Lab report Essay Example for Free

Lab report Essay A molecular diffusion experiment of acetone-air (redundant w/ last sentence. . concise)was conducted with the goal of determining the diffusion coefficient of acetone into air. For this experiment, acetone was placed in a test tub 3mm OD, 2mm ID . . (is that correct? ) NMR tube? e and was allowed to diffuse into non-diffusing air that was passed over the test tube. The air that passed over the tube was from natural circulation in the room and no air was forced over the top of the test tube. The diffusion occurred over a period of approximately eight hours, with readings taken each hour. After analyzing the data collected from the performance of this experiment, tThe diffusion coefficient was calculated to be 0. 098 + 0. 02 cm2/s at T = ?. After completing our calculations, oOur results were then compared using the Chapman-Enskog equation as well as the Fuller, Schettler, and Giddings method. The diffusion coefficient calculated by the Chapman-Enskog was 0. 990 + 0. 001 cm2/s and the result of the Fuller, Schettler, and Giddings method was 0. 104 + . 002 cm2/s. The literature value found in Perry’s Chemical Engineer’s Handbook was 0. 125 + 0. 00 cm2/s. (at T = ?. . . or extrapolated from? ) The agreement of our method with the other methods available for calculating the diffusion coefficient was very good (how good is â€Å"very† good. .. significant discrepencies or not? ), and also agreed well with the literature value found. This led to a conclusion that this method of determining the diffusion coefficient of acetone into air can be aconsidered a reasonably reliable method. BACKGROUND Molecular diffusion is the transfer or movement of individual molecules through a fluid by random molecular movements (Geankoplis 412, year of publication). In the diffusion process, the molecules of interest flow from regions of high concentration to low concentration. Molecular diffusion can occur in both directions with the system. In the case of the diffusion tube experiment, however, acetone diffuses through non-diffusing air, which is passed over the top of the test tube containing the acetone. The air is allowed into the test tube, but does not diffuse into the acetone. Molecular diffusion of gases has been studied for many years. Molecular diffusion is a mass transport process Motivation for its study comes from the fact that chemical separation processes such as distillation, drying, ion exchange systems as well as many other processes depend on molecular diffusion (Kirk-Othmer Vol 8, p 149(check format)). EXPERIMENTAL METHODS For the performance of this experiment, a small test tube was filled approximately a third full of acetoneBe specific. . how small, starting height, diam, etc. This test tube was then vertically placed in a 10mL graduated cylinder which contained small beads. The purpose of the beads was to ensure that the test tube remained vertical. This assembly was then placed on a digital scale. The amount of air movement provided by the ventilation system was assumed to be adequate so as to ensure that the concentration of the acetone at the top of the tube was zero. An initial acetone level in the test tube was taken, as well as the mass of the assembly and the temperature of the area surrounding the assembly. After this initial data was taken, the area temperature and mass of the assembly were taken approximately every hour for the next eight hours. The final level of the acetone in the test tube was taken when the final temperature and mass reading were taken. DISCUSSION OF RESULTS From the data collected from the experiment, the diffusion coefficient was calculated using equation 6. 2-26 from Geankoplis: (Equation 1) As the z value was only recorded at the beginning and the end of the experiment, the intermediate values of z had to be calculated. The following equation was used for the calculation of the intermediate z values: (Equation 2) Thus, all values but DAB were known and could be plotted versus time to obtain a linear plot. By rearranging equation 1, it can be seen that the slope of this plot will be equal to 1/ DAB : (Equation 1. 1) The initial plot of data which includes all points is shown below in Figure 1. This plot contains all points and has an R2 value of 0. 9478. From this plot the molecular diffusivity coefficient was determined to be 0. 108 + 0. 022 cm2/s. Figure 1: First plot of data in Equation 1 The second point in the data (t=2700s) showed no diffusion occurred in the first 45 minutes, which seems unlikely (yes, good- sensitivity of balance, etc). If this point is taken as erroneous, the R2 value goes up to 0. 9639 (more important here will be the confidence interval on the slop. . . get that from Tools- Data Analyis-Regression menu in Excel or else in Polymath or TableCureve, etc) and the molecular diffusivity calculates out to be 0. 098 + 0. 021 cm2/s. The plot of the experimental data excluding the second point is presented below in Figure 2. Figure 2: Second plot of data in Equation 1. . forcing through zero point is good. . . looks to me like first FOUR points would give a lower Dab then the last 4. Problems with next 3 that lie below line? Anytihing suspicious happening here? To determine the time it takes for the system to reach steady state, the following equation can be used to calculate the fraction of steady state the system is at: (Equation 3) By plotting the value of ((NA)t/(NA)t=? ) versus time, the curve in Figure 3 was generated which demonstrates the systems approach to steady state. Wow, great! Cite source.  (still wonder about SST conditions of 1st 4 pts though. . . Figure 3: Fraction of steady state versus time From this plot, it could be said that the system achieves steady state in 115 minutes; however, there is strong evidence this may not be accurate. As mentioned earlier, the second point may be erroneous. This would change the path of the curve. In addition, data was not collected at a high enough frequency for this curve to be highly accurate at predicting the time to steady state. If in fact the second point is erroneous, the system could have come to steady state well before 115 minutes. This time of 115 minutes at best, could be the upper bound (or lower bound according to Whitaker’s criteria in his article (handout). . . not sure!! for the time it takes for the system to come to steady state. The scatter in the data can be attributed to various factors in the experiment. The scatter could be attributed to the changes in temperature, as the temperature did fluctuate slightly through the duration of the experiment – Good!. At what time did it stabilize?. The change in temperature would cause a change in the partial pressure of the acetone leading to further deviations. In addition, there was no measure of airflow past the tube. Changes in the airflow could also have contributed to the scatter as it could effect the concentration of the acetone at the top of the test tube (Good! ). The diffusion coefficient was also calculated using the Chapman Enskog equation, (Equation 4) and the Fuller, Schettler and Giddings method. (Equation 5) A literature value was also found for acetone at K(check Perrys), which was corrected to our experimental temperature using the correlation (Equation 6) The values obtained with these methods as well as those from the experimental data are presented in Table 2. Table 1: Values of molecular diffusivity coefficients found. ** ** A very good way to show this graphically in Excel would be to use a bar graph showing the values of Dab as height of a bar by method used, and error bars to easily demonstrate any overlap of uncertainty, discrepancy, etc. Example: The Chapman Enskog method is accurate within 8% and the Fuller Schettler and Giddings value has a lower accuracy than the Chapman Enskog (Geankoplis 425). The Chapman Enskog value is less than 1% different than the experimental value and the Fuller Schettler and Giddings value only about 6% different. From this analysis, it seems these equations predicted the experimental value very well. These calculated values are about 20% lower than the literature value. This variance may come from the inconsistent temperature in the room or from pressure fluctuations in the room caused perhaps by the starting and stopping of the HVAC systems. For the derivation of Equation 1, several assumptions are made. Beginning with the general equation (Geankoplis 6.  2-14): (Equation 7) One assumption was that because the case examined was a diffusing A (acetone) into non-diffusing B (air), the diffusion flux of air into the acetone (NB) was equal to zero. Another assumption made was that since the total pressure was low, the acetone gas diffusing into air was an ideal gas. This allowed for the term c to be replaced with its ideal gas equivalent, P/RT. Add itionally, the air passing over the test tube was assumed to contain no water vapor. An average air velocity that was uniform was passing over the acetone containing test tube was also assumed. There are non-idealities that exist in the molecular diffusion of acetone into air. Some of these non-idealities are corrected for in the journal from Lee and Wilke. Acetone displays surface tension effects which, instead of having a perfectly horizontal liquid surface, give the liquid acetone a slightly downward curved liquid level. Because of this curvature, the actual diffusion path length that the acetone travels is smaller than what the diffusion length would appear to be based on center liquid level or calculated liquid volume (Lee 2384). Along with a non ideal liquid surface, the air passing over the open end of the tube may cause some turbulence to exist in the top portion of the tube. With its existence, the turbulent area of the tube will cause a length to exist inside the tube where the concentration of acetone is zero. With the presence of this acetone vapor-free region, the diffusion length is again shorter than it would appear to be. To account for the non-idealities in the diffusion process, Lee and Wilke do not use the apparent diffusion path. Instead, they use an effective average diffusion path which they give by: (Equation 8) Where x is the effective average diffusion path, ? xs is the length of the curvature of the non-ideal liquid to account for the surface tension forces, ? xe is the length of the tube where the acetone vapor-free region exists due to turbulence that exists from the passage of the air, and ? x ­ is the sum of ? xs and ? xe (Lee 2384). When this is substituted back into the diffusion equation, it becomes the following: (Equation 9) Where Da is the apparent diffusion coefficient and D is the true diffusion coefficient based on the true diffusion path (Lee 2384). The way our experiment was setup, the driving force for the air across the test tube was natural air flow and did not employ forced air flow. Because of this, the length of the tube where the turbulence existed in the Lee and Wilke journal would most likely not have been present in our experiment. Also, the initial liquid acetone level selected in our experiment was such that the length of the curvature due to the surface tension forces on the acetone would have been negligible when compared to the apparent diffusion length of the tube. The initial height of the liquid in the tube for this experiment was chosen wisely. The reason for this is that with the initial level that was chosen, a sufficiently long diffusion path existed such that the non-idealities that were accounted for in the Lee and Wilke journal entry would have had a very insignificant impact on the results of our experiment. CONCLUSIONS AND RECOMMENDATIONS From the data collected an analyzed, it has been determined that the experimental procedure used here can determine the molecular diffusivity coefficient with some level of accuracy. For future experiments, some form of air flow regulation should be investigated. Something as simple as a room fan could be placed next to the scale to ensure a more constant air flow. Another increase in accuracy could be achieved by regulating the temperature with more consistency. If the experiment could be performed in a large insulated room, the temperature may not vary as much. Good job on Discussion, Conclusions, etc. . . to improve maybe expand to relate what YOU think are the main ‘uncertaintys’ that caused problems in your particular case and show evidence to support.

