Compliance and Financial Regulation Essay Example | Topics and Well Written Essays - 2500 words

Compliance and Financial Regulation - Essay Example Whilst being not able to set out required decision taking details the Government’s strategy for administrative reconstruction it probably added some more twists to the pre said regulatory base which was explained inside Chancellor’s Mansion House lecture on June 16, 2010. Unavoidably the proposals from the Government need to dissolve the FSA and replace it with: (Norton Rose pp.2-3) †¢ Brand new macro-prudential controller, the FPC, made inside BoE. †¢ A new economical policy, known as PRA, created as a helpful of BoE. †¢ One fresh conduct of trade regulator, regionally named as Consumer Protection as well as Markets Authority (CP MA). The intrinsic rearrangement on April 4 is the opening move although the FSA clarified that at a point like this it will be stagnant and immobile to â€Å"twin peaks† administration. Instead of that little initiative moves in eventual manner prepare it till 2012 approach towards twin peak. The FPC’s suggested s tatutory target is summarized here. ... Summary of proposals for the Bank’s and FPC’s objectives The target of FPC is structured to connect to the Bank of England aims subsequently: †¢ The FPC has to be exercising its works with a motive to helping to the goals by the Bank of England of the economical Stability Objective. †¢ Liabilities of the FPC related to the getting the goals related fundamentally to the recognition, monitoring, and action taking to amputate or decrease, schematic risk factors with a motive to guard and enhance the flexibility of the United Kingdom economical system. †¢ These schematic risks include, particularly – systemic risk factors attributable to conformational features of commercial markets or may be to the administration of risk in the financial zones and destabilizing levels of influence, debt or capital outlay increment. †¢ It does not need or authorizes the FPC in exercising its works in a process that would be in its say similar of having a distincti ve adverse impact on the capability of the economical sector to help in the development of the United Kingdom finance in the long run. †¢ â€Å"Systemic risk† speaks of a risk factor to the balance of the United Kingdom economical regulation as a total or maybe to an important part of the system. (Great Britain: Parliament: House of Commons: Treasury Committee, House of Commons Treasury Committee (COR) pp. 10-13) PRA’s objectives Conference of the Government in July, it was adduced that the FCA along with PRA should function to their individual strategic and functional targets. The PRA would be having a strategic target concentrating on financial balance, with a regulatory objective that emphasizes the promotional part of PRA for soundness of the firms in a mode that never rules out the chance of firm

STRATEGIC MARKETING MANAGEMENT Assignment Example | Topics and Well Written Essays - 2500 words

STRATEGIC MARKETING MANAGEMENT - Assignment Example In consideration to the importance of technology in our daily lives, the industry, I have selected for Marketing Research and Planning is ‘Education IT products’. The company that has been selected is Lenovo. Lenovo is a manufacturer of PCs, laptops, desktops and other computer accessories. The history of Lenovo dates back to 1980s (Lenovo Website). Lenovo is operating in UK as well and it is considered as one of the top manufacturers of notebooks in the UK market (Schofield, 2010). The annual report 2009/2010 of Lenovo has revealed that shares of company in the mature markets including UK have declined as compared to its shares in China. Therefore, in this report strategic management analysis of Lenovo has been done and a new product plan has been proposed based on chosen future growth strategy. 2.0 CORPORATE OBJECTIVES The mission statement of Lenovo has been given below: â€Å"Lenovo strives to be a new world company that makes award-winning PCs for our customers. We operate as a company uninhibited by walls or organizational structures using world-sourcing to harness the power of innovation across our global team. We design innovative and exciting products and services to meet our customers’ needs.†(Lenovo Website) As mentioned in the annual report 2009 of Lenovo, the future corporate objectives of Lenovo are given below (Lenovo Website, 2010): Focus on maintaining its growth momentum in its core PC business whereas, exploring new opportunities. Reducing costs and increasing operational efficiency is another corporate objective and to achieve this objective, company has announced a global resource restructuring plan. To expand leadership position in China and to improve profitability in China To return to profitability and maintain and grow shares in the mature markets like UK, US etc To ensure faster end-to-end management in the mature and emerging markets To simplify the business model for global commercial accounts To explore n ew opportunities in mobile interest by coming up new products and through Lenovo Mobile unit 3.0 MARKET OVERVIEW 3.1 Products The current products of Lenovo have been classified into three categories including Professional Grade products, Lifestyle products and Accessories. Professional Grade Lifestyle Accessories ThinkPad Laptops IdeaPad Laptops Monitors ThinkCentre Desktops IdeaCentre Desktops Batteries & Power ThinkStation Workstations Essential Laptop/Desktop Storage ThinkServer Systems All Accessories Source: Lenovo Website The following figure shows sales of Lenovo’s products in 2009 and 2010. Figure shows that notebook computers contribute to the major chunk of the sales with 58 percent and 63 percent in 2009 and 2010 respectively. Figure 1: Sales Analysis by Product, 2009 Source: Lenovo Annual Report 2009/2010 3.2 Target Markets The company has categorised its markets into three groups including China, Mature Markets and Emerging Markets. The Executive Headquarter of Lenovo is in Morrisville, USA whereas, the Principal Operations are in Morrisville (targeting mature markets), Beijing (targeting China) and

International Research Practices Essay Example | Topics and Well Written Essays - 750 words

