any customer returns or service needs;
 * The information flow, which involves the transmission of orders and the update of the status of delivery; and
 * The finances flow, which consists of credit terms, payment schedules, and consignment and title ownership arrangements.

Some SCM applications are based on open data models that support the sharing of data both inside and outside the enterprise, called the extended enterprise, and includes key suppliers, manufacturers, and end customers of a specific company. Shared data resides in diverse database systems, or data warehouses, at several different sites and companies. Sharing this data “upstream” (with a company’s suppliers) and “downstream” (with a company’s clients) allows SCM applications to improve the time-to-market of products and reduce costs. It also allows all parties in the supply chain to better manage current resources and plan for future needs.30

'''Figure 6. Old Economy Relationships vs. New Economy Relationships'''

This image is available under the terms of GNU Free Documentation License and Creative Commons Attribution License 2.5

What is Google AdSense and how does it work for e-commerce
Google AdSense is a service offered by Google that allows website publishers to advertise on Google. It is Google's number 1 source of revenue. AdSense is used to advertise when users type in key words in Google's search engine. Ads are placed on the right hand side of the screen. The ads are text based and allow for links to the website on the advertisement as well.

The AdWords program determines the pricing for key words. AdWords is based on a Vickrey auction system. It is a sealed-bid auction, users submit bids not knowing what other users bid. The highest bidder wins but the second place person's bid is paid. There are pros and cons to this type of auction. The winners the vast majority of the time are the ones who bid the highest. A downside to this type of system is that there is no price discovery, which is a market failure known as imperfect information.

AdSense users generate revenue by having users click on their links and by having them buy what is offered on their website. AdSense has been a huge success for Google and the users of the system.


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A-level Applied Science/Finding out about Substances

About this Unit
From the AQA Specification:

 In this unit you will learn about:
 * how to take and prepare samples for analysis;
 * the use of standard procedures to ensure that the results of analysis can be replicated;
 * how to conduct qualitative analysis and a volumetric (quantitative) analysis;
 * how a chromatographic analysis and colorimetric analysis are conducted;
 * how to calculate a molar enthalpy change from experimentation and that energy changes take place during chemical reactions.

How you will be assessed
This unit is assessed through the work you complete for your portfolio.

The marking criteria are found in the AQA specification.

Scenario 1: Richmond Mine Water
"The Richmond Mine of the Iron Mountain copper deposit contains some of the most acid mine waters ever reported. Values of pH have been measured as low as −3.6, combined metal concentrations as high as 200 g/liter, and sulfate concentrations as high as 760 g/liter."

Molar concentrations of salts in Richmond Mine water sample.

In the investigations which follow, you will examine a sample of water with similar composition to confirm the acid concentration and the ions present. You will use qualitative analysis, titration, colorimetry, chromatography.

=References=

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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A-level Applied Science/Finding out about substances/Qualitative

The basic question addressed by qualitative analysis is: Is there any X in the sample?

In contrast, quantitative analysis answers the question: How much X is there in the sample?

In practice, qualitative analysis records if the amount of X is above a certain threshold value.

=Uses of qualitative analysis=

Reagent

Effects

6M HCl

Increases [H+] Increases [Cl-] Decreases [OH-] Dissolves insoluble carbonates, chromates, hydroxides, some sulfates Destroys hydroxo and NH3 complexes Precipitates insoluble chlorides

6M HNO3

Increases [H+] Decreases [OH-] Dissolves insoluble carbonates, chromates, and hydroxides Dissolves insoluble sulfides by oxidizing sulfide ion Destroys hydroxo and ammonia complexes Good oxidizing agent when hot

6 M NaOH

Increases [OH-] Decreases [H+] Forms hydroxo complexes Precipitates insoluble hydroxides

6M NH3

Increases [NH3] Increases [OH-] Decreases [H+] Precipitates insoluble hydroxides Forms NH3 complexes Forms a basic buffer with NH4+

Limitations
Group I: Ag+, Hg22+, Pb2+ Precipitated in 1 M HCl

Group II: Bi3+, Cd2+, Cu2+, Hg2+, (Pb2+), Sb3+ and Sb5+, Sn2+ and Sn4+ Precipitated in 0.1 M H2S solution at pH 0.5

Group III: Al3+, (Cd2+), Co2+, Cr3+, Fe2+ and Fe3+, Mn2+, Ni2+, Zn2+ Precipitated in 0.1 M H2S solution at pH 9

Group IV: Ba2+, Ca2+, K+, Mg2+, Na+, NH4+ Ba2+, Ca2+, and Mg2+ are precipitated in 0.2 M (NH4)2CO3 solution at pH 10; the other ions are soluble

Many reagents are used in qualitative analysis, but only a few are involved in nearly every group procedure. The four most commonly used reagents are 6M HCl, 6M HNO3, 6M NaOH, 6M NH3. Understanding the uses of the reagents is helpful when planning an analysis.

=Sample preparation=

=Standard procedures=

A. Cations

 * 1) To a 2 cm³ mine water sample: Add sodium hydroxide solution dropwise until it is in excess.
 * 2) Filter the mixture from (1) and add sulphuric acid dropwise to the filtrate.
 * 3) Add aqueous ammonia solution to the acidified filtrate from (2).
 * 4) To a 2 cm³ mine water sample: Add aqueous ammonia solution dropwise until it is in excess.
 * 5) Filter the mixture from (4) and add sulphuric acid dropwise to the filtrate.
 * 6) To a drop of mine water sample: Add a drop of potassium thiocyanate solution.
 * 7) To a drop of mine water sample: Add a drop of potassium hexacyanoferrate (III) solution.
 * 8) Flame test the mine water sample.

B. Anions

 * 1) Test the pH of the mine water sample. What anions would react to form gases at this pH?
 * 2) To a drop of mine water sample: Add a drop of barium nitrate solution.
 * 3) To a drop of mine water sample: Add a drop of silver nitrate solution.
 * 4) To a 1 cm³ mine water sample: Add powdered Al and aqueous NaOH – if a reaction occurs test gas with damp red litmus paper.

Questions

 * 1) Which ions have you identified as being present?
 * 2) Which ions are definitely not present?
 * 3) Are there any ions which you are unsure about?
 * 4) Write a report of this practical work. Discuss the limitations of qualitative analysis. Give a full account of all your experiments and observations.

=Risk evaluations=

=Observations=

=Interpretation, explanation and evaluation=


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A-level Applied Science/Finding out about substances/Titration

=Uses of titration=

Titration can produce one of two pieces of information:

 * 1) When both reagents are known, their reaction is known but only one concentration is known; titration can calculate the unknown concentration.
 * 2) When both reagents and their concentrations are known, but the reaction is unknown; titration can calculate the unknown reaction.

=Sample preparation=

Samples for titration must contain a known chemical so that a standard chemical can be chosen which will react with it.

The sample must not contain any impurities which would interfere with the main reaction.

Samples need to be in the form of solutions. To assay gases and solids the substances may be dissolved in a suitable solvent (e.g. water).

In some cases the sample is made to react with a solution and then the remaining reactant is titrated. This is known as a back reaction.

Example: 1.00 g of impure calcium carbonate reacted with 100 cm³ of 0.4 mol dm−3 hydrochloric acid. The acid concentration was found by titration to be 0.21 mol dm−3, which implies that only 0.0095 mol of carbonate reacted. This amount of carbonate would have a mass of 0.95 g so we can say that the calcium carbonate has 5% impurities.

