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Ryerson University Department of Chemical Engineering CHE 315 Lab Report Fall …2014…… Experiment No: 8 Experiment Title: Measurement of Gaseous Diffusion Coefficient Group No: F Section No: 02 Day of the Experiment: 29/10/2015 Professor: Dr. Mehrab Mehrvar Group Members: 1. Date Experiment Performed: 29/10/2014 Date Report Submitted: 05/11/2014 500062520065900Marking Scheme: Percentage Front Pages (Cover Page, Table of Contents, List of Figures, List of Tables,)... /3 Introduction (Maximum One Page) …………………………………………….. /5 Theoretical Background (Not more than 2 Pages) ………………………………. /7 Experimental Procedure (Schematic Diagram of the Experimental Set-UP, Any Deviation from the Manual …) ………………………………………………………………… /7 Results and Discussion ………………………………………………………… /40 Error Analysis ……………………………………………………………………. /10 Conclusions and Recommendations ……………………………………………... /10 References …………………………………………………………………..…… /3 Appendices (Raw Data*, Sample Calculations*, Any Repetitive Data,) ……… /10* General Appearance including Grammar and Spelling …………………………… /5 2857509017000 TOTAL …….………………….……………………………….………………..… /100 Note 1: The original data sheets must be included as an appendix in the laboratory report. If a report does not contain the signed raw data sheet, it results in automatic deduction of 30 marks from total mark for that report. Note 2: Any report that does not contain sample calculations will result in the deduction of 20 marks of the total marks for that report. Table of Contents List of Figures.................................................................................................................. 3 List of Tables....................................................................................................................3 Introduction..................................................................................................................... 4 Theoretical background.................................................................................................5-6 Experimental procedure................................................................................................. 7 . Results and Discussion.................................................................................................8-10 Error analysis.................................................................................................................11 . Conclusion and Recommendation.................................................................................12 Appendix.....................................................................................................................13-18 References...................................................................................................................19 List of figures: Figure 1: An illustration diagram of Diffusion of Acetone in Air Figure 2: Determine the diffusivity of acetone in air at 40oC and 1 atm pressure List of Tables: Table 1: The change in liquid level with respect to the time in (min) Table2: Antoine Equation Constants at temperature range (-12.9oC to 55.3oC) Table 3: Interpolation of acetone density Introduction Diffusivity is an essential consideration in most engineering industry application designs. Accordingly, the objective of this experiment was to determine the diffusivity of the vapour of acetone liquid in air though utilizing mass transfer theory. Also, diffusivity is a crucial factor in which fluid flow and mass transfer operations depend partially on this parameter especially in engineering plant design. In this laboratory experiment, Armfield Gaseous Diffusion Coefficient Apparatus was used to deliver data in which you can calculate the diffusivity of acetone in air to a reasonable degree of accuracy. The apparatus consisted of a glass capillary tube, which was placed, in a water bath at a constant temperature of 40oC. The capillary tube contains a small amount of volatile liquid which was acetone and at the top of the capillary tube, component B is present which in this experiment was air. A horizontal glass tube is attached to the upper end of the capillary tube and an air pump is used to draw air through this horizontal tube. This arrangement creates a partial pressure difference in the capillary tube between the gaseous acetone and the air. Moreover, the water bath was controlled at steady temperature of 40oC in order to increase the diffusion of acetone in air. Furthermore, a microscope with a sliding vernier is placed along the water bath and is used to measure the level of the meniscus of the capillary tube as the acetone diffuses in air. Thus, from the graph of the change of acetone liquid level with the slope and intercept was found