ABSTRACT

Diffusion of a gas experiment was conducted with the objective of determining the diffusion coefficient of ethanol into air. In this experiment, ethanol was placed in a capillary tube and was allowed to diffuse into non-diffusing air that was passed over the test tube at the temperature of 40oC. The temperature is kept constant and air stream is passedover the top of the tube to ensure that thepartial pressure of the vapor is transferred from the surface of the liquid to be air stream by molecular diffusion. The initial reading and every 10 minutes subsequent reading of the liquid ethanol level are determined, and the experiment is conducted for60 minutes. The experiment is repeated by changing temperature to 45 oC. A graph of t/L-Lo against L-Lo is plotted andbest fit of straight line and slope of the graph are obtained. The diffusivity of ethanol at two different temperatures is determined through calculation. The diffusivity of ethanol at temperature of 40 oC and 45 oC are 2.36 10-7 m2/s and 2.8010-7 m2/s respectively. Throughout the experiment, the diffusivity of ethanol is determined to be higher at higher temperature. This fits the theory where temperature of the substance will affects the diffusion rate.

INTRODUCTION

Mass transferis the net movement of mass from one location, usually meaning a stream, phase, fraction or component, to another. Mass transfer occurs in many process and gas and liquid diffusion are some of the examples. Gas diffusion occurred when diffusion of vapor takes place from volatile liquid (organic solvent) into anothergas (air). This process usedsame conceptasmass transfer where one constituent is transported from region of higher concentration to that of a lower concentration. Gas and liquid diffusion coefficients are particular importance in considering mass transfer in gas-liquid separation. In this experiment, the diffusivity of the vapor of a volatile liquid in air can be conveniently determined by Winklemanns method and ethanol is used as the organic substance.

The Stefen-Winklemanns method has been broadly used for measuring gas diffusion coefficients. The determination of the diffusion coefficient requires a previous knowledge of vapor pressure of the solvent, and therefore, the Stefen-Winklemanns method might be used to obtain vapor pressure data if the diffusivity coefficient is known.

OBJECTIVE

The objective of this experiment is to determine the diffusion coefficient of ethanol into air at different temperature

THEORY

The experiment to determine the diffusivity of gaseous is based on the Winkelmanns method. In this method, the volatile liquid allowed to evaporate in vertical glass over the top of which a stream of vapor-free gas is passed. A water bath is provided for maintaining a steady temperature so that there is no eddy current in the vertical tube and mass transfer takes place from the surface by molecular diffusion alone. By monitoring the evaporation rate, which is the rate of fall of liquid surface, and with the knowledge of concentration gradient, the diffusivity can be calculated

The rate of mass transfer is given byNA = D (CA/L)(CT/CBM)WhereCA = Saturation conc. at interface [kmol m-3 ]CBM = Logarithmic mean molecular conc. of vapor [kmol m-3 ]CT = Total molar conc. = CA + CBM [kmol m-3 ]L = Effective distance of mass transfer [mm] D = Diffusivity [m2 s -1 ]

Considering the evaporation of the liquid:Thus (L/M)(dL/dt) = D(CA/L)(CT/CBM)

Integrating and putting L = Lo at t = 0L2-L2o = (2MD/L)(CACT/CBM)tLo and L cannot be measured accurately but L-Lo can be measured accurately using the vernier on the microscope.

(L-Lo)(L-Lo+2Lo) = (2MD/L)(CACT/CBM)tOrt/(L-Lo) = (L/2MD)(CBM/ CACT)(L-Lo)+(LCBM/MDCACT)LoWhere:M = Molecular weight (kg/kmol)t = time (s)

If s is the slope of a graph of t/(L-Lo) against (L-Lo) then:s = (LCBM/2MDCACT) or D = (LCBM/2sMCACT)where:CT = (1/Kmol Vol)(Ts/Ta)CB1 = CTCB2 = (Pa-Pv/Pa)CTCBM = (CB1-CB2)/ln(CB1/CB2)CA = (Pv/Pa)CT

APPARATUS

Figure 1.0 The gas diffusion apparatus1. Gas Diffusion Apparatus

2. Ethanol

3. Water bath

4. Microscope

5. Capillary tube

6. Syringe

7. Stop watch

PROCEDURE

1. The distillate water was filled into the water bath until 35mm of the capillary tube was obtained.

2. The capillary tube is then filled with ethanol untilthe height is approximately 35mm with use syringe.

3. The air pump tube is filled into thecapillary tube until it had fully coveredthe entire upper side of the capillary tube then the capillary tube is inserted into the water bath.