=Standard procedures and equipment=

Standard Solution
A standard solution is a solution of known concentration. Units of concentration are moles per cubic decimetre i.e. mol dm−3

Primary Standard - This is a chemical which can be obtained in a pure state. It is the basis upon which the concentration of other solutions can be measured and it must possess the following properties:
 * it should not effloresce nor be deliquescent or hygroscopic
 * it must remain stable in solution for a sufficient length of time
 * it must possess a fairly large molar mass to reduce errors in weighing

Passing the mine water sample through an ion exchange resin can replace the metal ions with sodium ions. This process converts all the sulphate salts to sodium sulphate. The acid concentration is in the range 0.6-0.7 mol dm−3, but we need to measure it exactly by titration.

Experiment 1: Preparing the primary standard (sodium carbonate 0.5 mol dm−3)
 * 1) Place a weighing bottle on the balance and tare to obtain a zero reading. Weigh approximately 5.3g the sodium carbonate.
 * 2) Remove the weighing bottle from the balance, zero the balance, and weigh the full bottle.
 * 3) Tip the contents of the bottle into a clean beaker (100 cm³)- it doesn't have to be dry.
 * 4) Weigh the emptied bottle.
 * 5) Add deionised water to the beaker (about 50 cm³) and stir to dissolve the sodium carbonate. Leave the glass rod in the solution at all times - you will lose some to the bench if you put it down.
 * 6) Now transfer the solution via a funnel into a volumetric flask (100 cm³) and wash all remaining drops of solution into the flask with a wash bottle. Wash also the rod and funnel into the flask.
 * 7) Remove the funnel and make up the solution to the graduation mark i.e. until the bottom of the meniscus is just in line with the graduation mark on the neck of the flask - use a dropping pipette for this. Stopper the flask and mix the solution by inverting the flask at least 10 times (shaking is no good).
 * 8) Carefully top up the solution to 100 cm³ again if necessary.
 * 9) Label the flask immediately with your name, name of solution and its concentration.

Weighing Results

 * Mass of bottle with sample: ________ g
 * Mass of bottle empty: ________ g
 * Mass of sample: ________ g
 * Concentration of solution _________ g dm−3
 * Mr of sodium carbonate: _________
 * Molar concentration of solution: _________ mol dm−3

Titration
Using standard solution of sodium carbonate (0.5 mol dm−3) titrate this against the mine water in order to determine its acid content.

 * 1) Use the pipette to measure 25 cm³ aliquots of your mine water into 4 conical flasks.
 * 2) Add a few drops of methyl red or screened methyl orange indicator.
 * 3) Fill the burette with the sodium carbonate (0.5 mol dm−3)
 * 4) Titrate to obtain concordant results.
 * 5) Record the results in the table below

Indicator:

Mean titre:

Calculations
The acid contaminating the water is sulphuric acid.
 * 1) Write the balanced equation for the reaction of sodium carbonate with hydrochloric acid.
 * 2) Calculate the concentration of the acid.

=Risk Assessment=

=Observations and measurements=

phenopthalein:(indicator)

is added in the base solution

burette:

>Take acid in the burette as 50 ml.

>measuring cylinder take 25 ml base.

>now take five readings

>the readings must be in between 11 to 15 ml if these does not comes then there must be wrong in some titration reading.

=Interpretation, calculation and evaluation of results=

Exercise based on minewater scenario
The mine water sample can be purified by a cation-exchange resin so that it contains only sulphuric acid and sodium sulphate, which does not interfere with acid-base titrations.

The acid concentration is very high, so before titration it is diluted by pipetting 25 cm3 into a volumetric flask and making the solution up to 250 cm3.

The following data were obtained by six students:

A. 2.240 g of sodium carbonate decahydrate were dissolved to make 250 cm3 of solution. When this solution was titrated against 25 cm3 of mine water residue, 49.50 cm3 were required to neutralise the acid. What is the acid concentration?

B. 2.426 g of sodium carbonate decahydrate were dissolved to make 250 cm3 of solution. When this solution was titrated against 25 cm3 of mine water residue, 44.85 cm3 were required to neutralise the acid. What is the acid concentration?

C. 3.205 g of sodium carbonate decahydrate were dissolved to make 250 cm3 of solution. When this solution was titrated against 25 cm3 of mine water residue, 34.60 cm3 were required to neutralise the acid. What is the acid concentration?

D. 4.730 g of sodium carbonate decahydrate were dissolved to make 250 cm3 of solution. When this solution was titrated against 25 cm3 of mine water residue, 24.25 cm3 were required to neutralise the acid. What is the acid concentration?

E. 4.95 g of sodium carbonate decahydrate were dissolved to make 250 cm3 of solution. When this solution was titrated against 25 cm3 of mine water residue, 32.70 cm3 were required to neutralise the acid. What is the acid concentration?

F. 5.700 g of sodium carbonate decahydrate were dissolved to make 250 cm3 of solution. When this solution was titrated against 25 cm3 of mine water residue, 19.15 cm3 were required to neutralise the acid. What is the acid concentration?

Plot a graph of the mass of carbonate in 250 cm3 against the volume of carbonate used in the titration.

From the graph, identify which, if any, results is/are unreliable.

From the graph, estimate the average mass of carbonate and the average volume of carbonate required.

From your estimates, calculate the concentration of sulphuric acid.

Find out what percentage errors are associated with the apparatus used in the experiment.

Apparatus:
 * Burette error: 0.1 cm3
 * Pipette error: 0.06 cm3 out of 25 cm3.
 * Volumetric flask: 0.3 cm3 out of 250 cm3.
 * Top-pan balance error: 0.001 g

What is the percentage variation in the students’ estimates of the acid concentration?

Estimate the total error for this experiment.

=Experimental work for Scenario 1=

Analysis of the acid content of the mine water sample.

Passing the mine water sample through an ion exchange resin can replace the metal ions with sodium ions. This process converts all the sulphate salts to sodium sulphate. The acid concentration is in the range 0.6 - 0.7 mol dm−3, but we need to measure it exactly by titration.

Experiment 1: Preparing the primary standard
(sodium carbonate 0.064 mol dm-3)

Notes:

Standard Solution - This is a solution of known concentration. Units of concentration are moles per cubic decimetre i.e. mol dm-3

Primary Standard - This is a chemical which can be obtained in a pure state. It is the basis upon which the concentration of other solutions can be measured and it must possess the following properties

 * it should not effloresce nor be deliquescent or hygroscopic
 * it must remain stable in solution for a sufficient length of time
 * it must possess a fairly large molar mass to reduce errors in weighing

Method For Preparing A Standard Solution
1. Place a weighing bottle on the balance and tare to obtain a zero reading. Weigh approximately 4.55 g of the sodium carbonate.

2. Remove the weighing bottle from the balance, zero the balance, and weigh the full bottle.

3. Tip the contents of the bottle into a clean beaker (100 cm3)- it doesn't have to be dry.

4. Weigh the emptied bottle.

5. Add deionised water to the beaker (about 50cm3) and stir to dissolve the sodium carbonate. Leave the glass rod in the solution at all times - you will lose some to the bench if you put it down.

