ABSTRACT

The objectives of this experiment are to determine the diffusivity of the vapour of acetone as

well as to study the effect of temperature on the diffusivity. In this experiment, the main

apparatus used is Gaseous Diffusion Apparatus [Model: CER-A (ARMFIELD)]. This

experiment was conducted by using two set of temperatures, 45 ᴼC and 55 ᴼC as the

manipulating variable. For each temperature, the reading of the vernier scale was recorded at

every 5-minutes interval until the time reached 45 minutes. Before the reading was taken, the

vertical height of the microscope was adjusted until it was visible that the meniscus of the

capillary tube was set at the origin. At the end of the experiment, gas diffusivity of the of the

vapour of acetone was calculated along with 2 graphs being plotted for a clearer observations

of the experiment. The diffusivity of the vapour of acetone obtained at temperature 45 ᴼC and

55 ᴼC are 6.12 x 10−6 m2/s and 2.266 x 10−6 m2/s respectively. This shows that as temperature

increase, the diffusivity of the vapor of acetone decreases. However, this result deviates from

the theotrical results based on the principle of gas diffusion in which the diffusivity has to

increase when temperature increases.

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INTRODUCTIONS

Figure 1 : Gas Diffusion Apparatus

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 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.

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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.

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.

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OBJECTIVES

To :

(a) Determine the diffusivity of the vapour of acetone.

(b) 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. Normally, for

simple instructional purposes, gas B is air and vapour A is an organic solvent such as acetone

or methyl alcohol.

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.

The relation between the measured molar mass transfer rate (N’A per unit area), the partial

pressure gradient and the diffusion coefficient, D is deduced based on the following;

……………………….……….. Equation [1]

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 = CA + CBm (kmol/ m3)

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N’A = D {CA/L}{CT/CBM}

Considering the evaporation of the liquid:

……………………. Equation [2]

Where ρ is the density of liquid

Thus,

………………. Equation [3]

Integrating and putting L - Lo at t = 0

…………… Equation [4]

Lo and L cannot be measured accurately but L-Lo can be measured accurately using

thevernier on the microscope

…. Equation [5]

Or

where:

M = molecular weight (kg/mol)

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N’A = {ρL/M}{dL/dt}

{ρL/M}{dL/dt} = D {CA/L}{CT/CBM}

L2 – L20 = {2DM/ρL}{(CA×CT)/CBm}t

(L – L0)(L-L0+2L0) = {2DM/ ρL}{(CA×CT)/CBm}t

t/(L-L0) = { ρL/2MD}{ CBm/( CA×CT)}(L-L0) + {(ρL × CBm)/( CA×CT×MD)}L0

t = time(s)

where

 s are the slopes of a graph t/(L-L0) against L - Lo then:

……………. Equation [6]

……..……….. Equation [7]

APPARATUS

1) TR 14 Membrane Test Unit apparatus.

2) 500 mL beakers.

3) Electronic balance.

4) Capillary tube

5) Gloves

6) Ruler

MATERIALS

1) Acetone

2) Sodium Chloride

3) Water

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s = (ρL × CBm)/( CA×CT×2MD)

D = (ρL × CBm)/( CA×CT×2sM)

PROCEDURE

1. The capillary tube is partially filled with acetone to a depth of approximately 33.03mm.

The top nut was removed from metal fitting.

2. Carefully, the capillary tube was inserted through the rubber ring, inside the metal nut

until the top of the tube rests on the top of the nut.

3. Gently the assembly is screwed onto the top plate, with the ‘T’ piece normal to the

microscope. The flexible air tube was connected to one end of the ‘T’ piece. The object

lens is adjusted to within 20-30 mm from the tank.

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

When the meniscus has been determined, the vernier scale should be aligned with a

suitable graduation on the fixed scale.

5. Then, the air pump was switched on.

6. The level inside the capillary tube was recorded.

7. The temperature controlled water bath was switched on and a steady temperature was

obtained.

8. The reading was taken every 5 minutes for 10 times. The experiment was done at

temperature 45°C and repeat step by using temperature at 55°C and initial length

acetone at 38.04mm.

