Diffusion Coefficient Full Report Tiqa

TABLE OF CONTENTS CONTENT

PAGE

•

Abstract / summary

•

Introduction

•

Aims / objectives

•

Theory

•

Apparatus

•

Experimental procedure

6-7

•

Result

8-9

•

Calculation

10-13

•

Discussion

14-15

•

Conclusion

15

•

Recommendation

16

•

References

17

•

Appendices

18-20

2 2-3 3 3-6 6

1

ABSTRACT/SUMMARY Regarding to the experiment objectives which is to determine the diffusivity of the vapour of acetone and to study the effect of temperature on the diffusivity, this experiment is based on the mass transfer theory. The instrument used is the Gas Dispersion Apparatus that consists of an acrylic assembly which is sub-divided into two compartments. One compartment is constructed from clear acrylic and is used as a constant temperature water bath. The other compartment is incorporates an air pump and the necessary electrical controls for the equipment. The experiment is run by using two difference temperatures in order to study the effect of temperature on the diffusivity of the vapour of acetone. At temperature of 40˚C, the diffusivity of acetone that obtained is 2.054 x 10-7 m2/s. Meanwhile, at temperature of 50˚C, the diffusivity of acetone that obtained is 8.875 x 10-7 m2/s. As the temperature increase, the diffusivity of the vapour of acetone also increases.

INTRODUCTION

Gaseous diffusivity or gas dispersion apparatus which involves diffusion with bulk flow is one of the items of laboratory equipment that have been designed to allow measurement of molecular diffusivities and also to make the students become more familiar with the basic notions of mass transfer theory. This apparatus is a bench mounted apparatus for the determination of diffusion coefficients of a vapour in air, which uses the method of measuring the rate of evaporation of a liquid through a stagnant layer into a flowing air stream, comprising a precision bore capillary tube, which may be filled from a syringe and 2

the top of which means are provided to pass air (or an inert gas) stream to remove vapour. The apparatus also comprise an air pump, a travelling microscope with accurate focus adjustment and mounted for vertical axis movement against a Vernier scale and a thermostatically controlled water bath, in which to place the capillary tube, capable of accurate temperature control.[1] The experimental capabilities of this apparatus are direct measurement of mass transfer rates in the absence convective effects, use of a gas laws to calculate concentrations differences in terms of partial pressures, use of Fick’s Law to measure diffusion coefficients in the presence of a stationary gas, measurement of the effect of temperature on diffusion coefficients and gaining familiarity with the use of laboratory instruments to achieve accurate measurements of data required for industrial process design. [1] The diffusivity of the vapour of a volatile liquid in air can be conveniently determined by Winklemann’s method in which liquid is contained in a narrow diameter vertical tube, maintained at a constant temperature, and an air stream is passed over the top of the tube to ensure the partial pressure of the vapour is transferred from the surface of the liquid to the air stream by molecular diffusion. The molecular diffusivity, D, is a kinetic parameter associated with static and dynamic conditions of a process. All the complexity and unwieldiness of many calculations is, indeed, connected with the determination of this quantity.[2]

OBJECTIVE The objective of this experiment is 1. To determine the diffusivity of the vapour of acetone. 2. To study the effect of temperature on the diffusivity.

THEORY 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.

3

Normally, for simple instructional purposes, gas B is air and vapour A is an organic solvent such as acetone or methyl alcohol.[1] The apparatus consist essentially of a glass capillary tube placed in a transparent-sided temperature controlled water bath. A horizontal glass tube is fixed to the upper end of the capillary tube and air is blown through this by a small air pump included within the unit. This arrangement allows the maintenance of a partial pressure difference within the capillary tube between the evaporating liquid surfaces and the flowing air stream. A travelling microscope, with sliding vernier scale, is mounted on a rigid stand alongside the thermostatic bath and is used to measure the rate of fall of the solvent or air meniscus within the capillary.[1] The relation between the measured molar mass transfer rate (NʹA per unit area), the partial pressure gradient and the diffusion coefficient, D is deduced based on the following;

Where D = Diffusivity (m2/s) CA = Saturation concentration at interface (kmol/ m3) L = Effective distance of mass transfer (mm) CBm = Logarithmic mean molecular concentration of vapour (kmol/ m3) CT = Total molar concentration =

+

(kmol/ m3)

CA CBm

Considering the evaporation of the liquid:

4

where

ρL

is the density of the liquid.

