ACETONE DIFFUSION THROUGH AIR

Contents

Introduction3 Theory 4-5 Experimental Apparatus 6 Experimental Method7 Results8-9 Discussion 10 Conclusions11 References 12 List of Symbols 13 Appendices14

Introduction

A molecular diffusion experiment was set up, with several aims. These were to illustrate the theory of mass transfer, to calculate the diffusivity of acetone through air, to examine the influence of temperature on the diffusivity and finally to compare the results obtained with those obtained with different experimental methods. The flow of mass in a liquid or gas generally involves the flow of fluid through a material; solids however can support shear stresses and hence mass is transferred by diffusion. Diffusion can be described as either diffusion in a uniform concentration or diffusion in a non-uniform concentration. Uniform concentration obeys Ficks first law, where the constant of proportionality is known as the diffusion coefficient. Ficks first law applies to a steady state flux in a uniform concentration gradient. Diffusion in a non-uniform concentration gradient obeys Ficks second law of diffusion, with the assumption that diffusivity is independent of the concentration.

Theory

The flux of acetone molecules can be calculated from Ficks Law through a stagnant layer of air molecules which are non-diffusing, this gives the equation:

In the case of this experiment, acetone is diffusing through the air, however air is not diffusing back into the acetone. The cross-sectional area through which the diffusion occurs is constant along the length of the tube throughout the experiment. This allows the flux to be calculated. The air passing over the top of the tube has no acetone, hence is zero. can be calculated for any given water temperature, using vapour pressure data for acetone from this the rate of diffusion is also calculated from the rate of evaporation, as shown in Equation 2:

Equating and integrating these two equations give Equation 3 as follows:

From this, the diffusivity of acetone in air can be found by plotting a graph of against and taking the gradient from the straight lines plotted. With this information, the relationship between temperature and diffusivity in the gas state can be seen.

Fuler, et al developed the relationship between the total pressure, absolute temperature and diffusivity. This is shown below:

From this, it can be seen that the diffusivity should be proportional to the absolute temperature raised to the power of 1.75.

Experimental Apparatus

The apparatus was set up as follows:

Figure 1: Schematic of experimental set up

Figure 2: Photograph of experimental set upExperimental Method

The ambient pressure of the room was taken prior to the experiment commencing. The air pump was set up to initiate a gentle air flow through the T-piece. The water bath was filled with water at the required temperature for run 1, this was then followed by the test tube being filled to the highest graduation with acetone, so as to match the level of water in the bath. The T-piece was then re-attached and the experiment could commence. The graduation level of liquid meniscus was read every 2 minutes for 20 minutes. Once this was completed, the same procedure was carried out with differing temperatures for different runs, with the acetone being replenished each time.

Results

Run123

Water Bath Temperature( Deg C)354550

Time (Mins)Distance below top of tube (m)

00.0450.0300.050

20.0500.0350.055

40.0550.0360.057

60.0550.0380.057

80.0560.0390.058

100.0570.0400.059

120.0580.0450.060

140.0580.0480.061

160.0580.0500.061

180.0580.0510.062

200.0590.0520.064

(zf^2 - zo^2)

00.0000.0000.000

20.0000.0000.001

40.0010.0000.001

60.0010.0010.001

80.0010.0010.001

100.0010.0010.001

120.0010.0010.001

140.0010.0010.001

160.0010.0020.001

180.0010.0020.001

200.0010.0020.002

Gradient of Plot9.00E-056.00E-056.00E-052

Absolute Temperature (K)308318323

Total System Pressure (mmHg)750.81750.81750.81

Vapour pressure of acetone at liquid surface (mmHg)322.62509.55611.67

Diffusivity of Acetone in air (m^2/s)2.59E-041.34E-048.89E-05

Discussion

The aim of this experiment was to calculate the diffusivity of acetone through air, to examine the influence of temperature on the diffusivity and finally to compare the results obtained with those obtained with different experimental methods.The results obtained for the diffusivity of acetone in air experimentally, by using the gradient of the graph, are very close to those obtained by calculation using the equations mentioned previously. This would suggest the experiment was a success. As well as this, the influence on temperature on the diffusivity has been proven as shown in the results the results were as expected in the hypothesis. Finally, the results obtained experimentally for the diffusivity of acetone in air, are again very close to those obtained experimentally using other methods. This again would suggest the experiment was a success.Despite the apparent success of the experiment, there were several sources of error in this experiment. Due to the practical set up of the test tube in the water bath, it was very difficult to measure the meniscus level accurately if this experiment were to be repeated, a graduated test tube would be used as this would ensure greater accuracy in measuring the meniscus level. Furthermore, the assumption was made that the temperature remained constant whilst the experiment was being carried out this, however, is unlikely to be true if this experiment were to be repeated a method of ensuring the temperature was kept constant would be explored.

Conclusion

To conclude, this experiment can be considered a success for the aforementioned reasons. The diffusivity determined experimentally was very similar to that obtained by calculation using different methods. As well as this the effect of temperature on diffusivity was proven to be as hypothesised. The slight difference in between experimental and calculation can partly be attributed to the sources of error mentioned previously the inaccuracy in measuring due to the equipment used, as well as the fact that the temperature of the water bath did not remain constant throughout the experiment. If this experiment were to be repeated a graduated test tube would be used and a method of keeping the water temperature constant would be explored, in order to ensure greater accuracy.

References

Incropera, F.P., D.P. DeWitt (1996), Fundamentals of Heat and Mass Transfer, John Wiley & Sons, Pages 460, 582-612. (1996)Sinnott, R. and Towler, G. (2010). Coulson and Richardson's Chemical engineering. Amsterdam: Elsevier. Pages 634-650Maloney, J. (2008). Perry's chemical engineers' handbook. [New York]: McGraw-Hill.

List of Symbols

Appendices

Appendix 1 Sample CalculationsAll calculations are based on results from Run 1

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