Procedures in the Physical Sciences Essay Example | Topics and Well Written Essays - 1000 words - 1

Procedures in the Physical Sciences - Essay Example Science can be defined to be a systematic knowledge of the physical material contained on earth and even beyond. This knowledge is gained through experiments and observations. Identify three (3) specific challenges to making direct measurements in the fields of astronomy, chemistry, physics, or earth science. Describe how scientists have utilized indirect forms of measure to overcome these challenges. Challenges’ arise in the quest to gain this knowledge, for example, ; it becomes difficult sometimes to measure some elements and phenomena directly. Astronomy as a science has been around for quite a while. Astronomy is defined as a natural science that studies objects in the universe such as planets, stars galaxies, moons and even nebulae. This study involves the physics chemistry mathematics and evolution associated with this objects not excluding the phenomena that originates outside the atmosphere of the earth (Neugebauer,50). Astronomy provides an opportunity for armatures to contribute. These contributions are responsible for major developments in this field. This does not imply that all or most discoveries have been carried out. Challenges have risen from different angles, for instance one of the major problems they have encountered is finding the accurate distance of planets and stars from planet earth. However, with the advancements made in the field discoveries such as the use of luminosity and brightness of the astronomical objects to figure out their distance from the earth. Luminosity is a way of measuring the amount of brightness or energy emitted by any form of matter in the universe (Salpeter,10-30). This implies that light that travels to reach the earth can be measured. A hypothesis is made that stars shift off the main sequence after they burn up to about 10% of the hydrogen they contain and that there is an uniform creation of stars in the universe. Using this hypothesis and the luminosity function that has been observed, the rate that stare created as a function of stellar mass is then calculated. These calculations are deemed to assist to indirectly give the distance of a body from the earth. Another possible indirect way of doing this is a method called parallax, which involves triangulation. The major process involved is looking at the records of a star and then looking at it six months later. Astronomers can measure the distance of the angle of viewing .the combination of this work with the orbital diameter of the earth to sun and some involved produces the distance of that body. Objects in space are not the only challenge that astronomers face. Another challenge that astronomers have faced is the determination of the age of the universe. There is no direct way of measuring how long the universe has been around. For a while in the 90s the estimated age of the universe was ten billion years, however, age estimates for the stars and the galaxy were about 13 and 18 billion years respectively. This implies that s ome bodies in the universe are older than the universe itself. Better estimates of distance to the stars used in measuring age have reduced the disparities down to only a few billion years. Giving a consideration at dark energy into the cosmological model pushed the age estimates of the universe to the current value of 13.80 billion years. Choose two (2) of the most historically influential tools or techniques in the physical sciences. Explain how these techniques or tools work, and how they helped to advance our

TQM (total quality management) Essay Example | Topics and Well Written Essays - 2250 words

TQM (total quality management) - Essay Example These concerns, alongside various others, gave rise to the breed of management called Total Quality Management.      Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Total Quality Management (TQM) is a management system that aims to achieve the ultimate customer experience, whether meeting the expectation of the customers or going beyond what they anticipated (Dale, 1999). Dale (1999) expresses that in order achieve the goal of TQM, strong cooperation and involvement from the entirety of the company is needed. Thus, TQM requires active participation and synergy of all employees and focusing that synergy towards meeting the customers expectations and improving overall business processes. To attain improvement in the company, various researchers said that the key to improvement is constant upgrading and development (Goetsch & Davis, 1994). Management should not stop upgrading because all processes can still be improve and be better. Once they stop improving, they could be left behind by their competitors. Based on this discussion, TQM seems to be a management concept only. However, TQM also has a quantitative and more defin ed facet (Priporas and Psychogios, 2007). Priporas and Psychogios (2007) identified some of the quantitative aspect or measure of TQM, which includes Statistical Process Control, ISO 9000 standards, Pareto Analysis, Histograms, among others. On the other hand, the qualitative ideas that constitute TQM are overall workers’ participation; uninterrupted upgrading; incessant coaching; cooperative relation among employees; self-motivated employees; full dedication and support from high-tiered officers; independent and autonomous administration approach; consumer happiness; and business surrounding alterations (Priporas and Psychogios, 2007).   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  The main purpose of TQM is already well-known to everyone—customer satisfaction. However, to achieve this employee satisfaction should be fulfilled. Once the employee is satisfied and happy, it will be his innate response and goal to