6. Now transfer the solution via a funnel into a volumetric flask (250 cm3) and wash all remaining drops of solution into the flask with a wash bottle. Wash also the rod and funnel into the flask.

7. Remove the funnel and make up the solution to the graduation mark i.e. until the bottom of the meniscus is just in line with the graduation mark on the neck of the flask - use a dropping pipette for this. Stopper the flask and mix the solution by inverting the flask at least 10 times (shaking is no good).

8. Carefully top up the solution to 250 cm3 again if necessary.

9. Label the flask immediately with your name, name of solution and its concentration.

Weighing Results
 * Mass of bottle with sample ________ g
 * Mass of bottle empty ________ g
 * Mass of sample ________ g
 * Concentration of solution _________ g per 100 cm3
 * _________ g dm-3
 * Mr of sodium carbonate _________
 * Molar concentration of solution _________ mol dm-3

Titration
Using standard solution of sodium carbonate (approx 0.064 mol dm-3) titrate this against the mine water in order to determine its acid content.

Procedure
Dilution

1. Use the pipette to measure a 25cm3 sample of your mine water into a clean 250 cm3 volumetric flask.

2. Add water to make the solution up to 250 cm3

Titration

3. Use the pipette to measure 25cm3 samples of your diluted mine water into 4 conical flasks.
 * Solution in burette: (give concentration)
 * Solution in pipette:
 * Volume of pipette:
 * Indicator:
 * Colour change:
 * Other details:

4. Add a few drops of methyl red or screened methyl orange indicator.

5. Fill the burette with the sodium carbonate (0.064 mol dm-3)

6. Titrate to obtain concordant results.

7. Record the results in the table below

Calculations
The acid contaminating the water is sulphuric acid.

In your report of this practical:

1. Write the balanced equation for the reaction of sodium carbonate with hydrochloric acid.

2. Calculate the concentration of the acid from the mean titre.

Mean titre =                    cm3 Percentage error: (show calculation)

Your report should include:
 * A description of the sample and its preparation for the titration (ion-exchange resin, dilution).
 * An account of the methods you used to estimate the acid concentration
 * Calculation of the concentration of acid and an evaluation of the method and results.

=Errors=

The equipment we use in titration has the following tolerances:
 * Burette 0.1 cm3
 * 25 cm3 pipette 0.06 cm3
 * 250 cm3 volumetric flask 0.3 cm3
 * 3 decimal place balances: 0.001 g

Each item of equipment will introduce a random error to the result. The only way to reduce this error is to repeat the experiment or use more accurate equipment – and we do not have the time or the money.

To calculate the total error we can add the errors from each item of equipment. First the errors must be written as percentages:

23.2 cm3 reading on burette – error is 0.1 cm3, which is _________ %

25 cm3 pipette with a tolerance of 0.06 cm3; __________ %

1.372 g reading on balance with accuracy of ± 0.001 g; _________ %

250 cm3 volumetric flask used to make up solution; __________ %

So, the answer to question (3) has a total error of ___________ %

Errors in the way you perform the experiment are less easy to spot, but if you take several titration readings, you can estimate the random error you have caused by the way you titrate:

The simplest way of considering the uncertainty in the final results is to look at the deviation of the titrations from the average value, so that, for example, a deviation of 0.15 cm3 in 25.15 cm3 leads to an uncertainty of 0.6%.

Readings used to calculate mean titre:

25.0	25.1	25.2	25.3

Precision is best given as the ‘spread’ of possible values e.g. 25.15 ± 0.15 or 25.15 ± 0.6%. The ‘spread’ is usually the ‘standard deviation’, which can be estimated from the range: Divide the range by a conversion factor from the following table:

So, for our four values: 25.0	25.1	25.2	25.3

The range is 0.3, so the standard deviation is 0.3/2.5 = 0.12 cm3 or 0.48%

Result: 25.15 ± 0.12 cm3 or 25.15 cm3 ± 0.48%

What is the standard deviation for these values:

23.1	23.3

What is the standard deviation for these values:

23.1	23.3	23.2	23.1	23.3	23.2	23.1	23.3	23.2

Notice how, with more readings, the standard deviation decreases. Notice also that the error calculated in this way can be added to the equipment errors to estimate the total error.


text:
A-level Applied Science/Finding out about substances/Chromatography

=Important note=

The experimental details given here are given in good faith and are believed to be safe and workable methods. However, the authors cannot take responsibility for the consequences of performing these experiments.

The experiments are written for experienced science teaching staff to use as instructions for a supervised class of students. The experiments are not designed for students or inexperienced members of the public to perform without supervision. If you wish to attempt the experiments, ensure that you have completed a legally adequate risk assessment beforehand and that you work within the constraints of the risk assessment.

=Uses of chromatography=

Chromatography separates a mixture of solutes in a solution. The solvent may be water, but it is often a buffer solution, a mixture of organic solvents, or even a gas. A solvent can be anything from water to alcohol etc. . Most of the chromatography that is done is paper chromatography but this is not often used in industry.

Separation can be used to identify the components of the mixture, or it can be used to isolate pure chemicals.

=Sample preparation=

Sample preparation varies widely from one type of chromatography to the next, but all types of chromatography require the sample to have a small volume and therefore a high concentration. This is because the separation is done by allowing the solutes to move apart. If they are in a small volume to begin with, it does not take much movement to separate the mixture.

In paper and thin-layer chromatography, the sample is often applied many times to the same spot, and the solvent is allowed to evaporate between applications. This concentrates the sample at that point.

In gas and column chromatography it is usually necessary to concentrate the sample as much as possible before application. Some chromatography columns will adsorb the solutes strongly at the top of the column if the sample solvent is chosen carefully. This process concentrates the sample at the top of the column before a second solvent is used to move the solutes through the column to achieve separation.

=Standard procedures and equipment=

Paper chromatography of mine water sample
The mine water sample consists of a number of metal ions in the form of their sulphate salts. To separate them, we can use paper chromatography.

Solvent
Diethyl ether: Methanol: Water: conc HCl (50: 30: 15: 4 by volume). To minimise esterification, mix the reagents in the order water, acid, ether, alcohol. Measure water and acid using burettes or pipettes.

Method
Place 50 cm³ solvent in the bottom of the tank.

The solvent is very volatile and will saturate the air in the tank (‘equilibration’). Improved separation is obtained if the solvent is allowed to equilibrate with the tank atmosphere for one hour.

Spot the solutions along the starting line of the chromatography paper. Each solution should be spotted twice so that the chromatogram can be cut into two halves afterwards.

Spot two samples for the minewater, one with a single addition of solution and one with multiple additions. For the standards, use multiple additions to create 5 mm spots.

Form the paper into a cylinder. Place the cylinder, spotted end down, into the tank. Make sure the paper does not touch the sides of the tank.

Close the lid of the tank.

Prepare the locating reagents.

After three hours, remove the chromatogram from the tank. Open out the paper. Mark the solvent front with a pencil. Leave to dry.

Cut the chromatogram into two and treat the two halves as follows. Spray both sides of the paper. Take great care to avoid excessive spraying. An assistant will use the spray in a fume cupboard:

1) Spray with potassium thiocyanate in acetone. (50 cm³ saturated KCNS in water [200 g in 100 cm³ water], 50 cm³ propanone).