International Research Practices - Essay Example Considering budget, it would be more practical to just select a local firm that can be the company's partner who will be able to make the company's goal of expanding internationally possible. Finding the right partner, though, is an additional task to the company as it is not that easy to find the right partner to do business with. This paper tries to answer particular questions raised with regard to expanding business internationally and business research practices for the coffee brewing systems company, JavaJoy. Since it is too tasking to conduct the research as an employee of the company, a third-party company is contracted to conduct the research on potential international markets. As mentioned above, expanding business globally is a big decision to make and before making the decision, there is lots of work needed to be done. It is not easy to find a country that can be a potential market, more so, find a business partner to represent the company. Extensive research should be done in order to make a sound decision. The research to be conducted is not as simple as it sounds. The tasks can be daunting and time consuming for an inexperienced company. Thus, it is better to just designate the work to a third-party research firm to be the company's partner in making the right decision. With the nature of the tasks to be done, this research firm partner should be well-experienced when it comes to conducting international business researches. They should have a proven track record in terms of making businesses going international successful. The company can seek referrals from other companies who have worked with research firms. One other thing to consider is the services the research firm offers. It is best to have one specific point person who is in-charge of all the transactions of the company and who will be able to answer all queries by the company. It is also best if the research firm can provide different options and suggestions in order to come up with the right decision. The research firm should indeed act as a partner or an ally of the company in making its goals of going global come true. What would you expect of them The partner in conducting the research should be able to understand how the entire business works. It may not be able to determine the right type of market or find the right local company to work with if it does not fully understand the missions and visions of the company. The first thing that I would expect them to do is to take time in understanding and learning the processes of the company, JavaJoy, what types of market does it cater to and what are the goals of the company. They should be able to show an effort that they need to know these things. One other thing that I would be expecting of them is a regular progress report of their research findings as the company, being the customer, should be well informed all the time. They should also be able to provide the company with a detailed breakdown of all the expenses made in order to gather all the information and research data needed. Overall, I would say that these would all sum up to professionalism. The partner to conduct inte rnational market research should be professional enough in the services they render. How would you go in finding such a partner and what would your selection criteria be Before starting to look for the right partner, there should be

The Sequestration Essay Example | Topics and Well Written Essays - 500 words

The Sequestration - Essay Example One of the challenges that I have had to deal with is the introduction of unpaid off days as one way of reducing budgetary allocations at my work place. One requirement of the sequestration is to carry out deductions on employees pay on the total number of days the employee was off from work. As a result of this move by the government, it has become a necessity to look for part time jobs in order to compensate for the reduced income. Maneuvering between my workplace and my part time job is a real challenge. The second challenge is that I have to make reductions on expenditures on certain luxuries I and my family used to like. This poses a psychological challenge based on the fact that it is difficult to accept that I can no longer afford some services that were part and parcel of my life. Therefore, my performance at the workplace becomes compromised because I can no longer perform to the maximum. Some of the areas that I have been forced to make reductions on include expenditures on cell phone services, movie night and restaurants, cancelling vacations, and general reductions on family expenditures. Servicing mortgages, car loans, and other loans have become real challenges since the introduction of the sequestration strategy of dealing with budgetary deficits. This is as a result of the unexpected reduction in income at a time when mortgages and other loans were under servicing. This is frustrating in the sense that members of the congress who are imposing the sequestering policies may not be subjected to pay cuts similar to those of federal workers (Lee et al, 2012). The fact that reductions on budgetary allocations on government programs are likely to cause layoffs of government workers keeps every government worker with a lot of worries. It is projected that thousands of government workers are likely to lose their jobs as a result of the

Poor Interpersonal Skills Essay Example | Topics and Well Written Essays - 500 words

Poor Interpersonal Skills - Essay Example The action plan to deal with the situation is to have a personal meeting with Bethany to address the issue. I must come prepared with evidence of the problem including employee complaints, a periodical evaluation of her performance, and any other source documents to establish a pattern of her inability to communicate effectively. In the meeting I should reiterate to Bethany that the company believes in her abilities as a professional in the accounting field, but that it is imperative for her to improve certain aspects of her behavior at work particularly those associated with her interpersonal abilities. As a manager Bethany now has more responsibilities and the firm expects more out of her. In the meeting I will tell Bethany that her job is not at risk and that an action is going to be created to remedy the situation. After the initial meeting I will arrange another meeting in two weeks to provide an action plan for Bethany to improve her communication skills. I will seek the assist ance of the human resource department in this matter.