Thus,

Integrating and putting L - Lo at t = 0

Lo and L cannot be measured accurately but L-Lo can be measured accurately using the vernier on the microscope

or

where: M = molecular weight (kg/mol) t = time(s) where

are the slopes of a graph

s

against L - Lo then: t ( L − LO ) 5

or

where:

APPARATUS 1. 2. 3. 4. 5. 6.

Gas dispersion or gaseous coefficient apparatus Water bath Microscope Capillary tube Thermometer Acetone

PROCEDURE

6

Temperature controller Capillary tube Air pump switch Vernier scale

Microscope

Heater switch

1. A capillary tube was filled with acetone to a high approximately 35 mm by using

syringe. 2. The air pump and water bath temperature was switched on. 3. The air pump was tested and adjusted. 4. The water temperature was set up to 40oC and the steady temperature was obtained.

5. The capillary tube was placed in the water bath and the air pump tube was placed in one side of the capillary tube. 6. The vertical height of the microscope was adjusted until the capillary tube is visible. If the capillary tube is visible, the distance from the object lens to the tank is adjusted. 7. The position of the viewing lens was adjusted in or out of the microscope body in order to get the clearer and well defined view of the meniscus inside the capillary tube. 8. Note that when viewing the capillary tube, the image will be upside down, so that the bottom of the tube is at the top of the image. 9. When the meniscus had been determined, the sliding vernier scale was aligned with a suitable graduation on the fixed scale. 10. The level inside the capillary tube (L) was recorded at t = 0 min and every 10 minutes

for 60 minutes. 11. The experiment is repeated at different temperature of 50oC.

7

RESULT •

Temperature = 40˚C

•

Lo = 40.0 mm

Time, t (min)

Time, t (s)

Reading of

Liquid level

t/(L – Lo)

vernier, L

(L – Lo)

(min/mm)

(mm)

(mm)

t/(L – Lo) (s/mm)

0

0

40.0

0.0

0.00

0.00

10

600

40.4

0.4

25.00

1500.00

20

1200

40.6

0.6

33.33

2000.00

30

1800

40.9

0.9

33.33

2000.00

40

2400

41.1

1.1

36.36

2181.82

50

3000

41.4

1.4

35.71

2142.86

60

3600

41.7

1.7

35.29

2117.65

Reading of

Liquid level

t/(L – Lo)

t/(L – Lo)

vernier, L

(L – Lo)

(mm)

(mm)

(min/mm)

(s/mm)

•

Temperature = 50˚C

•

Lo = 50.0 mm

Time, t (min)

Time, t (s)

0

0

41.4

0.0

0.00

0.00

10

600

42.1

0.7

14.29

857.14

20

1200

42.5

1.1

18.18

1090.90

30

1800

43.2

1.8

16.67

1000.00

40

2400

43.7

2.3

17.39

1043.48

50

3000

44.1

2.7

18.52

1111.11

60

3600

44.7

3.3

18.18

1090.91

8

•

Graph for temperature at 40˚C

•

Graph for temperature at 50˚C

•

The diffusivity of the vapour of acetone Temperature, ˚C

Diffusivity, D (m2/s)

40

2.054 x 10-7

50

8.875 x 10-7

CALCULATIONS •

Calculation for temperature at 40˚C Molecular weight, M = 58.08 kg/kmol Temperature, Ta = 40˚C (313 K) Pressure, Pa = 101.3 kN/m2 Kmol volume = 22.4 m3 Density, ρL = 760 kg/m3 Vapour pressure, Pv = 56 kN/m2