2) Spray with oxine (8-hydroxyquinoline – 0.5 g in 80:20 ethanol:water). Hold over '880' ammonia fumes. Place under UV light to observe fluorescence.

=Risk assessment= Slipping on water - Make sure ground is always dry.

Glass breaking - Make sure your handling your equipment carefully to counter this.

Various chemicals in use may be dangerous and require individual risk assessments.

All experiments must take place in the fume cupboard, this inhales all the toxins and poisonous gases whilst experiment is taking place.

=Observations and measurements=

=Results, calculation and evaluation=

 * The Rf value of each solute can be calculated from the following formula

Distance from origin to solute

Distance from origin to solvent front to the center

 * Which solutes can you identify?
 * How do your Rf values compare to the published ones?
 * How do your results compare with those of other students?

=The underlying scientific principles behind chromatography=

Chromatography involves the physical separation of a mixture of compounds. Chromatography can be used as a purification method but also sees wide use for the identification of compounds based on their chromatographic behavior.

Theory
There are many variations of chromatography, but all involve the dissolution of an analyte into a fluid known as the mobile phase and the passage of this fluid solution across a stationary phase, often a solid or liquid-coated solid.

As the mobile phase comes into contact with the stationary phase, some of the analyte molecules dissolve or adsorb onto the mobile phase. The more the molecules of that substance are retained, the slower their progress through the chromatographic apparatus. Different substances will then move through at different rates, ideally resulting in distinctly identifiable retention times for each substance.

Alternatively, if the solutes are retained on the chromatogram instead of eluted from its far end, one can calculate the ratio of the distance traveled by the solute compared to the distance traveled by the solvent. The is the Rf value.

Commonly used chromatographic techniques are identified through the nature of the stationary and mobile phases used, the method for passing the mobile phase through the apparatus, and how separated components are identified.

As the chromatogram develops (l-r) the two components of the mixture separate.

Paper chromatography
In paper chromatography the stationary phase is paper and the mobile phase is generally some liquid that will dissolve the analyte and wet the paper, often water or an aqueous solution.

Thin layer chromatography
In thin layer chromatography (TLC) a plastic or glass plate is coated with the stationary phase, often alumina, silica, or alkylated silica. The analyte is dissolved in a quick-drying solvent and spotted near the bottom of the plate. The edge of the plate beneath the spot or spots is then dipped and left in a solution of the mobile phase, either an organic solvent or aqueous solution (depending on the nature of the analyte and stationary phase). Capillary action is then allowed to draw the solvent front through the spotted analyte, carrying with it and in the process separating out the analyte's components.

Gas chromatoɡraphy
In gas chromatography (GC) the analyte and mobile phase must both be gases or be readily introduced into the gas phase by heating. The mobile phase gas must be inert and not reacting with the sample to be analysed. Examples of inert gases are helium and nitrogen gas.

The gases are passed through a long, narrow (and most often, coiled) tube either packed with a porous stationary phase or whose inner walls are coated with a stationary phase, and the analyte components are detected as they emerge from the far end of the tube. The tube is commonly known as GC column.

Often a time-varying temperature gradient, from lower temperature to higher temperature, is applied to the tube. This first allows the analyte components to partition into the stationary phase and then, as the temperature rises, to differentially force them back into the mobile phase.

Common detectors for gas chromatography are flame ionization detector (FID), electron capture detector (ECD) and mass spectrometry (MS). Different types of sample analysis would require the use of a different type of detectors.

Column chromatography
Column chromatography, like gas chromatography, uses a tube packed with a stationary phase, but the mobile phase is a liquid instead of a gas (It is sometimes known as 'liquid chromatography or LC). Instead of temperature gradients, a gradient in the composition of the liquid phase can be used to separate components.

Column chromatography can be performed on larger molecules which may not be readily introduced into the gas phase. On the other hand, because of the increased viscosity of liquids compared with gases, liquid chromatography can be a more ponderous process. HPLC (variously high-pressure liquid chromatography or high-performance liquid chromatography) speeds the process and improves its selectivity and sensitivity to a significant degree by forcing the mobile phase through the chromatographic column with high-pressure pumps.

Detection methods
The first root of the word chromatography, chroma, indicates that the separated components in some forms of the technique can be identified by their colour alone. But chromatography has now long been performed on colourless compounds that can be identified in other ways.

Analyte components on thin-layer chromatography plates are often identified under ultraviolet light, or by chemical staining in, for example, an iodine chamber or potassium permanganate. Gas chromatographic anolytes are detected by changes in the ionisation levels of a flame at the output end of the column or by changes in the electrical conductivity of the gas mixture at the end of the column. Liquid chromatography fractions are often analysed through spectrophotometric techniques, notably UV-visible spectroscopy. When separation with GC or LC is performed in tandem with mass spectrometry (the "hypenated" techniques of GC-MS and LC-MS), masses of individual fractions is rapidly determined. These methods are frequently employed in analytical and forensic science.


text:
A-level Applied Science/Finding out about substances/Colorimetry

Uses of colorimetry
Colorimetry is used in chemistry and in other sorts of places such as in industries, color printing, textile manufacturing, paint manufacturing and in food industries (including the chocolate industry). Colorimetry is also used in aspirin.

Colorimetry can detect the smallest colour difference that the human eye cannot pick up. Under the action of chemical agents, samples develop a specific colour that shows the concentration of the substance being tested.

Colorimetry is just one of the types of photometric analysis techniques i.e. it is a way of measuring light.

Below are most possible colorimetric tests:

Colorimetry can be used to find out the concentration of any coloured substance.

Food & Beverage Quality Control

 * 1) Alpha Amylase Activity
 * 2) Milk Quality
 * 3) Miscellaneous Quality Tests

Mineral Oils & Fuels

 * 1) Anti-Icing Additive in Aviation Fuels
 * 2) Marked Oils
 * 3) Carbonisable Substances
 * 4) Lead content

Medical & Clinical Tests

 * 1) Alpha Amylase in Blood or Urine
 * 2) Bilirubin
 * 3) Cholesterol
 * 4) Cholinesterase, Activity in Blood
 * 5) Haemoglobin Content of Blood cells
 * 6) Iron in Serum
 * 7) Lactate Dehydrogenase
 * 8) Lead in Urine/Feaces
 * 9) pH Value of Blood/Urine
 * 10) Phenolsulphophhtalein (Phenol Red) Excretion Test
 * 11) Phenylpyruvic Acid
 * 12) Phosphatase in Blood
 * 13) Phosphorus, Inorganic, in Blood
 * 14) Proteins
 * 15) Salicylate In Blood
 * 16) Sugar/Glucose in Blood
 * 17) Sulphobromophthalein Retention
 * 18) Sulphonamides in Blood/Urine
 * 19) Trichloroaccetic Acid
 * 20) Urea in Blood
 * 21) Uric Acid in Serum

Air Monitoring Tests

 * 1) Chromium
 * 2) Lead
 * 3) Pipino

Method
Colorimetry measurements are made by using a light which passes through a colour filter. The light then passes through a little box (cuvette) with the actual chemical substance. The light leaving the actual sample should be less than the light that actually entered the compound. The loss of light always reflects the concentration of the compound.

Colorimetry can only be done to measurements which are within the visible region of the electromagnetic spectrum, which is 380 – 780 nm. The main general factors which affect the amount of light absorbed by the sample are the wavelength of the light and the colour of the solution.