Chipotle Mexican Grill Essay Example for Free

Chipotle Mexican Grill Essay I. Key Problem What Steven Ells began with a small taqueria in Denver, Colorado in 1993, one may not have foreseen this venture to become the fastest growing restaurant chain in the last decade. By 2006, Ells’ idea made its initial public offering with 535 restaurants throughout the world. Things were going tremendously well for CMG until late afternoon on October 18, 2012 when Ells finished receiving the company’s third quarter results. While data indicated an overall satisfactory outcome, it was the competition from Yum Brands’ Taco Bell and their recent launch of the Cantina Bell menu that would result in what seemed to be the onset of a major problem. Taco Bell had now become a major competitor to Chipotle since the launch of their new Cantina Bell menu allowing them to enter into the fast-casual segment in offering similar ingredients and items as Chipotle had. At the same time CMG paid a significant amount more for their products forcing them to charge a higher price on their menu items. Taco Bell, however, now offered similar items for half the price. The bottom line: competition was the root of this problem. The fact that Chipotle menu prices were higher as compared to that of Taco Bell’s new menu would lead to consumers or normally loyal customers to give the Cantina Bell menu a try. After the launch of the Cantina Bell menu in the summer of 2012, CMG stock significantly declined just after third quarter results were announced. To add insult to injury, Jeff Einhorn, a hedge fund leader, presented at the Value Investors Conference in New York City proclaiming that CMG was an attractive stock for short-sellers because of the considerable competition from Taco Bell. He further stated, â€Å"23% of Chipotle customers had already tried Taco Bell’s Cantina Bell menu†¦and two-thirds of those customers indicated they would return. What’s more, the customers most likely to return to Taco Bell were also those most likely to eat at Chipotle, a dynamic that indicates to me that Chipotle is most at risk of losing its frequent customers.† This message led to CMG’s stock falling by more than 4% within hours of the conclusion of the presentation. The announcement of projected increases in food costs on the part of CMG also contributed to the competition between them and Taco Bell. While Chipotle stood by its belief that it is â€Å"Food with Integrity† because of better ingredients, the Cantina Bell menu produced something similar while lowering the cost a customer would have to pay for a meal, therefore, causing further competition between the two. II. Relevant Theory By looking at the items offered on the Cantina Bell menu versus those on Chipotle’s menu, I determined that they both have a competitive advantage. Chipotle is a premium product offered at a higher price where it reaches a broader market share that is willing to pay more money. On the other hand, Taco Bell’s main strategic course is cost leadership which enables them to reach a broader market share with a lower price for the desired item. As shown on Example 1 the Competitive Advantage and Economic Value Created are somewhat different between the two companies. Since Chipotle offers a better quality of ingredients, consumers are willing to pay a higher price. As a result, creating a higher Value (V) for a burrito is at the same time creating a greater economic value (Value-Cost.) Meanwhile the economic value created by Taco Bell is smaller since the value of their product is less and consumer’s maximum willingness to pay will be lower. Example 1 Since Yum Brands launching of the new Cantina Bell menu, this new organic ingredient-driven list of selections has been a pretty obvious attempt to compete with fast casual giant Chipotle. This is what has become the major concern for Chipotle where competition is becoming fierce and for practically half the price the Cantina Bell menu is a definite value. However, you do get what you pay for and the overall quality and taste of Chipotle still has a slightly greater edge over Taco Bell. The value someone will be willing to pay for a Taco Bell burrito will be less than the value Chipotle has created with their better quality ingredients, hence creating a greater economic value. III. Assessment of Alternatives How could Chipotle effectively approach their key problem which is Taco Bell’s new Cantina Bell menu? What seems to be the main concern for Chipotle is that Taco Bell is trying to provide a similar product for half the price. Some of the alternatives available to Chipotle to are: †¢ Buy low cost goods to reduce prices using Concentrated Animal Feeding Operations (CAFOs) †¢ Another option could be to offer a smaller burrito for a smaller price, or to include less amounts of meat as Taco Bell does †¢ Continue doing what they do best and differentiate themselves Should Chipotle buy low cost goods to reduce prices using