–

From the graph plotted; Slope, s = 1.057 x 109s/m²

–

Molecular weight, M (kg/kmol) Molecular weight of acetone

58.08 g /mol

58.08 kg/kmol

9

Total molar concentration, CT (kmol/ m3)

–

= 122.4273313

=0.0389 kmol/m³ Logarithmic mean molecular concentration of vapour, CBm (kmol/ m3)

–

CB1 = CT CB1

= 0.0389 kmol / m³

 Pa −Pv  CB 2 = CT Pa  

CB2 = 101.3-56101.3×0.0389 kmol/m³=0.0174kmol/m³

(CB1 −CB 2 )

CBm =

CB1  ln   CB 2 

= (0.0389-0.0174)ln0.03890.0174 0.0267 kmol / m³

Saturation concentration at interface, CA (kmol/ m3)

–

 PV  CA =  CT  Pa  = 56101.30.0389 =0.0215 kmol / m³ –

Diffusivity, D (m2/s)

10

D=

( ρLCBm )

s ( 2 MCACT )

ρL = 790kg /m³

D = 2.054 x 10-7 m2/s

D=

(790 kg/m³)(0.0267kmol/m³) [1.057 x 109s/m²][(2)(58.08 kg/kmol)(0.0215 kmol/m³)(0.0389 kmol/m³)]

11

•

Calculation for temperature at 50˚C Molecular weight, M = 58.08 kg/kmol Temperature, Ta = 50˚C (323 K) Pressure, Pa = 101.3 kN/m2 Kmol volume = 22.4 m3 Density, ρL = 760 kg/m3 Vapour pressure, Pv = 56 kN/m2

–

From the graph plotted; Slope, s = 2.531 x 108s/m²

–

Molecular weight, M (kg/kmol) Molecular weight of acetone = 58.08 g /mol = 58.08 kg/kmol

–

Total molar concentration, CT (kmol/ m3)

= 122.4273323

=0.0377 kmol/m³ –

Logarithmic mean molecular concentration of vapour, CBm (kmol/ m3) CB1 = CT CB1

= 0.0377 kmol / m³

 Pa −Pv  CB 2 = CT Pa  

CB2 = 101.3-56101.3×0.0377 kmol/m³=0.0169kmol/m³

12

(CB1 −CB 2 )

CBm =

CB1  ln   CB 2 

= (0.0389-0.0169)ln0.03890.0169 = 0.0259 kmol / m³

Saturation concentration at interface, CA (kmol/ m3)

–

 PV  CA =  CT  Pa  = 56101.30.0377 =0.0208 kmol / m³ –

Diffusivity, D (m2/s) D=

( ρLCBm )

s ( 2 MCACT )

ρL = 790kg /m³

D=

(790 kg/m³)(0.0259kmol/m³) [2.531 x 108s/m²][(2)(58.08 kg/kmol)(0.0208 kmol/m³)(0.0377 kmol/m³)]

D = 8.875 x 10-7 m2/s

13

DISCUSSION The objectives of this experiment are to determine the diffusivity of the vapour of acetone and to study the effect of temperature on the diffusivity which based on the mass transfer theory of the molecular diffusion in gases. To archive the objectives of this experiment, the gas dispersion apparatus is used. This apparatus is combined with vernier scale and microscope which is used to measure and read the level of meniscus in the capillary tube which contains acetone. The diffusion of the vapour of acetone (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 of evaporation into a stream of gas passed across the top of the tube. The experiment is divided into two parts which differ in terms of temperature. First part, the experiment is run by using temperature of 40˚C and the diffusivity of the vapour of acetone obtained is 2.054 x 10-7 m2/s. For the second part, the experiment is repeated by using temperature of 50˚C and the diffusivity of the vapour of acetone obtained is 8.875 x 10 -7 m2/s. Based on the result obtained from both part, the graph of t/(L – L o) against (L – Lo) was plotted. From the graph, it can be observed that the graph plotted for the temperature of 40˚C is a little bit steeper than the graph plotted for the temperature of 50˚C. 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. From the calculation that has been done, it is shows that the value of diffusivity is affected by the temperature. The higher the temperature, the diffusivity of the vapour or the diffusion coefficient of acetone would increase. Diffusion is the movement of molecules from an area of high concentration to an area of lower concentration and this is increased with increasing temperature which means when the temperature increase the diffusion will speeds up.[4] Thus, if the temperature is higher, then probably it would increase the rate of diffusion by 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 membrane would be much better.[5] Therefore, the molecules spread from high to low concentration more rapidly.[6] There is much difference in the value of diffusivity obtained from both temperature which is determine by 6.821 x 10-7 m2/s. The higher temperature used in this experiment is only 50˚C. As we know, the boiling point of acetone is 56.5˚C and if the temperature is exceeding the boiling point temperature the diffusivity will not be feasible. This is caused by the characteristics of the acetone 14