When manufactures are using a colorimeter, they have a choice of which wavelength they use. The options are:

 * 1) Gelatin filters
 * 2) Interference filters
 * 3) Grating Monochromators
 * 4) Prisms

Sample preparation
Weighed into the crucible, the cotton thread is attached to the wire, and the crucible is put into the vessel. This applies to powdery substances

Colorimetric Measurement of Iron Concentrations
By making several solutions of iron (II) sulfate with known concentrations, the absorbance of each can be determined and a calibration curve can be constructed. Given a solution of unknown concentration, its concentration can be determined from its absorbance.

You will be given iron (II) sulfate solution of known concentration.

Equipment

 * Volumetric flasks, 100cm³
 * Colorimeter
 * graduated Pipette
 * Pipette filler
 * cuvette

Reagents

 * Iron (II) sulfate (0.100 mol dm-3)

Precautions
Wear eye protection, protective gloves and laboratory coat at all times. Make sure you wear shoes.

Procedure

 * 1) Use the colorimeter to measure the absorbance of the water sample and the standard solutions across a range of wavelengths. Choose a suitable wavelength for the rest of the experiments.
 * 2) As a group, decide on how you will need to dilute the standard solutions. You will need to make a series of dilutions which will have absorbances similar to the water sample.
 * 3) Use a colorimeter to determine the absorbance, at the appropriate wavelength of every diluted standard solution made.

Results

 * Plot a graph of absorbance against wavelength for the unknown sample and the standard solutions.
 * Explain your choice of wavelength.
 * Plot a graph of absorbance against concentration for the diluted standard solutions.
 * Calculate the concentration of the unknown solution.
 * Comment on the shape on the graph: According to the Beer Lambert Law it should be a straight line passing through the origin (i.e. directly proportional).

Risk assessment

 * Experiment or Activity: Colorimetry
 * Material used or Procedure:Hazard
 * (the harm it can cause):Risk
 * (the chance of harm):Reducing the risk
 * (What can be done to make it safer):Emergency Procedures (What to do if something goes wrong, e.g. First Aid)
 * Nitric acid
 * Phosphoric acid
 * Potassium iodate
 * Potassium mangonate

All of these are harmful to skin. If in contact with skin they are an irritant. Also can cause burns to skin if left in contact too long. Also can get in eyes and cause blindness

Wear protective gloves when handling acid. Wear protective goggles at all times when conducting experiment.

If in contact with skin run under cold water immediately. If acid gets in eyes rinse and wash out eyes.

Observations and measurements
once you have carried out they experiment your results should show a clear pattern. As the concentration of the solution increases so should the absorbance recorded, meaning they are proportional to one another.

Results, calculation and evaluation
Percentage %Unknown (A)0.1 M (A) 100%        0.13         0.29 75%         0.10         0.24 50%         0.08         0.15 25%         0.06         0.11

Evaluation of our colorimetry experiment: The good thing about our experiment is that we got good results and it compared well against the rest of the class because there percentages as seen of the graph were around the same mark as ours was. A bad thing about our colorimetry experiment is that the colorimeter was playing up and sometimes gave us the wrong readings and this set us back a bit because we had to change the colorimeter meaning again we could not repeat.

Scientific principles behind colorimetry
Colorimetry is the science that describes colours in numbers. It is used in chemistry, and in industries such as colour printing, textile manufacturing, and paint manufacturing.

A colorimeter measures the intensity of light shining through a coloured solution compared to the intensity of light passing into the solution. A detector measures the transmittance (T) (% of light passing through) of the solution. This is mathematically converted to absorbance (A = #log10T). The absorbance is directly proportional to the concentration (Beer#Lambert law). The colorimetry of sulfuric acid is a blue colour and will give an absorption of 0.42 when doing serial dilution.


text:
A-level Applied Science/Finding out about substances/Combustion

Representation of methane burning to produce carbon dioxide and water. =Carrying out the reaction following standard procedure= =Taking appropriate measurements= =Calculating the molar enthalpy change=

A simple method to calculate the enthalpy change of a reaction is to measure the temperature change caused by the reaction. The temperature decrease, ΔT depends on:

 * ΔH, the enthalpy of the reaction.
 * m, the mass of the sample which changes temperature.
 * cp, the heat capacity of the substance which changes temperature.

The heat capacity measures how much energy is required to change the temperature of 1 g of the substance by 1 oC.

ΔH = m cp ΔT

This will give the energy released during the reaction i.e. kJ. To calculate the molar enthalpy change, kJ mol−1, we have to divide by the number of moles used in the reaction.

=Bond breaking and bond formation=

Consider the enthalpy change which accompanies the reaction occurring when a particular bond is broken in a molecule: e.g. in the methane molecule there are four carbon - hydrogen bonds and each could be broken in turn. The energy required at each stage is different since the C-H bond is in a different molecular species i.e. a different atomic environment.

 * CH4(g) → CH3(g) + H(g) 	ΔH = 435 kJ mol-1
 * CH3(g) → CH2(g) + H(g) 	ΔH = 444 kJ mol-1
 * CH2(g) → CH(g) + H(g)	ΔH = 440 kJ mol-1
 * CH(g) → C(g) + H(g) 	ΔH = 343 kJ mol-1

Since bond enthalpy is defined as the enthalpy required to break a bond, all values will be positive.

Now the C-H bond enthalpy will be slightly different in particular molecules e.g. methane, ethane, benzene, ethanol etc. However these differences are not significantly large and we are able to use bond energy terms to make useful predictions.

The average bond enthalpy is the average of the bond enthalpies as measured for the particular bond in a wide variety of “representative” molecules. It is also known as the bond energy term. (See table below).

Table of average bond enthalpies at 298 K
To estimate the reaction enthalpy from bond enthalpies: i)	Add the energy required to break all the bonds in the reactants. This is an endothermic process. ii)	Subtract the energy released when the bonds of the products form. Bond formation is exothermic. e.g. 2 H2 (g) + O2 (g) → 2 H2O (l)
 * 2 H-H bonds and one O=O are broken:
 * 2 x 436 + 496 = + 1368 kJ mol−1
 * 4 O-H bonds are formed:
 * 4 x –463 = -1858 kJ mol−1

Summing the two processes: 1368-1858 = -490 kJ mol−1

This is a good estimate of the enthalpy of formation of two moles of water. The experimental enthalpy of formation of water is –285.9 kJ mol−1 i.e. -571.8 kJ mol−1 for two moles of water.
 * Estimate the enthalpy of formation of hydrogen peroxide. The O-O bond energy is 146 kJ mol−1.

The bond enthalpies for the formation of HI are as follows:

 * H-H	436 kJ mol-1
 * I-I	151 kJ mol-1
 * H-I	299 kJ mol-1

H2 + I2 → 2 HI

A bond consists of two molecules e.g. carbon or hydrogen and the overall reaction has an enthalpy change of 11.
 * Bonds broken: 436 + 151 = 587 kJ mol−1
 * Bonds formed: -2 x 299 = 598 kJ mol−1
 * The overall reaction has an enthalpy change of –11 kJ mol−1, according to this calculation. This compares well with the experimental value of +26.5  kJ mol−1 (value has to be multiplied by 2 because 2 moles HI are formed in the reaction). In the experimental value the sublimation energy is also included:  I2(g) -> I2(v) -63 kJmol−1. Taken this into account will show only minor differences between the calculation and the experimental values. But errors of a few tens of  kJ mol−1 are expected because the bond enthalpies are average values.