Concentrated Animal Feeding Operations (CAFOs), it would allow them to offer menu items at a lower cost to the consumer providing greater competition between them and Taco Bell’s Cantina Bell menu. However, in doing so would contradict their philosophy of providing the best quality ingredients in their food. In doing so, it will change CMG’s strategy from being a premium product and higher price to a cost leadership strategy and at the same time reducing the value of its product. Another option could be to offer a smaller burrito for a smaller price, or to include less amounts of meat as Taco Bell does in its Cantina Bell menu. This would also allow for cost effectiveness on both the consumer and Chipotle’s side, however, it would go against CMG’s mission statement of being â€Å"Food with Integrity†, lower its value and become a cost leadership strategy as opposed to being a premium product and higher price. A third alternative is for CMG to continue to compete effectively by doing what they already are doing which is differentiation based on quality and sustainability. This approach supports its philosophical message of better food for the consumer and community as well as being environmentally conscious. This allows CMG to maintain its values and remain within their strategy segment. On the contrary, this alternative force Chipotle to increase their menu prices while reducing its consumer surplus. IV. Suggested Course of Action After carefully analyzing the different alternatives, the best course of action is to continue to compete effectively on differentiation based on quality and sustainability given the mounting competitive and sourcing challenges. Even thought Taco Bell’s new menu seems like a significant threat they are far from creating the same value and reputation Chipotle has created since it opened its first restaurant in 1993. Not only does Chipotle provide the freshest and best ingredients with a bold flavor, they are setting themselves apart from any other restaurant chain and main competitor since they continuously are working toward better practices. They continue to push to sustainable sourcing like getting their meat form non Concentrated Animal Feeding Operations (CAFOs) while at the same time contributing to the promotion of good animal health and fighting against animal abuse. In addition, CMG buys products from local farms, builds restaurants to be eco friendly and LEED certified (leadership in Energy and Environmental Design) while trying to keep the cost and price of other items down. As their value statement proclaims, â€Å"Food with Integrity† is a mission of serving good quality food with inputs sourced using sustainable farming practices. Even thought new threats like Taco Bell’s Cantina Bell menu are presenting a challenge there will always be competition. CMG upholds strong beliefs to do what is best for the environment and for its communities in order to provide the best products to its consumers. This is precisely why they have grown so fast from the opening of their first taqueria, to the capital infusion from McDonald’s, to its initial Public offering (IPO.) They have been the fastest growing chain in the last decade and just like any fast growing business, regardless of their success, they will reach a slower growth as they approach maturity. There will still be opportunity for expansion. Chipotle is certainly heading toward a different direction than their competitors making them stand out and become a lot harder to imitate. This alternative is truly the only logical option for Chipotle as it continues to enforce its philosophy of providing â€Å"Food with Integrity.† There will always be competition between companies and products, however, if Chipotle chooses another route for combating this rivalry with Taco Bell, it would not allow itself to differentiate from them. V. Key Takeaways Before reading this case, I knew nothing about Chipotle but after reading it I am quite impressed by the approach CMG has taken choosing to go a different route most companies are afraid of doing because of higher cost prices. I was equally impressed they choose organic products, to buy from local farms, being against massive animal feeding as well as animal cruelty and that they are eco friendly and are looking to make all their restaurants like this. Of course, I should also mention that one knows one will be eating the best ingredients and most fresh available foods. I am confident as the values of this company are brought to the attention of more of the public, Chipotle will reach a bigger market share as the public demand will rise. I would also predict other companies and restaurants will follow similar suit. As mentioned earlier, there will always be competition in business, but a firm must find their differentiation advantage. As individuals become more educated and understand the factor facing the environment people will be willing to make a change and help make a difference.