Employment Law Essay Example | Topics and Well Written Essays - 1500 words

Employment Law - Essay Example The company should complete the ET3 form so that they can be able to defend the claimant’s claim of unfair dismissal then present it to the employment tribunal within 28days from the time it received the claimants form. The Employment tribunal is mandated to listen to cases that arise in employment, concerning the employer or the employees over their employment rights. If the company does not present its ET3 form to the employment tribunal default judgment is likely to be entered against them, which will then preclude the company from taking part in the proceedings. If the respondent presents their ET3 form to the tribunal, the tribunal has the power to order for disclosure of all the relevant materials pertaining to the case. The employment rights are enumerated under the employment rights act. The act provides under section 36 that an agreement will be deemed to be terminated upon the last day of the period that is agreed upon. The company gave Jack a notice of termination o f his employment and therefore by virtue of the notice his employment was terminated upon the lapse of the period given for termination. ... When it comes to poor performance and misconduct the employment rights act stipulates under sections 38(2) and (3) that an employer shall only terminate the employee’s contract of employment if there is no other cause of action that can be taken. Further, the act states that, when there is a charge made against the employee for misconduct or poor performance the employee should be given the chance to respond to such a charge. It is after the employee has responded to such a charge that the employer can then effect his termination. Gross misconduct is whereby the employee conducts himself so badly that his behaviour ruins the relationship between him and his employer that leads to immediate dismissal. In the above case, the company did not give the employee an opportunity to reply to a charge of misconduct or poor performance. The company raised the allegations of his misconduct and poor performance after his contract had already been terminated. We see that it is only after th e termination of Jack’s contract that the employer became aware of the fact that he had a drinking problem and discovered the empty bottles of alcohol in his desk. Apart from Jack coming to work in an unacceptable condition, all the reasons were brought up after the employee had left the premises of the company that proves that he was not given a chance to respond to any charge that was brought against him and he was neither given a reason for his termination. The company acted wisely in giving the employee a notice of termination instead of instant termination. The tribunal considers instant termination seriously; it looks to see if the employer’s reasons for termination were reasonable and if it was fair considering the circumstances of the case. This will mean

Commincation 2 page document Essay Example | Topics and Well Written Essays - 750 words

Commincation 2 page document - Essay Example The University Houston of Downtown (UHD) located at the heart of Houston is an institution offers excellent educational opportunities and has been recognized for its outstanding academic success over the years. The institution aims at preparing students to be responsible members of the society who are capable of thriving in multicultural workplaces. However, lack of efficient communication can affect the institutional excellence if some members lack adequate communication skills. Nevertheless, different ways have been analyzed to be efficient in minimizing obstacle at the UHD that prevent effective exchange of thoughts and ideas. Such communication barriers revolve around gender differences, cultural differences, biases and the immediate organizational environment (Thill, 2003). Physical distractions such as screening of chairs and any other form of external noise can be a main cause of disturbance that hinders effective communication between the teacher and the learner blocking effective communication. To overcome these disturbances, the leaders should ensure that there are minimal noises in the UHD learning environment especially closing all the doors and windows to avoid the students from being uneasy (Hargie & Dickson, 2009). When students experience external emotional distractions either from home or within the school, it becomes so difficult for a teacher to communicate efficiently with the student. Personal differences among the institutions management too can be a source of distraction in achieving the academic prosperity. Students that have destructive emotions are always filled with anxiety, fear and anger and will always be absent minded when something is being explained to them. This greatly impacts communication process. To help overcome this type of barrier leaders should try to find the problems that the students are going through and

Discuss the causes and consequences of infertility for individuals, Essay

Discuss the causes and consequences of infertility for individuals, families and wider society - Essay Example In addition, infertility can also entail the inability to carry a pregnancy to full term leading to miscarriages (Perkins & Jackie, 2011, p.1). Infertility does not only affect the couple trying to have children but it also impacts greatly on their families and the wider society, especially in the contemporary western culture (Peters, Jackson & Rudge, 2011, p.130). Nevertheless, this topic remains a taboo issue that people do not want to talk about yet it interferes with the most fundamental human activity of building a family. Infertility is a very serious reproductive health problem that may result from a number of preventable and non-preventable conditions related to both males and females and it may have far-reaching consequences on the individuals trying to conceive, their families and the wider society. Infertility has numerous causes. Initially, people thought that only women were infertile but the truth is males-factor conditions are responsible for half of all the couples who are infertile. The non-preventable conditions that may cause infertility include various genetic, immunological, hormonal and anatomical problems that are responsible for preventing successful pregnancies (Solinger, 2013, p.100). The prevalence of non-preventable conditions is the same within and across populations and is responsible for causing infertility in five percent of all infertile couples. Most of the times infertility is due to preventable conditions and this is the reason why the variations in infertility rates are significant in any given population due to the preventable conditions being more or less prevalent in a given population. The preventable infertility causes are due to occupational or environmental factors and various infections (Kirch, 2009, p.782). There are some sexually transmitted infections (STIs) related to infertility such as gonorrhea (Fauser & Devroey, 2011). Since these symptoms