Examples
1.	(i) Using the average bond enthalpy values, calculate a value for the enthalpy change of the following reaction. [5] CH3OH + HBr → CH3Br + H2O (ii) The value for this reaction was experimentally determined. It was found to be significantly different from the value you have calculated in (i). By significantly different we mean that the difference is greater than the experimental errors (precision / tolerance). Suggest two different possible reasons for this. [2] (iii) Which would you say is the correct value – that calculated in (i) or that given in (ii)? [1] 2.	For the combustion of propane, C3H8: (i)	Describe the changes in bonding that take place during this reaction. [4] (ii)	Write a balanced equation for this reaction and calculate the enthalpy change using the bond enthalpies below. [6]

=Uses of combustion reactions=

Combustion reactions have been used as a source of heat and light throughout human history. Fire has also been used in warfare, to clear forested areas, in metallurgy and as a source of smoke. Since the Industrial Revolution, combustion reactions have also been used to power machinery and vehicles. Electricity is generated by combustion of fuels such as gas, oil and coal.

In the blast furnace reaction, combustion creates carbon monoxide as well as heat. CO is the reducing agent which converts iron ore to iron.

''Animation of a four-stroke petrol engine. 1. Intake 2. Compression 3. Ignition/Expansion 4. Exhaust''

Annual carbon dioxide emission broken down into various fuel types during 1800-2004 AD. Shows the increasing rate at which fossil fuels are being consumed.

About 80% of global energy production is from combustion of fossil fuels. For the UK the figure is 90%


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User:Tyrenius

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You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page.

Good luck! -- Herby talk thyme 10:36, 27 October 2006 (UTC)

Wikibooks Newsletter, Volume 1
(Wikibooks gazette home | Discuss | Bulletin board | Subscription list)

This is a short newsletter that is being distributed to all active wikibookians. You are getting this message because you are recognized as an established contributor to the project. This newsletter will be distributed on a regular basis to help share news, information, and tips. It comes from a bot account, User:The Staff. User:The Staff is currently operated by a team of wikibooks admins, the complete list of which is available on the user page of the bot. If you would like to not receive this newletter anymore, please remove your name from the list at Active wikibookians.

The work you do at Wikibooks is greatly appreciated. However there are plenty of other opportunities for you to get involved and help us to create a thriving Wikibooks community. We are sure that there are things we can do to help you and your understanding of Wikibooks and similarly there are certainly things you could do to help Wikibooks become a better place.

We would like to ask all wikibookians to add the Bulletin Board to your watchlists. The Bulletin Board is a fast and easy way for wikibookians to communicate important news and events to the entire community. If you have important news to share with the community, you can feel free to add your own entry to that page.

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Sometimes it is easy to forget that the Wikibooks community is much larger and more diverse then the people who work in a single book, or on a single bookshelf. Hopefully, together we can all make Wikibooks a better place, and a more valuable educational resource.

The Staff 04:16, 19 December 2006 (UTC)

Blanking pages
Please don't remove content without explanation. If you want a page deleted, please add to the top of the page. Thanks. – Mike.lifeguard  | talk 18:52, 7 March 2008 (UTC)

Tip
If you want something to not be formatted, you can put    and     around whatever it is. This way you could have written     on Mike's page, and it would have ended up saying    without tagging Mike's page for deletion. Νεοπτόλεμος ( talk | email | contribs ) 19:08, 7 March 2008 (UTC)
 * No worries, not a mistake at all. It took me forever to figure out you could do that. Νεοπτόλεμος ( talk | email | contribs ) 19:18, 7 March 2008 (UTC)

title: User talk:The Kid


text:
User talk:87.74.16.153

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 11:31, 27 October 2006 (UTC)

title: User talk:87.74.16.153


text:
User:Badlydrawnjeff

Mostly working at en, preemptive username reservation.

title: User:Badlydrawnjeff


text:
User:The Halo~enwikibooks

''' The Halo can be found at the English Wikipedia. '''

title: User:The Halo~enwikibooks


text:
Horticulture/Celastrus orbiculatus

Celastrus orbiculatus, Chinese Bittersweet, Oriental Bittersweet, or Oriental Staff Vine is a twining woody vine native to East Asia, but naturalised in other parts of the world, and invasive in a large region of North America. The vine was introduced into North America in 1879, and has since become a damaging weed.

Description
The defining characteristic are the vines themselves. Young vines are thin spindly, with silver to reddish brown bark. Older vines become thick and trunk-like, with a somewhat shiny gray bark with prominent dots (lenticels). When growing without supports to climb it forms shrubby thickets, but more commonly is found growing over trees or shrubs climbing by twisting around the branches or trunks. The encircling vines frequently girdle the supporting tree or branch.

The leaves are round and glossy, 2–12 cm long, have toothed margins and grow in alternate patterns along the vines. Small green flowers produce the distinctive red seeds. The seeds are encased in yellow pods that break open during autumn. All parts of the plant are poisonous.

Ecology
Before it was recognized as a destructive invasive species, Oriental staff vine was planted along roadsides to help control soil erosion. The orange red berries and the vines that hold them are popular as holiday decorations.

Because of these uses, Oriental staff vine has taken over landscapes, roadsides, and woods. In the United States it can be found as far south as Virginia, as far north as New York, and as far west as the Rocky Mountains. It prefers mesic woods, where it has been known to eclipse native plants.

Control
Oriental staff vine has spread very quickly in the United States, and can be quite damaging to native plants and ecosystems. The easiest way to get rid of a small infestation is by ripping the plants out of the ground by their roots. If there is a large colony of them the recommended course of action is to cut at the root, and apply glyphosphate, as most herbicides have no effect on the vine. The application of glyphosphate should be done at the beginning of winter.

title: Horticulture/Celastrus orbiculatus


text:
User talk:147.252.234.179

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 12:47, 27 October 2006 (UTC)

title: User talk:147.252.234.179


text:
User:Duja

wikipedia:en:user:Duja

title: User:Duja


text: User:Epikuros

title: User:Epikuros


text:
User talk:209.7.119.196

Your recent edits actually removed material from European History/Absolutism in Europe as well as introducing spelling errors. Please be careful in your edits - thanks -- Herby talk thyme 13:52, 27 October 2006 (UTC)

title: User talk:209.7.119.196


text:
User talk:168.9.38.24

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 14:38, 27 October 2006 (UTC)

title: User talk:168.9.38.24


text:
User talk:161.132.77.15

Please do not replace Wikibooks pages with blank content. Blank pages are harmful to Wikibooks because they have a tendency to confuse readers. If it is a duplicate article, please redirect it to an appropriate existing page. If the page has been vandalised, please revert it to the last legitimate version. If you feel that the content of a page is inappropriate, please edit the page and replace it with appropriate content. If you believe there is no hope for the page, please see the deletion policy for how to proceed. If page is no longer useful, insert delete to its top. Thanks for contributing to Wikibooks! -- Herby talk thyme 14:43, 27 October 2006 (UTC)

Welcome to Wikibooks. We invite everyone to contribute constructively to our collection. Take a look at the welcome page if you would like to learn more about contributing. However, unconstructive edits are considered vandalism, and if you continue in this manner you may be blocked from editing without further warning. Please stop, and consider improving rather than damaging the hard work of others. Thanks. -- Herby talk thyme 14:45, 27 October 2006 (UTC)

title: User talk:161.132.77.15


text:
User talk:81.179.171.95

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 14:49, 27 October 2006 (UTC)

title: User talk:81.179.171.95


text:
The Cold War/The Space Race

While intelligence was being gathered, propaganda was being handed out, weapons were being developed, wars were breaking out across the globe, a totally different kind of conflict was happening above it. From 1957 to circa. 1975 the two superpowers were locked in a competition to be the first to explore outer space. The race to conquer space was dubbed as the "Space Race".