FTIR spectroscopy of SO2

FTIR spectroscopy of SO2 Abstract In this lab, the IR spectrum of SO2 gas was taken. The spectrum was then used to determine which peaks corresponded to the vibrational modes of SO2 ­. Once the modes had been determined, the experimental wavenumbers of the v1 and v3 modes and the overtones were used to determine the anharmonicity of the two different modes. While there was a difference between the two modes anharmonicity, overall there was not a significant difference. The modes and their corresponding wavenumbers were also used to calculate the force constants of SO2. The experimental data produced a force constant k1 with 3.112% error while the kÃŽ ´/l2 constant had a 2.963% error. Introductions IR spectroscopy is the detection of a transmittance or absorption intensity of change as a function of frequency1. In recent years, Fourier transform spectrometers replaced the traditional dispersive spectrometer because they are faster and more sensitive. They have made it possible to analyze many areas which were not possible with the dispersive spectrophotometer. The difference is the simultaneous examination of all frequencies. The three basic spectrometer components in a FT system are the radiation source, interferometer and detector. The radiation source in precision FTIR instruments is often water-cooled in give it more power and stability2. Figure 1. shows a diagram of the interferometer and the schematics of the spectrophotometer as a whole. The interferometer has the following three components: a moving mirror, fixed mirror, and a beamsplitter.. The beamsplitter is a semireflecting geranium thin film of small particles deposited on flat KBr substrate. Radiation from the broadband IR source is focused into the interferometer, and hits the beamsplitter. Once the beam hits the beam splitter, half of it is transmitted to the fixed mirror while the other half is transmitted to the moving mirror. The changing position of the moving mirror relative to the fixed one generates an interference pattern and causes the two beams to oscillate in and out of phase. When the beams are in phase, there is a constructive interference resulting in the maximum detector response. However, when the beam is out of phase, there is a deconstructive interference between the two beams. Once they have been reflected from both mirrors, they recombi ne at the beam splitter. The recombined beam passes through the sample and then focuses on the detector2. The intensity of the radiation hitting the detector will vary in a sinusoidal manner while the mirror is moving at constant velocity. The record of the interference signal is the interferogram and is a time domain spectrum. The detectors response changes versus time within the mirror scan are recorded. When a sample absorbs at a certain frequency, the amplitude of the sinusoidal wave reduces proportionally to the amount of sample in the beam. In an IR spectrophotometer, this process happens in three component frequencies, which creates a more complex interferogram2. To convert these interferogram recordings to the IR spectrum, a Fourier transformation is used. Small, precise intervals are used during the mirror scan. The rate of the sampling behavior is controlled by a monochromatic beam produced by a helium neon laser focused on a separate detector2. For this analysis, the mid IR spectrophotometer utilized a KBr beamsplitter and a mercury cadmium telluride (MCT) detector. MCT detectors are photon detector with a dependence on the quantum nature of radiation. They also exhibit very fast responses. They must be at a constant temperature of 77^(o)K, the temperature of liquid nitrogen. It is faster and more sensitive than the alternative detector, the deuterated triglycine sulfate (DTGS) 2, which was used for the far IR analysis. The cell used to hold the SO2 gas can be seen in Figure 2. A molecules energy can be split into three components: the electrons motion, the constituent atoms vibrations and the whole rotation of the molecule. While electronic transitions happen on a short timescale, rotational transitions happen on a longer time scale. When a molecule is placed in an electromagnetic field, such as light, energy from the light is transferred from the field to the molecule. This happens upon the satisfaction of Bohrs frequency condition: ΔE = hv When a molecule is excited from one state to another, the energy difference between the two states is absorbed by the molecule. When the molecule reverts back to the previous state, the change in energy which was absorbed upon excitation is then emitted1*. A molecule will be excited by photons which possess the appropriate energy3. Vibrational transitions are observed in the infrared (IR) spectra which are about the 103 ~ 104 cm-1 region. These transitions are caused by the vibration of the nuclei constituting the molecule. The rotational transitions occur at 1-103 cm-1 region, the microwave region, while the electronic transitions occur at 104-106 cm-1 region, the UV-visible region. As the vibrational quantum number v increases, the rotational intervals tend to decrease. The vibrational fine structure of electronic transitions can give insight to the structural and bonding information about molecules which are electronically excited1*. A system displaced from its