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.
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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 “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. Additionally, 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.