to be-0.4744 min/mm2, 23.411min/mm respectively. The intercept was used to calculate the diffusivity coefficient. Experimentally the diffusivity was 0.1525 cm2/s, however theoretically it was 0.066 cm2/s which resulted in an error of 57%. Theoretical and Background The diffusion of vapour A from a volatile liquid into another gas B can be conveniently studied by confining a small sample of the liquid in a narrow vertical tube and observing its rate of evaporation into a stream of gas B passed across the top of the tube. Commonly, component B is air and the acetone vapour component is defined as A. The apparatus consists basically of a glass capillary tube placed in a transparent-sided temperature controlled water bath at 40oC. A horizontal glass tube is fixed to the upper end of the capillary tube and air was blown through it by a small air pump included within the unit. This arrangement had allowed partial pressure difference maintained within the capillary tube between the evaporating liquid surfaces and the flowing air stream. A travelling microscope, with a sliding vernier scale, is mounted on a rigid stand alongside the thermostatic bath and is used to measure the decreasing rate of the solvent or air meniscus within the capillary. The figure below is an illustration of the capillary tube in the Armfield Gaseous Diffusion Coefficient Apparatus. Lo represents the empty space in the capillary tube above the acetone and L represents the distance from the top of the capillary tube to the acetone level in the tube. 122872529464000Figure 1: An illustration diagram of Diffusion of Acetone in Air 2275205135001000As it shown in figure 1 the Armfield Gaseous Diffusion Coefficient Apparatus can be utilized to get a fairly accurate value of the Diffusion Coefficient. If the drop in liquid A (Acetone) over a time period t to t0 is small especially compared to the total diffusion path, and the time interval (t to t0) is considered a large time interval than the molar flux in the gas phase can be found using this formula: Where: yA1 is the mole fraction at L = 0 and YA2 is the mole fraction of A at the gas liquid interface. Molar Flux is related to the amount of A leaving the liquid by: is the Molar density of A in the liquid phase If the above two equations are combined = And integrated from t=0 to t ad z=L0 to z=L and Solve for t: Rearrange and linearize the equation to the form of the equation of a line (y=mx+b): If is plotted against the diffusion coefficient can be found from the slope of the line. Experimental Procedure To begin the experimental procedure, first started with filling up the capillary tube with Acetone to the depth was about 36 mm. The bath tub was already filled up with approximately 3.8L of distilled water. Next, the capillary tube was inserted through the rubber ring, so that the tube rests on the on the top of the nut. Gently screwed the tube using fingers as a T shaped normal to the microscope, then adjusted the object length to about 20-30 mm from the tank. Then, the vertical height of the microscope was adjusted until the capillary tube started to be visible, and defined the meniscus of Acetone inside the tube as well. Then, the Vernier scale aligned with a suitable graduation on the fixed scale. Next step, the air pump was switched on, and the temperature controlled water bath as well with adjusted it to 40 degree Celsius. After obtaining a constant temperature, recorded the change of the Acetone level inside the tube every ten minutes for two hours. Next, turned off the air pump and the water bath temperature, waited for the system to cool for about ten minutes, and then cleaned up the capillary tube with distilled water and placed it back. Lastly, the power was disconnected from the main power supply. Result and Discussion The objective of this experiment was to determine the diffusion coefficient of acetone in air by applying mass transfer fundamental and utilizing the Armfield apparatus. The change in acetone liquid level has been calculated as shown in table 1 below: Table 1: The change in liquid level with respect to the time in (min) Time (min) Acetone level inside the Capillary (mm) Liquid Level (L-Lo) (mm) t/(L-Lo) (min/mm) 0 22.0 0.0 0.00 10 22.3 0.3 33.33 15 22.5 0.5 30.00 20 22.7 0.7 28.57 25 22.8 0.8 31.25 30 23.3 1.3 23.08 35 23.7 1.7 20.59 40 24.0 2.0 20.00 45 24.2 2.2 20.45 50 24.5 2.5 20.00 55 24.7 2.7 20.37 60 24.8 2.8 21.43 65 24.9 2.9 22.41 70 25.0 3.0 23.33 75 25.3 3.3 22.73 80 25.5 3.5 22.86 85 25.8 3.8 22.37 90 26.0 4.0 22.50 95 26.3 4.3 22.09 100 26.8 4.8 20.83 105 27.1 5.1 20.59 110 27.5 5.5 20.00 115 27.8 5.8 19.83 120 27.9 5.9 20.34 The liquid level and the diffusivity was related by the linear equation: t(L-Lo)=?A, L2 MADABCB, lmCA CTL-Lo+ ?A, L