Apart from a few posters and articles, a television or a radio broadcast, both superpowers were convinced that the ultimate "nuclear bomb" of propaganda weapons was staying ahead in the Space Race, through magnificent and mouth-dropping accomplishments which showed to the world how modern and advanced their political system was.

Background
The world's first rockets were the V-6 and V-8 rockets, made by German rocket scientists in 1942 during World War Two. These were designed to carry 1000kg bombs over a long distance and were fired to a target where the bombs would explode on impact. In 1944, Hitler decided to unleash his "secret weapon" and thousands of these rockets were launched at south-east Britain causing a lot of damage both physically and mentally.

But as the war was drawing to a close Germany was being squeezed from the Allies on one side and the Soviets on the other, hundreds of V-1 and V-2 rockets, and their scientists were captured by both sides and transported back to the home countries where they were "encouraged" to work and share their knowledge with them.

Launch of Sputnik: The Space Race Begins
The Soviet Union kick-started the Space Race when they launched the first ever satellite, called Sputnik 1 into orbit, on October 4th 1957. The event caused so much fear (Since in Soviet easily can replace the payload with warhead) and jealousy within the American public and government that the US government was forced to respond by revamping the whole education system and taking other desperate measures, in order to produce budding rocket scientists in the homeland. This was called the "Sputnik Crisis".

After some embarrassing failures at trying to launch a rocket in Cape Canaveral, and after four months of waiting, the Americans finally managed to successfully launch their own satellite, Explorer 1.

While launching Explorer 1 the United States realized that what the Soviet Union did by deploying Sputnik 1 into orbit redefined the ability to cross another nations borders without provoking military escalation. Even though an aircraft could not cross the border of another nation, it was ok for a satellite to cross that line. Thus the Soviet Union set the ground work for future spy satellite missions by the United States and within a few short years, Corona was born.

First Man Enters Space
On the 4th November 1957, a dog named Laika paved the way for man to enter space, which eventually happened on the 12th April 1961, when the Soviet cosmonaut Yuri Gagarin became the first human to orbit the Earth, in the Vostok I spaceship. This was another embarrassing blow to the USA and showed to the world again how technologically advanced their country was. Then, in 1963, Valentina Tereshkova became the first woman in space.

The Americans put their own man in space a year later. The USA was lagging behind their communist rival in the Space Race and they were going to have to take the initiative soon.

Moon Landings
President John Kennedy famously predicted in 1961 that the Americans would put the first man on the moon before the end of the decade. The statement was a pretty daring one, especially at a time when the USA was being repeatedly humiliated by the Soviets in outer space. Some people were inspired by it while, to others, it was an empty promise that was just going to add to the long list of US embarrassments. But to the amazement of the world, his prediction turned into reality in 1969.

Neil Armstrong and Buzz Aldrin became the first people to set foot on the moon, on 21st July 1969. Over 300 million people around the world watched the event through their television screens. It was a terrific achievement that more than made up for the bad start in the Space Race. The first words of Neil Armstrong were:

One small step for a man, one giant leap for mankind

"a"- added in 2006 with the discovery of a blip in the recordings

The Soviets had to watch helplessly as all memory of their own accomplishments of putting man, woman and dog into space were all immediately washed away.

End of the Space Race

The cost of being in the Space Race was in the billions, and both the USA and the USSR knew that their economies wouldn't be able to handle this cost for long - each new achievement was even more expensive than the last one. After 1969, the Space Race was massively toned down and the idea that there was a "Space Race" going was starting to get out of date. Although the Sputnik launch obviously began the Space Race, what ended it is a matter of debate today.

Most people accept that it ended in 1975, when Soviet and American astronauts met, shook hands and ate together in a friendly meeting during the Apollo-Soyuz mission. The act was a friendly gesture and symbolized the USA and USSR's strengthening relationship, during a 10-year period of 'peaceful co-existence', called "Dètente".

title: The Cold War/The Space Race


text:
User:Durova

I'm an editor the English language edition of Wikipedia. If you'd like to contact me, the most effective way is to go to en:User:Durova.

title: User:Durova


text:
User talk:24.155.128.7

Please do not replace Wikibooks pages with blank content. Blank pages are harmful to Wikibooks because they have a tendency to confuse readers. If it is a duplicate article, please redirect it to an appropriate existing page. If the page has been vandalised, please revert it to the last legitimate version. If you feel that the content of a page is inappropriate, please edit the page and replace it with appropriate content. If you believe there is no hope for the page, please see the deletion policy for how to proceed. If page is no longer useful, insert delete to its top. Thanks for contributing to Wikibooks! -- Herby talk thyme 16:04, 27 October 2006 (UTC)

title: User talk:24.155.128.7


text:
Analog and Digital Conversion/Other Reconstructors

Other Reconstruction Circuits
There are a number of other types of reconstruction circuits available besides the holding circuits that were described in the last chapter. Here we will talk about some of those circuits.


text:
Control Systems/Controllability and Observability

System Interaction
In the world of control engineering, there are a slew of systems available that need to be controlled. The task of a control engineer is to design controller and compensator units to interact with these pre-existing systems. However, some systems simply cannot be controlled (or, more often, cannot be controlled in specific ways). The concept of controllability refers to the ability of a controller to arbitrarily alter the functionality of the system plant.

The state-variable of a system, x, represents the internal workings of the system that can be separate from the regular input-output relationship of the system. This also needs to be measured, or observed. The term observability describes whether the internal state variables of the system can be externally measured.

Controllability
Complete state controllability (or simply controllability if no other context is given) describes the ability of an external input to move the internal state of a system from any initial state to any other final state in a finite time interval

We will start off with the definitions of the term controllability, and the related terms reachability and stabilizability.

We can also write out the definition of reachability more precisely:

Similarly, we can more precisely define the concept of controllability:

Controllability Matrix
For LTI (linear time-invariant) systems, a system is reachable if and only if its controllability matrix, ζ, has a full row rank of p, where p is the dimension of the matrix A, and p × q is the dimension of matrix B.

 * $$\zeta = \begin{bmatrix}B & AB & A^2B & \cdots & A^{p-1}B\end{bmatrix} \in R^{p \times pq}$$

A system is controllable or "Controllable to the origin" when any state x1 can be driven to the zero state x = 0 in a finite number of steps.

A system is controllable when the rank of the system matrix A is p, and the rank of the controllability matrix is equal to:

 * $$Rank(\zeta) = Rank(A^{-1}\zeta) = p$$

If the second equation is not satisfied, the system is not.