Personality Attributes Essay Example for Free

Personality Attributes Essay Locus of control  is a theory in  personality psychology  referring to the extent to which individuals believe that they can control events that affect them. Understanding of the concept was developed by  Julian B. Rotter  in 1954, and has since become an aspect of personality studies. A persons locus (Latin for place or location) is conceptualised as either internal (the person believes they can control their life) or external (meaning they believe that their decisions and life are controlled by environmental factors which they cannot influence). Individuals with a high internal locus of control believe that events in their life derive primarily from their own actions; for example, if a person with an internal locus of control does not perform as well as they wanted to on a test, they would blame it on lack of preparedness on their part. If they performed well on a test, they would attribute this to ability to study. [1]. In the test-performance example, if a person with a high external locus of control does poorly on a test, they might attribute this to the difficulty of the test questions. If they performed well on a test, they might think the teacher was lenient or that they were lucky. [1] Those with a high internal locus of control exhibit better control of their behavior[citation needed], tend to be more politically involved[citation needed]  and are more likely to attempt to influence others than are those with an external locus of control. [citation needed]  They also assign greater likelihood to their efforts being successful, and more actively seek information concerning their situation. [citation needed] Locus of control has generated much research in a variety of areas in psychology. The construct is applicable to fields such as educational psychology, health psychology or clinical psychology. There will probably continue to be debate about whether specific or more global measures of locus of control will prove to be more useful. Careful distinctions should also be made between locus of control (a concept linked with expectancies about the future) and attributional style (a concept linked with explanations for past outcomes), or between locus of control and concepts such as self-efficacy. The importance of locus of control as a topic in psychology is likely to remain quite central for many years. Locus of control has also been included as one of four dimensions of  core self-evaluations  Ã¢â‚¬â€œ ones fundamental appraisal of oneself – along with  neuroticism,  self-efficacy, and  self-esteem. [2]  The concept of core self-evaluations was first examined by Judge, Locke, and Durham (1997), and since has proven to have the ability to predict several work outcomes, specifically, job satisfaction and job performance 2. Machiavelllianism: Machiavellianism is also a term that some social and personality  psychologists  use to describe a persons tendency to be emotionally cool and detached, and thus more able to detach from conventional morality and to  deceive  and  manipulate  others. In the 1960s, Richard Christie and Florence L. Geis developed a test for measuring a persons level of Machiavellianism. Measured on the Mach-IV scale, males are on average slightly more Machiavellian than females  [6]  [8]. Motivation: A 1992 review described Machiavellian motivation as related to cold selfishness and pure instrumentality, and those high on the trait were assumed to pursue their motives (e. g. sex, achievement, sociality) in duplicitous ways. More recent research on the motivations of high Machs compared to low Machs found that they gave high priority to money, power, and competition and relatively low priority to community building, self-love, and family concerns. High Machs admitted to focusing on unmitigated achievement and winning at any cost. Due to their skill at interpersonal manipulation, there has often been an assumption that high Machs possess superior intelligence, or ability to understand other people in social situations. However, research has firmly established that Machiavellianism is unrelated to  IQ. Furthermore, studies on  emotional intelligence  have found that high Machiavellianism actually tends to be associated with low emotional intelligence as assessed by both performance and questionnaire measures. Both empathy and emotion recognition have been shown to have negative correlations with Machiavellianism. Additionally, research has shown that Machiavellianism is unrelated to a more advanced theory of mind, that is, the ability to anticipate what others are thinking in social situations. If high Machs actually are skilled at manipulating others this appears to be unrelated to any special cognitive abilities as such Self esteem: Self-esteem  is a term in  psychology  to reflect a  persons overall evaluation or appraisal of his or her own worth. Conversely, low self-monitors do not participate, to the same degree, in expressive control and do not share similar concern for situational appropriateness. Low self-monitors tend to exhibit expressive controls congruent with their own internal states; i. e. beliefs,  attitudes, and  dispositions  regardless of social circumstance. Low self-monitors are often less observant of social context and consider expressing a self-presentation dissimilar from their internal states as a falsehood and undesirable.

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