judahs Triumph :: essays research papers

Judah’s Triumph   Ã‚  Ã‚  Ã‚  Ã‚     Ã‚  Ã‚  Ã‚  Ã‚  William Wyler is the director of the 1959 award-winning version of Ben-Hur. The film is an adaptation of General Lew Wallace’s novel. Karl Tunberg is credited with the actual screenplay. Sam Zimbalist was the original producer of Ben-Hur, but he died before the completion of filming. The two main characters are Judah Ben-Hur (Charlton Heston) and Messala (Stephen Boyd). Another important person involved in this film is Miklos Rozsa. He composed the award-winning musical score in a total of eight weeks. Ben-Hur was released in New York City on November 18, 1959, and in Los Angeles on November 24, 1959. It was re-released in the USA in 1969. This film has grossed $70 million in the United States alone. As for location, this film was shot in entirely in Italy. Ben-Hur is one of two films to win eleven Academy Awards, the other movie being Titanic. The awards include best leading and supporting actors, best cinematography, best director, best music, best sound, and more. This film has some interesting behind the scenes trivia, most of which is in connection to the stadium or the chariot racing. According to The Internet Movie Database the design of the stadium was a controversy. â€Å"MGM asked an archaeologist what the stadium in Jerusalem had looked like. ‘Roman,’ came the reply. A second archaeologist was asked. ‘It was in a Phoenician style,’ he said. A third archaeologist was consulted, who said: ‘Stadium? I was not aware that Jerusalem had one!’ MGM engineers eventually sat down and carefully studied Ben-Hur (1926), and based their design on that.† Another intriguing fact is during the chariot race Charlton Heston’s stunt double was flipped out of the chariot. The stunt man hung on to the reigns and climbed back into the chariot. That blooper was left in the film to add more action. Marketing for this film was almost as big as the movie itself. Hundreds of toys were created, as well as Ã¢â‚¬Ë œBen-his’ and ‘Ben-hers’ bathroom towels. The Internet Movie Database also points out another big goof in editing. â€Å"Nine chariots start the chariot race. After the first crash, there appear still to be nine chariots in the race. After the third crash, six are shown, but as Ben Hur passes to catch up, clearly there [are] a total of seven in the race. After five have crashed, five are left. Messala is the sixth chariot to crash, but Ben Hur and three others finish the race.

Provide two reasons why Medicaid violations do not generally receive media attention Essay

One of the most frequent crimes of the affluent and the high-class of the society is Medicaid fraud. These frauds can be committed by several parties including the recipients and the providers. Medicaid is a government program that utilizes the taxpayer’s money to provide healthcare to the low income groups of the society. It is basically setup to help the weaker sections of the society including individuals above the age of 65, the disabled, the medically compromised and the low-income groups. The nations would be happy if the money is spending to help people in need, but frequently several providers and recipients indulge in fraud and abuse of the funds set aside under Medicaid. Some of the abuses committed by recipients include forging prescription, giving the medical card to another party, using several cards, duplicating or consuming excessive healthcare services, and selling the items received under Medicaid to others. Some of the abuses that can be committed by the providers include providing false bills, duplicating bills, providing unwanted medical care, doing unnecessary tests, billing in excess, compromising the quality of care under Medicaid services, and including the names of others in the bills (NY State, 2006). One of the reasons why Medicaid violations are not given great amount of media attention is because these crimes are usually committed by affluent. These crimes are often great amount of protection and secrecy, so as to gain for profit. In the US, it is estimated that Medicaid fraud cost the nation about forty billion dollars in the year 1993. Usually, a certain person rather than an organization would be involved in committing a Medicaid fraud. The White collar staffs who commit these crimes frequently think that they are above the law. They feel that committing such crimes is justified as it is anyway a part of the system. They would go to any extent to cover their crimes. The media would not like to get involved in covering such events, as they feel that they would later be harassed by the White collared staff. Besides, they also feel that they would not be getting any kind of requests they may have, as the white collared staff would be using their powers to avenge for the media attention given. It is found that the business-minded white collared staffs are more frequently involved in committing Medicaid frauds rather than the professional staff (Cullen, 2008). The media feels that the people who are victims by the crimes of Medicaid fraud are usually not the class who would be customers to their services. They may find that covering such events would not be beneficial to them in anyway, and would instead get them in bad looks with the high-class. The poor, elders and the disabled are less likely to be customers of the media services. They would also not stand up to fight their rights. The beneficiaries of Medicaid frequently are not aware of their rights. They may be often abused or neglected by the healthcare organization which may include the white collared staff. Frequently, the person getting abused may be physically and mentally helpless and would depend on the care provider for help. However, the care giver would be providing low quality healthcare and instead use the funds other Medicaid for other purposes (including gaining profits). Medicaid fraud is a criminal offence and involves abusing taxpayer’s money. It has been set aside for helping the weaker sections of the society, but instead these funds are ending up in the hands of the rich, thus making the rich richer and the poor poorer. At any cost, the media would have to change their policy of reporting cases of Medicaid fraud to the public.

What Are The Four Functions Of An Economic System

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