solution which is volatile. An increase in pressure has a significant effect on the relative volatility of the component in a liquid mixture. Since an increase in the pressure requires an increases in the temperature, then an increase in temperature also effects the relative volatility.[7] Therefore, the temperature conducted in this experiment must not exceed the boiling point of the acetone because it will increase the rate of volatility of acetone. 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 may be some error occur during the experiment is done. The common error that always occurs is the position of the eye during taking the volume at the burette. 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 3 times to get the accurate values and this can reduce the mistake during the experiment is done. CONCLUSION As a conclusion: 1. At temperature of 40˚C, the diffusivity of the vapour of acetone is 2.054 x 10-7 m2/s

meanwhile at temperature of 50˚C, the diffusivity of the vapour of acetone obtained is 8.875 x 10-7 m2/s. 2. From the graphs plotted, it can be conclude that flowing air significantly increases the diffusion coefficient thus increasing the mass transfer. 3. Other than that, it can be concluded that the higher temperature affect the diffusivity

of the vapour. Faster diffusion will take place if the surrounding is warmer. Increase in temperature means an increase in molecules’ speed (kinetic energy). Therefore, the molecules move faster and there will be more spontaneous spreading of material which means that diffusion occurs quicker.[3] Therefore, the higher the temperature, the higher the diffusivity of the vapour.

15

RECOMMENDATION

1. To evaporate quickly the best way would be to pass air flow over the liquid, if want a

fluid to evaporate slowly would not pass air over. 2. The flow rate of flowing air must be constant throughout this experiment.

3. The level of meniscus must be correctly observed on the microscope and also read on the vernier scale. 4. Repeat the experiment twice for each set of temperature to get the average reading for more accurate result. 5. Clean up the apparatus before start the experiment. 6. Make sure the microscope is in good condition before run the experiment. 7. Changes the water bath when want to start a new set of temperature. 8. Always checks the air pump (make sure it functions all the time during the experiment).

16

REFERNCES

1. CERa/CERb Mass Transfer and Diffusion Coefficients – Issue 10, 1 October 2010 at

http://www.discoverarmfield.co.uk/data/cer/?js=enabled 2. Determining the diffusivity of nitrogen tetroxide, 1 October 2010 at

http://www.springerlink.com/content/k0501550x585x0kn/ 3. How does the temperature affect the diffudion rate?, 1 October 2010 at

http://wiki.answers.com/Q/How_does_temperature_affect_diffusion_rate 4. How does temperature affect the rate of diffusion?, 1 October 2010, at

http://www.studyzones.com/questionzone/answer/73267x1565/How-doestemperature-affect-the-rate-of-diffusion 5. How temperature affects diffusion, 1 October 2010, at http://www.biology-

online.org/biology-forum/about2736.html?hilit=Balloon+cell 6. Does temperature effect diffusion rate, 1 October 2010, at

http://www.reference.com/motif/Science/does-temperature-effect-diffusion-rate 7. Relative volatility, 1 October 2010, at

http://en.citizendium.org/wiki/Relative_volatility 8. Christie John Geankoplis (University of Minnesota), Transport Processes and Separation Process Principles (Includes Unit Operations) – fourth edition, Pearson Education International.

17

APPENDICES

18

Figure 1

19