CB, lmMADAB CACT Lo Where the slope is?A, L2 MADABCB, lmCA CT, and the intercept is?A, L CB, lmMADAB CACTLo. This linear relation can be plotted using liquid Level (L-Lo) (mm) vs. t/ (L-Lo) (min/mm), the slope was found to be -0.4744 min/mm2 and the intercept was 23.411min/mm as shown in Figure 2. The negative slope of the linear relation indicates the decrease of the acetone concentration due to diffusivity. Using the intercept obtained from the graph diffusivity can be calculated using this relation ?A, L CB, lmMADAB CACT as shown in the calculation part. Figure 2: Determine the diffusivity of acetone in air at 40oC and 1 atm pressure Although the diffusivity depends on the temperature, the temperature was maintained constant throughout the experiment. The diffusivity increases at high temperature and decrease at low temperature and this is due to the high kinetic energy of the molecules at the high temperature. Higher kinetic energy means higher movement of the molecules and a faster spread of the acetone particles in air which result in a high diffusion rate. Therefore the diffusivity of acetone in air at room temperature is less that the diffusivity at 40C°. Also, the high kinetic energy of the molecules will result in a breakage of the bond between the acetone’s particles which will decrease the concentration of the acetone and lead to a higher diffusion coefficient, The diffusivity of acetone in air was calculated to be 0.1525 cm2S at 40 °C, which is an optimal temperature for acetone since the acetone boils at a temperature of 56.6 °C, however at the same time diffusivity is better at high temperature. The literature value of diffusivity is 0.066 cm2S at 40 C° which varies from the experimental value due to some human and experimental sources of error. Error Analysis The percentage error was calculated to be 57%, showed in the results and calculation part of this experiment. The error has been found due to some of sources might affected the final value. First error that has been noticed was the temperature reading. The temperature should be constant throughout the experiment; however the temperature of the water bath was between 39.9°C and 40.0°C. This slight variation in temperature might have affected the rate of mass transfer and the diffusion coefficient. And since the temperature have a large effect on diffusivity. The second important source of error need to be considered is human error, which is reading error since the measurement was not digital, it was hard to read the exact height level of the meniscus. Also, the lens wasn’t clear enough to see the level accurately. Furthermore, the degree of precision could be also consider as source of error since the smallest precision scale was 0.1 mm, which wasn’t enough to be more precise getting the values. Last but not least source of error could be lack of calibration of the apparatus. There weren’t any calibrations signs on the apparatus that could be used as a calibration reference. The temperature controller and the air pump might not be calibrated, which might have big affect on the last reading. Therefore, all the sources of errors discussed above can affect the final value. Conclusion and recommendation In many chemical engineering application, diffusivity is one of the most important parameter that need to be considered in chemical reactor design. Thus, diffusivity of acetone in air was measured in this experiment. Diffusion of the acetone is the movement of the acetone’s particles from the high concentration to low concentration which indicated that the concentration gradient is the driving force in the measurement of mass diffusivity. Mass transfer was applied in this experiment for the diffusion of the air in acetone, it was used to understand and calculated the diffusivity of the gas through the liquid and it also helped in understanding the effect of temperature on diffusivity. Air was used as the gas and the acetone was the liquid, air diffusivity was monitored for 120 minutes and data was ecorded every 5 minutes under a constant temperature of 40C. The diffusivity of acetone in air was calculated experimentally and found to be 0.1525cm2S, however, it is 0.066 cm2S theoretically, which resulted a parentage error of 57%. The sources of error were human and experiential error and were explained earlier. Few changes can be applied in order to reduce the percentage error and to obtain better results. Firstly, the liquid level reading could be digitalized, to obtain a better reading that will affect the accuracy of the measurements which will help to reduce the human error. Also, a temperature controller could be used to maintain the apparatus temperature since there was a minor temperature fluctuation; this controller