MATLAB allows one to easily create the controllability matrix with the ctrb command. To create the controllability matrix $$\zeta$$ simply type

 * $$\zeta=ctrb(A,B)$$

where A and B are mentioned above. Then in order to determine if the system is controllable or not one can use the rank command to determine if it has full rank.

If

 * $$Rank(A) < p$$

Then controllability does not imply reachability.

 * Reachability always implies controllability.
 * Controllability only implies reachability when the state transition matrix is nonsingular.

Determining Reachability
There are four methods that can be used to determine if a system is reachable or not:
 * 1) If the p rows of $$\phi(t, \tau)B(t)$$ are linearly independent over the field of complex numbers. That is, if the rank of the product of those two matrices is equal to p for all values of t and τ
 * 2) If the rank of the controllability matrix is the same as the rank of the system matrix A.
 * 3) If the rank of $$\operatorname{rank}[\lambda I - A, B] = p$$ for all eigenvalues λ of the matrix A.
 * 4) If the rank of the reachability gramian (described below) is equal to the rank of the system matrix A.

Each one of these conditions is both necessary and sufficient. If any one test fails, all the tests will fail, and the system is not reachable. If any test is positive, then all the tests will be positive, and the system is reachable.

Gramians
Gramians are complicated mathematical functions that can be used to determine specific things about a system. For instance, we can use gramians to determine whether a system is controllable or reachable. Gramians, because they are more complicated than other methods, are typically only used when other methods of analyzing a system fail (or are too difficult).

All the gramians presented on this page are all matrices with dimension p × p (the same size as the system matrix A).

All the gramians presented here will be described using the general case of Linear time-variant systems. To change these into LTI (time-invariant equations), the following substitutions can be used:

 * $$\phi(t, \tau) \to e^{A(t-\tau)}$$
 * $$\phi'(t, \tau) \to e^{A'(t-\tau)}$$

Where we are using the notation X' to denote the transpose of a matrix X (as opposed to the traditional notation XT).

Reachability Gramian
We can define the reachability gramian as the following integral:

 * $$W_r(t_0, t_1) = \int_{t_0}^{t_1}\phi(t_1, \tau)B(\tau)B'(\tau)\phi'(t_1, \tau)d\tau$$

The system is reachable if the rank of the reachability gramian is the same as the rank of the system matrix:

 * $$\operatorname{rank}(W_r) = p$$

/control{range}

Controllability Gramian
We can define the controllability gramian of a system (A, B) as:

 * $$W_c(t_0, t_1) = \int_{t_0}^{t_1}\phi(t_0, \tau)B(\tau)B'(\tau)\phi'(t_0, \tau)d\tau$$

The system is controllable if the rank of the controllability gramian is the same as the rank of the system matrix:

 * $$\operatorname{rank}(W_c) = p$$

If the system is time-invariant, there are two important points to be made. First, the reachability gramian and the controllability gramian reduce to be the same equation. Therefore, for LTI systems, if we have found one gramian, then we automatically know both gramians. Second, the controllability gramian can also be found as the solution to the following Lyapunov equation:

 * $$AW_c + W_cA' = -BB'$$

Many software packages, notably MATLAB, have functions to solve the Lyapunov equation. By using this last relation, we can also solve for the controllability gramian using these existing functions.

Observability
The state-variables of a system might not be able to be measured for any of the following reasons:

 * 1) The location of the particular state variable might not be physically accessible (a capacitor or a spring, for instance).
 * 2) There are no appropriate instruments to measure the state variable, or the state-variable might be measured in units for which there does not exist any measurement device.
 * 3) The state-variable is a derived "dummy" variable that has no physical meaning.

If things cannot be directly observed, for any of the reasons above, it can be necessary to calculate or estimate the values of the internal state variables, using only the input/output relation of the system, and the output history of the system from the starting time. In other words, we must ask whether or not it is possible to determine what the inside of the system (the internal system states) is like, by only observing the outside performance of the system (input and output)? We can provide the following formal definition of mathematical observability:

A system state xi is unobservable at a given time ti if the zero-input response of the system is zero for all time t. If a system is observable, then the only state that produces a zero output for all time is the zero state. We can use this concept to define the term state-observability.

Constructability
A state x is unconstructable at a time t1 if for every finite time t < t1 the zero input response of the system is zero for all time t.

A system is completely state constructable at time t1 if the only state x that is unconstructable at t0 is x = 0.

If a system is observable at an initial time t0, then it is constructable at some time t > t0, if it is constructable at t1.

Observability Matrix
The observability of the system is dependent only on the system states and the system output, so we can simplify our state equations to remove the input terms:

 * $$x'(t) = Ax(t)$$
 * $$y(t) = Cx(t)$$

Therefore, we can show that the observability of the system is dependent only on the coefficient matrices A and C. We can show precisely how to determine whether a system is observable, using only these two matrices. If we have the observability matrix Q:

 * $$Q = \begin{bmatrix}C\\CA\\CA^2\\\vdots\\CA^{p-1}\end{bmatrix}$$

we can show that the system is observable if and only if the Q matrix has a rank of p. Notice that the Q matrix has the dimensions pr × p.

MATLAB allows one to easily create the observability matrix with the obsv command. To create the observability matrix $$Q$$ simply type

 * Q=obsv(A,C)

where A and C are mentioned above. Then in order to determine if the system is observable or not one can use the rank command to determine if it has full rank.

Observability Gramian
We can define an observability gramian as:

 * $$W_o(t_0, t_1) = \int_{t_0}^{t_1} \phi'(\tau, t_0)C'(\tau)C(\tau)\phi(\tau, t_0)d\tau$$

A system is completely state observable at time t0 < t < t1 if and only if the rank of the observability gramian is equal to the size p of the system matrix A.

If the system (A, B, C, D) is time-invariant, we can construct the observability gramian as the solution to the Lyapunov equation:

 * $$A'W_o + W_oA = -C'C$$

Constructability Gramian
We can define a constructability gramian as:

 * $$W_{cn}(t_0, t_1) = \int_{t_0}^{t_1} \phi'(\tau, t_1)C'(\tau)C(\tau)\phi(\tau, t_1)d\tau$$

A system is completely state observable at an initial time t0 if and only if there exists a finite t1 such that:

 * $$\operatorname{rank} (W_0) = \operatorname{rank} (W_{cn}) = p$$

Notice that the constructability and observability gramians are very similar, and typically they can both be calculated at the same time, only substituting in different values into the state-transition matrix.

Duality Principle
The concepts of controllability and observability are very similar. In fact, there is a concrete relationship between the two. We can say that a system (A, B) is controllable if and only if the system (A', C, B', D) is observable. This fact can be proven by plugging A' in for A, and B' in for C into the observability Gramian. The resulting equation will exactly mirror the formula for the controllability gramian, implying that the two results are the same.


text:
User talk:70.88.249.173

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 17:33, 27 October 2006 (UTC)

title: User talk:70.88.249.173


text:
User talk:Gwern

haskell wikibook mailing list
Hi! Perhaps you would be interested in joining our mailing list? We're also on GMane if you just want to follow the archives. -- Kowey 06:54, 15 February 2007 (UTC)

 * Didn't know there was one. I'll give it a shot. --Gwern (contribs) 14:43, 15 February 2007 (UTC)

title: User talk:Gwern