equilibrium force will be restored due to a restoring force provided by the elasticity of the system. However, there is a property of inertia which causes the system to over correct for the displacement. The back and forth actions of elasticity and inertia cause the system to have oscillatory motion4. When the potential energy is graphed versus the internuclear separation, a perfect harmonic oscillator forms a parabola. The energy spacing in a harmonic oscillator does not change throughout the well of the parabola and is equal to hω where ω=km12 and the zero point energy is Eo= 12hω When a system is not a perfect harmonic oscillator, it is considered anharmonic. Anharmonicity forces the right side of the parabola to widen and asymptotically approach zero. The spaces between the permitted states are not evenly spaced as they were in the harmonic system5. The comparison of the two graphs can be seen if Figure 3. One of the possible ways to calculate xe, a term which shows the anharmonicity of a system is to graph ?G/? versus (?+1). This yields a graph with an equation as follows ΔGv=v+ 1xeve+ ve By dividing the xeve term by ve, the xe term is found. The larger this number, the more anharmonic the system is and vise versa5. Covalent bonds of molecules are not rigid as ball and stick models would suggest, but rather they can be compared to stiff springs which are capable of stretching and bending. More energy is required to stretch and compress a bond than it does to bend it. There is a direct relationship between the energy or frequency which characterizes the stretching vibration of a bond and the bond dissociation energy3. The major factors which are influencial in the stretching frequency of a covalent bond can be seen in the following equation: v = 12rck(m1+m2)m1+m2 where v is the frequency, k is the force constant, c is the speed of light, and m1 and m2 are the masses of the two atoms on each end of the bond. This equation corresponds to the rigidness of the oscillation. However, it should be noted that not all molecular vibrations are capable of being observed in the infrared region. In order to be seen in an IR spectrum, a vibration must cause a change in the dipole of a molecule. This change in charge distribution allows the molecule to absorb infrared light. There is a proportional relationship between the change in charge distribution and the absorption: the greater the change, the stronger the absorption3. All vibrating physical objects have a set of normal modes6. A normal mode can be defined as a simple harmonic oscillation which occurs about an area which is local and low in energy. The normal modes are determined by the systems structure R and its energy function V(R ). Any motion can be expressed as a superposition of normal modes when a pure harmonic V(R ) is being considered. However, the near minimum potential can still be approximated by a harmonic potential for an anharmonic V(R ). Also, small-amplitude motions can still be described by the sum of normal modes. This means that all systems behave harmonically at low temperatures7. For SO2, it is necessary to have nine Cartesian coordinates in order to determine the positions of all three nuclei. Therefore, the molecule is considered to have nine nuclear degrees of freedom. The first three are necessary to describe the position of the center of mass of the molecule. If these three degrees change, it represents the translational movement of the molecule in space. The next three degrees of freedom refer to the orientation of the molecule. These three degrees can be described as the angles of the molecule. If these three degrees change, then the molecule has rotated. The three remaining coordinates are those used to describe the relative positions of the three atoms. These are called vibrational coordinates8. To describe the vibrations of a bent trigonal molecule, it makes sense to use the valence coordinates. The valence coordinates consist of the two bond lengths and the bond angle. However, they do possess a drawback. If energy is put into a bond so that it stretches, to observe how the molecule reacts is difficult due to the energy put into the stretched bond quickly flowing into the vibrations of the other bond in the molecule. Because of this, it is said that the stretching of a single bond and other vibrational motions are coupled8. By varying the coordinates, which are the linear combinations of changes in the bond lengths and bond angles, a good uncoupled approximation can be made. These coordinates are called the normal coordinates. Motions which take place in these coordinates are appropriately called normal modes of vibration. The center of mass does not move in these coordinates8. A non symmetric molecule with N number of atoms will have 3N-6 normal modes. This means SO2 will have 3(3)-6 = 3 normal modes. The normal modes for SO2 can be seen in Figure 3. The symmetric stretch is labeled as v1, the bend is labeled v2, and the asymmetric stretch is labeled v3. When a molecule is exhibiting one of the vibrational modes, it travels the path indicated by the arrow, stops, and then returns back to its starting position8. It is possibly to express the three normal modes as a potential-energy function written in terms of bond stretching and angle bending as shown in the following equation: V = 12k1(R1-Re)2+ 12k1(R1-Re)2+ 12kb(ÃŽ ¸-ÃŽ ¸e)2 where R1 and R2 are the first and second bond length of S-O, Re is the equilibrium S-O bond length, ? is the bond angle of O-S-O, and ?e is the equilibrium value. The constants ks and kb ­ are for the stretching and bending respectively9 ­. Though the derivations are difficult, it was found that the following equations are derived from eq. (1) and are used to calculate both constants: 4r2v32 = 1+2momssin2ÃŽ ±k1mo 16r4v12v22 = 21+2momssin2k1moÃŽ ±kÃŽ ´l2 4r2v12+v22 = 1+2momscos2ÃŽ ±k1mo+2mo1+2momssin2ÃŽ ±kÃŽ ´l2 where v# is the wavenumber of that particular mode, 4?3 is expressed as 5. 