4. The vertical height of the microscope was then adjusted until the capillary tube was visible.

5. If the capillary tube was not visible, the distance fromthe object lens was adjusted tothe tank until the meniscus of the ethanol inside the capillary tube was clearer and if necessary the position of the viewing lens in or out the microscope body can be adjusted.

6. When the capillary tube was viewed, theimage of the meniscus will beupside down so that the bottom of the meniscus of ethanol would be at the top of image.

7. When the meniscus of the ethanol has been determined, the sliding vernier scale shouldbe aligned with a suitable graduation on the fixed scale.

8. The air pump and the water bath heater are turned on.

9. The initial value of the ethanol inside the capillary was observed and recorded.

10. The temperature was set to 40 0C and a steady temperature was obtained.

11. The level of the ethanol insidethe capillary was recorded for every 10minutes. The experiment was then repeated at 45 oC.

RESULT

40Time(Min)Level Of Ethanol, L(mm)Liquid Level,(L-L0)(mm)T/(L-L0)(min/mm)

010.100

1010.30.250

2010.50.450

3010.80.742.86

4011.00.944.44

5011.21.145.45

6011.41.346.15

45Time(Min)Level Of Ethanol, L(mm)Liquid Level,(L-L0)(mm)T/(L-L0)(min/mm)

021.300

1021.90.616.67

2022.20.922.22

3022.81.520

4023.01.723.53

5023.21.926.32

6023.52.227.27

SAMPLE CALCULATION

Calculation for 40 Liquid level, L-L0 = 10.3-10.1 = 0.2mm

t/(L-L0) = 10/0.2 = 50min/mm

From slope of the graph, = = s/m2

Total Molar Concentration, CT (kmol/m3) CT = = = 0.0389 kmol/m3 Log Mean Molecular Concentration vapour, (kmol/m3) Cb1=Ct Cb1= 0.0389 Cb2 = Ct Cb2 = Cb2 = 0.0174 kmol/m3

Cbm = Cbm = 0.0267 kmol/m3

Saturation Concentration at interface, Ca Ca = Ca= 0.0215 kmol/m3

Diffusitivity, D (m2/s) PL = 790 Kg/m3

D=

D=

D40 = 2.36 10-7 m2/s

= 2.80 10-7 m2/s

DISCUSSIONS

The basic principle of diffusion that occurs in the capillary tube is from high concentration to low concentration. The objectives of this experiment are to determine the gas diffusion coefficient ofethanol using the established Winkelmanns method. The diffusion of the vapour of ethanol (volatile liquid) into another gas can be conveniently studied can by confining a small sample of the liquid in a narrow vertical tube, and observing its rate ofevaporation into a stream of gas passed across the top of the tube. The surface of ethanol with high concentration and the air inside the tube has low concentration. This will make the ethanol become vapor when it is heated with warm water that was boiled at 40oC and 45oC. The ethanol become vapor and diffused to the air.