will help reducing the experimental error. Appendix Sample Calculation The change in the acetone liquid level was calculated as shown below: The level of acetone liquid initially Lo (t=0) = 22.0 mm The level of acetone liquid after 10 minutes L (t=10) = 22.3 mm ?Lacetone = L-Lo = (22.3 – 22.0) mm = 0.3 mm Calculation of the change in acetone liquid level per time t?L=tL-Lo =10 min0.3 mm=33.3 min/mm Calculation of the diffusivity coefficient DAB of the acetone liquid in air at 40oC and 1 atm pressure using the diffusivity equation (5). t(L-Lo)=?A, L2 MADABCB, lmCA CTL-Lo+ ?A, L CB, lmMADAB CACT Lo (5) The intercept was determined from the Figure 2 Intercept=?A, L CB, lmMADAB CACT Lo Intercept=23.411 min/mm Intercept=23.411minmm x 10 mm1 cm=234.11mincm By rearranging and substituting the intercept equation above, the diffusivity will be calculated using the equation below: DAB=?A,L CB, lmMA Intercept CACTL0 The vapor concentration CT was calculated as below: CT=PR T The conversion in absolute temperature since the temperature of the water bath was at 40oC T (K) = 40oC + 273 K= 313 K CT=1 atm 8.21 x10-5 atm m3mol K (313 K) CT=38.91molm3 CT=38.91molm3 x 1 m31,000,000 cm3=3.89 x10-5molcm3 The molecular weight (molar mass) of acetone C3H6O was calculated as indicated below: MA=312.01+61.01+116=58.09 gmol The concentration of CB,LM was computed as follow: CB, Lm=CB1 -CB2Ln(CB1CB2) Assume the vapor concentration of acetone CT= CB1 CB1= 3.89 x10-5molcm3 The concentration of acetone CB2 was calculated as below: CB2=P-PvapPCT Where P=1 atm, the atmospheric pressure The vapor pressure of acetone was found using Antoine Equation: log10 P*=A-BT+C Where P* = Pvap in mm Hg Table2: Antoine Equation Constants at temperature range (-12.9oC to 55.3oC) Compound A B C Acetone C3H6O 7.11714 1210.595 229.664 log10 PAcetone (40 0C) *=7.11714-1210.59540 0C+229.664 log10 PAcetone (40 0C) *=2.627868165 PAcetone (40 0C) *=102.627868165 PAcetone (40 0C) *=424.49 mm Hg x 1 atm760 mm Hg PAcetone (40 0C) *=0.5585 atm CB2=1 atm-0.5585 atm1 atmx 3.89 x10-5molcm3= 1.72 x10-5molcm3 The concentration of the CB, Lm was calculated as follow: CB, Lm=3.89 x10-5molcm3 -1.72 x10-5molcm3Ln(3.89 x10-5molcm31.72 x10-5molcm3) CB, Lm=2.66 x10-5molcm3 The interface concentration of acetone was computed as below: CA=yA CT (*) To find yA Raoul’s law applies to relate the equilibrium concentration in the liquid and gas (air) phases as follows: P yA=xA PAcetone * yA= PAcetone *P (**) Where xA is the xAcetone =1 pure acetone P*Acetone is the vapor pressure of pure acetone at the equilibrium temperature 40oC P is the equilibrium pressure By substituting equation (**) into (*) equation to find the concentration at the interface CA= PAcetone *P CT CA=0.5585 atm1 atm CT CA=2.17 x10-5molcm3 The density of acetone at 40oC was determined from the CSR hand chemistry book as below: The density of acetone liquid at 40oC was interpolated with respect to different densities as a function of absolute temperature as shown in table 3 below: Table 3: Interpolation of acetone density Acetone temperature (K) Density (Kg/m3) 308.15 773.0 313.15 X=? 323.15 753.2 y- yox-xo =y1- yox1-xo 313.15- 308.15x-773.0 =323.15- 308.15753.2-773.0 -99 =15x-11595 x=766.4 Kgm3 x=766.4 Kgm3 x 1 m31,000,000 cm3x 1000 g1 Kg=0.7664 gcm3 ?A,L= 0.7664 gcm3 DAB=?A,L CB, lmMA Intercept CACTL0 DAB=(0.7664 gcm3) x (2.66 x10-5molcm3)58.09 gmolx 234.11mincmx 2.17 x10-5molcm3x (3.89 x10-5molcm3) x (2.23 cm) DAB=3.96 cm2min x 1 min60 S = 0.0660 cm2S DAB= 6.60 x10-2cm2s Percentage Error Calculation % Error= DAB Theoretical-DAB ExperimentalDAB Theoreticalx100 To determine the theoretical diffusivity using empirical equation of Fuller, Schettler and Giddings equation as follow: DAB=0.00143 T1.75P MAB1/2vA1/3+v1/3B2 Where v is the summation of atomic and structural diffusion value from table 3.1 seader book, A is acetone component and B is the air component. MAB=21MA+1MB MAB=2158.08+128.97=38.67gmol vacetone=15.9 x 3+2.31x 6+(6.11 x 1)=67.67 vair=19.7 DAB=0.00143 x (313K1.75)1 atm x 38.67gmol1/2x 67.671/3+19.71/3=0.1525cm2s DAB, Theoretical= 0.1525cm2s at 40oC and 1 atm % Error= 0.1525cm2s -0.066 cm2S0.1525cm2s x 100 % Error= 57% References Felder, Richard M., and Ronald W. Rousseau. Elementary Principles of Chemical Processes. New York: Wiley, 1986. Print. Seader, J. D., Ernest J. Henley, and D. Keith. Roper. Separation Process Principles: Chemical and Biochemical Operations. Hoboken, NJ: Wiley, 2011. Print. "Measurements of Gaseous Diffusion Coefficient." Unit Operation Laboratory. N.p.: Dr. Mehrab Mehrvar, 2014. 47-52. Print. "Diffusion of Gases in Liquids." - Industrial & Engineering Chemistry Fundamentals (ACS Publications). Web. 02 Nov. 2014. <http://pubs.acs.org/doi/abs/10.1021/i160043a016>.