8918E-5 in order to obtain units of Nm-1, mo is the mass of oxygen, ms is the mass of sulfur, ? is 59.75^(o), and k?/l2 is the same as the kb constant used in equation (6)10. Diatomic molecules possess only one vibrational coordinate which is quantized. This means that only specific results will be obtained for the value of the vibration. The quantum mechanical harmonic oscillator upon first approximation gives the allowed levels of a diatomic molecule. Polyatomic molecules are similar. Each normal mode has quantized energy, and can be approximated by the harmonic oscillator model when at low energy levels. The frequencies associated with bending tend to be lower than the frequencies associated with stretching10. It is possible to see normal modes via IR spectroscopy if they have a change in dipole in the molecule when it stretches or bends10. All of the normal modes in SO2 are IR active and therefore can all be seen in the IR spectrum at the fundamental frequency. It is possible to observe other weak bands in the spectrum which are a result of overtones. Overtones occur because anharmonicities. They usually happen at integer multiples of 2 or 3 of the fundamental frequencies and are caused by two modes being simultaneously excited10. These bands are located at frequencies which are approximately the sum or difference of the two modes which were excited and are weak10. Method About 1.5g of drierite was weighed out and placed in the barrel of a syringe and the plunger was inserted almost entirely into the barrel. A 3 cm piece of rubber tubing was attached to the tip of the syringe. A 1.5 g of sodium hydrogen sulfite was measured and placed in a vial cap that was small enough to fit into the syringe barrel. The filled vial cap was then into the syringe using a bent spatula to prevent the sodium hydrogen sulfite from spilling into the barrel. The plunger was pushed into the syringe as far as it would go. To ensure that none of the sodium hydrogen sulfite was spilled, the syringe was placed tip down in a beaker. The next step was placing 15 mL of 6 M HCl into a small beaker. All of the acid was then drawn into the syringe containing the vial cap very carefully as to not let any of the acid mix with the sodium hydrogen sulfite. The plastic lid was then screwed onto the syringe. Once the cap was secure on the tip, the syringe was shaken so that the acid and the sodium hydrogen sulfite mixed. As SO2 gas was being produced, the plunger on the syringe was pulled out simultaneously. The high pressure of the gas in the syringe caused the cap on the tip to leak so it was necessary to apply pressure to the tip to prevent it from spitting acid out. Once the reaction had stopped producing gas, the syringe was inverted so that the tip was pointing up and the liquid was at the bottom of the barrel. The cap was removed and the tip was connected to the other end of the rubber tubing attached to the syringe containing drierite. At this point the syringe containing drierite was above the syringe containing the SO2 gas. As the plunger in the bottom syringe was being pushed in, the plunger in the top syringe was being pulled out; making sure no liquid was pushed through the tubing and into the top syringe. The top syringe, now containing the SO2 gas, was capped and allowed to sit for five minutes in order for the drierite to dry the SO2 gas. The excess HCl in the reaction syringe was expelled into a waste beaker. 15 mL of NaOH was placed in a beaker and then drawn up into the syringe in order to destroy any remaining SO2. The NaOH was then also expelled into the waste beaker. After the syringe containing the gas had sat for five minutes, the IR gas cell was placed in the hood. The syringe containing the SO2 was then attached connected to the gas cell using another piece of rubber tubing. Both stopcocks on the gas cell were opened and the gas was pushed into the cell. Both stopcocks were then immediately closed to prevent any of the SO2 from leaking out. A spectrum in the range of 700-2500 cm-1 was obtained using an FTIR spectrophotometer. In order to get a good spectrum from the mid IR range, the cell was undiluted. However, to obtain a good spectrum in the far IR range, it was necessary to dilute the gas cell. Once the spectrum had been obtained, the gas cell was placed inside a fume hood. Both stopcocks were opened up and a syringe was used to flush air through the gas cell. The gas cell was then placed in a vacuum sealed dessicator with the stopcocks open in order to dry out any moisture that may have entered the cell during the experiment. Results The IR spectra of SO2 can be seen in Figure 5. By looking at what wavenumbers the peaks appeared at, it could