The trend of graph is directly proportional. The equation used to get the slope is y = mx + c and the value of the slope at 40oC is 19.396 while at 45oC the slope is 16.283 . The diffusivity value at 40oC and 45oC is 1.872 x 107 and 2.22 x 10-7 respectively. The significance of correlation for 40oC and 45oC is 0.2734 and 0.7035 respectively which is lesser than expected. From the graph, it can be observed that the graph plotted for the temperature of 40oC is a little bit steeper than the graph plotted for the temperature of 45oC. Other than that, from the graph plotted, the value of slope can be obtained easily and the calculation of diffusivity of the vapour can be proceeding. The value of diffusivity is affected by the temperature. The higher the temperature, the diffusivity of the vapour or the diffusion coefficient of ethanol would increase. Diffusion is the movement of molecules from an areaof high concentration toan areaof lower concentration andthis is increased with increasing temperature which means when the temperature increase the diffusion will speeds up (Faghri et.al, 2010). Thus, if the temperature is higher, then probably it would increase the rate of diffusionby increasing the kinetic activity of the solution. The molecules of the solution would be moving more vigorously and so naturally the chances of them moving through pores in a membranewouldbemuchbetter (Cussler, 2009). Therefore,themoleculesspreadfromhightolow concentration more rapidly.Partial pressure and concentration give an effect on the rate of diffusion (Roger, 1950). From the Antoine equation, the correlation between partial pressure and concentration is when the partial pressure increases, it is easier for the solvent to evaporate due to pressure that affects the movement of the molecular particles in the solvent (Bengt, 1997). But for the concentration, an increase in concentration, the diffusion takes a longer time because more particles are there in the solvent.

The fact is the boilingpointof ethanol is78.37C andif thetemperature of the ethanol isexceeding theboiling pointtemperature the diffusivitywillnot beimplemented.Thisiscaused bythe characteristicsofthe ethanol solution which is volatile. An increase in pressure has a significant effect on the relative volatility ofthe component ina liquid mixture like the ethanol. Therefore, the temperature conducted in this experiment must not exceed theboiling point of the ethanol because it will increase the rate of volatility of ethanol (Cameron, 1999). Thus, it will be harder to read the level of meniscus on the sliding vernier scale since the solution is volatile rapidly.

The value obtain from the result might be different with the actual because there maybe some erroroccur during the experiment isdone. The common error that always occurs is the position of the eye during taking the volume at the telescope. The eye position should be straight to the scale and must be parallel to the meniscus. Other than that, the experiment should be repeated at least three times to get the accurate values and this can reduce the mistake during the experiment is done.

CONCLUSION

This experiment was performed to determine the diffusivity of the vapour and to study the effect of temperature on the diffusivity. From the analysed data and calculated results the diffusivity of the vapour of ethanol at 40 c and 45 cwere determined which were2.36 10-7 m2/s and 2.80 10-7 m2/s respectively. We can conclude that diffusivity of the ethanol with higher temperature will have a higher value. Besides that, it has been theoretically proved that higher temperature cause the molecules of substance to gain higher kinetic energy. The kinetic energy that it gains makes it moves randomly and freely hence increasing the rate of diffusion. Finally, the experiment has accomplished us with the study of diffusivity coefficient and familiarity with the use of laboratory instruments to achieve accurate measurements of data required for industrial process design.

RECOMMENDATIONS

Before the ethanol was pumped, make sure there was no air bubble inside the capillary tube. Use different capillary tube when start with different temperature. The travelling microscope that attached to the vernier scale must be tightly installed and stable. The level of the travelling microscope also must be paralleled with the capillary tube. Eye level also must be parallel to the meniscus level. When adjusting the vernier scale, the position of the travelling microscope should not be disturbed. The method of recording the reading from the vernier scale must be correct. The velocity of the air flow must be constant.

REFERENCE

1. Faghri. A, Zhang. Y, Howell. J, (2010), Advanced Heat and Mass Transfer, USA, page 345. 2. Cussler, E.L, (2009), Diffusion: Mass Transfer in Fluid System, 3rd Edition, USA, page 200.3. Bengt, S, (1997) Advanced Computational Methods and Experiments in Heat Transfer 11, WIT Press, pp 174-176.4. Cameron, T, (1999) Springer Handbook of Experimental Fluid Mechanics, Volume 1, Springer, pp. 45-47. 5. Roger, A.S, (1950) A Determination of Diffusion Coefficients for Gaseous Systems at Various Temperatures, University of Wisconsin--Madison, pp. 78-89.

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