be concluded which peak corresponded to each vibrational mode of SO2. The bending of a molecule happens at lower wavenumbers, so it was concluded that graph in the top right corner corresponds to the ?2 vibration. It was known from literature that the stretches occur somewhere between 1000 and 1500 cm-1 so the graph in the bottom right must correspond to the overtones of SO2s ?3 and ?1 modes. It is known that asymmetric stretches always correspond to higher wavenumbers. So it was concluded that the next two peaks on the spectrum were ?1 and ?3 respectively. The actual experimental wavelengths of each mode can be seen it Table 1. There are two overtones present, one from the ?1 mode and another from the ?3 mode. The lower frequency overtone corresponds to the lower-frequency mode. Thus the lowest overtone is that of ?1 while the second seen overtone comes from the ?2 mode. Using the experimental wavenumbers for each mode, both constants could be found using eq. (7) first to solve for k1. This values was calculated to be 1000.858 Nm-1. The litereature value is 1033 Nm-1 and the percent error in the experimental value was 3.112% The calculated value of k1 was then used in eq. (8) to find the k?/l3 constant. The second constant was calculated to be 78.60 Nm-1. Literature value for this constant is 81 Nm-1 and the percent error in the experimental calculation was 2.963%. To evaluate the effectiveness of this method for finding the constants, both sides of eq. (9) were solved for. The left side equaled 93.77 Nm-1 while the right side equaled 95.54 Nm-1. The percent difference between these two values is 1.85%. In order to determine the harmonicity of each of the modes of vibration, the ve and vexe values were calculated. This was done by graphing ?G/v versus (v + 1) in Microsoft Excel. The ?G corresponds to the wavenumber of the overtone seen on the IR spectrum. ?G was then divided by v. The overtones corresponded to v=2 while the normal mode bands corresponded to ?=1. Graphs for both the ?1 mode and ?2 mode can be seen in Figure 6. Excel was then used to fit a trend line and produce a y = mx + b equation for the data. The slope of the equation was vexe and the intercept was ve. To determine the anharmonicity of the two modes, it was necessary to solve for xe. This was done using eq (4). The calculated values for xe in the ?1 mode was 1.0612 and for the ?3 mode was 0.07891. This means that the ?1 mode is more anharmonic than the ?3 mode. Conclusion For this lab, SO2 ­ was prepared and then studied via FTIR spectroscopy. The three modes of SO2 were identified on the IR spectra obtained. It was determined that the lowest energy of bending correlated to the lowest frequency peak. The second highest frequency peak was determined to be ?1 since the symmetric stretch is lower in energy than the asymmetric stretch (?3) which is the third highest frequency peak. The wavelengths determined from the IR spectra were used to calculate the constants k1 and k?/l3. It was determined from the numbers crunched from eq. (6) that the used method of determining the constants was an accurate method. Also, the anharmonicity of the modes ?1 and ?2 were calculated and compared. The graph of ?G/vversus (v + 1) produce an equation of y = mx + b which provided the values of xeve and v ­e. These values were then used to find xe, which described the anharmonicity of each mode. The ?1 mode was found to be more anharmonic due to its greater xe value whil e the ?3 was found to be more harmonic. Refrences What is Infrared Spectroscopy?. (n.d.). Mount Holyoke College, South Hadley, Massachusetts. Retrieved December 11, 2009, from http://www.mtholyoke.edu/~mlyount/MySites/ForensicSpectroscopy/WhatIsIR.html Nakamoto, Kazuo.Infrared and Raman Spectra of Inorganic and Coordination Compounds. Sixth Edition ed. Hoboken, NJ: Wiley Sons, Inc., 2009. Print. Hsu, S. (n.d.). Infrared Spectroscopy. prenhall.com. Retrieved December 6, 2009, from www.prenhall.com/settle/chapters/ch15.pdf Chem.msu.edu. (n.d.). Nature of Vibrational Spectroscopy. Retrieved November 30, 2009, from 2http://www.cem.msu.edu/~reusch/VirtualText/Spectrpy/InfraRed/irspec1.htm#ir1 The Simple Harmonic Oscillator. (n.d.). PAWS Personal Accessible Web Space Kettering University. Retrieved December 12, 2009, from http://paws.kettering.edu/~drussell/Demos/SHO/mass.html Atkins, P., Friedman, R., Paula, J. D. (2008). Rotational and Vibrational Spectra. Quanta, Matter and Change: A Molecular Appraoch to Physical Change (pp. 315-318). New York: W. H. Freeman. Normal mode Wikipedia, the free encyclopedia. (n.d.). Wikipedia, the free encyclopedia. Retrieved December 11, 2009, from http://en.wikipedia.org/wiki/Normal_mode Normal Mode (Harmonic) Analysis. (n.d.). Center for Molecular Modeling. Retrieved December 11, 2009, from http://cmm.cit.nih.gov/intro_simulation/node26.html Vibrational Spectroscopy. (n.d.). med.upenn.edu. Retrieved December 10, 2009, from www.med.upenn.edu/bmbgrad/Faculty/Master_List/Vanderkooi/course_notes/8.vibrational.pdf Sulfer Dioxide Vibration. (n.d.). d.umn.edu. Retrieved November 30, 2009, from www.d.umn.edu/~psiders/courses/chem4644/labinstructions/SO2spartan.pdf Infrared Spectroscopy of SO2. (n.d.). Spectroscopy and Structure Chem 4591. Retrieved November 30, 2009, from 3http://www.colorado.edu/chemistry/chem4581_91/SO2.pdf