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RESULTS

Temperature: 45 ºC

Initial length: 33.03 mm

Time (ks) Reading scale (mm) (L - Lo) (mm) tL−Lo

(ks/mm)

0.3 34.04 1.01 0.290.6 36.06 3.03 0.190.9 38.08 5.05 0.181.2 40.10 7.07 0.171.5 33.02 0.00 1.501.8 35.04 2.01 0.892.1 36.05 3.02 0.692.4 38.07 5.04 0.482.7 40.09 7.06 0.38

Temperature: 55 ºC

Initial length: 38.04 mm

Time (min) Reading scale (mm) (L - Lo) (mm) tL−Lo

(ks/mm)

0.3 34.03 4.01 0.070.6 40.09 2.05 0.290.9 35.03 3.01 0.291.2 41.09 3.05 0.391.5 37.04 1.00 1.501.8 43.10 5.06 0.362.1 39.05 1.01 2.082.4 36.01 2.03 1.182.7 41.06 3.02 0.89

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CALCULATIONS

5min x 60 s

1min ÷1000 = 0.3ks

Temperature: 45 ºC

1.01 3.03 5.05 7.07 0 2.01 3.02 5.04 7.060

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Graph of t/(L−Lo) versus (L - Lo )

(L - Lo )

t/(L

−Lo)

Density of acetone, ρ = 790 kg/m3

Gas constant, R = 8.314Jmol

. K

Molecular weight of acetone = 58.08kgmol

Vapor pressure, Pv = 56 kN/m3

Slope, s = 0.036 ks /mm2 = 3.6 x 107 s/m2

Assume standard conditions (P = 101.32 kN/m2, V=22.4 m3, T = 273 K)

Tempereature, Ta = 45 ᴼC = 318 K

CT = (1/V )(T / Ta )

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= (1/22.4)(273/318)

= 0.0383 kmol/m3

CB1 = CT = 0.0383 kmol/m3

To find CB2 :

CB2 = (Pa – Pv / Pa)CT

= (101.32-56/ 101.32) 0.0383

= 0.0171 kmol/m3

To find CBM :

CBM = (CB1-CB2)/ln (CB1/CB2)

= (0.0383 – 0.0171)/ln (0.0383/0.0171)

= 0.0263

To find Ca :

Ca = (Pv/Pa)CT

= (56/101.32) 0.0383

= 0.0212 kmol/m3

To find diffusivity,D :

D = (790x0.0263)/(0.0212x0.0383x2x3.6x107x58.08)

D = 6.12 x 10−6 m2/s

Temperature :55 ºC

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D = (ρL × CBm)/( CA×CT×2sM)

4.01 2.05 3.01 3.05 1 5.06 1.01 2.03 3.020

0.5

1

1.5

2

2.5

Graph of t/(L−Lo) versus (L - Lo )

(L - Lo )

t/(L

−Lo)

Density of acetone, ρ = 790 kg/m3

Gas constant, R = 8.314Jmol

. K

Molecular weight of acetone = 58.08kgmol

Vapor pressure, Pv = 56 kN/m3

Slope, s = 0.1 ks /mm2 = 1.0 x 108 s/m2

Assume standard conditions (P = 101.32 kN/m2, V=22.4 m3, T = 273 K)

Tempereature, Ta = 55 ᴼC = 328 K

CT = (1/V )(T / Ta )

= (1/22.4)(273/328)

= 0.0372 kmol/m3

CB1 = CT = 0.0372 kmol/m3

To find CB2 :

CB2 = (Pa – Pv / Pa)CT

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= (101.32-56/ 101.32) 0.0372

= 0.0166 kmol/m3

To find CBM :

CBM = (CB1-CB2)/ln (CB1/CB2)

= (0.0372 - 0.0166)/ln (0.0372/0.0166)

= 0.02553

To find Ca :

Ca = (Pv/Pa)CT

= (56/101.32) 0.0372

= 0.0206 kmol/m3

To find diffusivity,D :

D = (790x0.02553)/(0.0206x0.0372x2x1.0 x 108 x58.08)

D = 2.266 x 10−6 m2/s

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D = (ρL × CBm)/( CA×CT×2sM)

DISCUSSIONS

This experiment was conducted to obtain the gas diffusion coefficient and its relationship with

the change in temperature. The manipulating variable involved is the temperature and the

responding variable was the level inside the capillary tube, L which was taken every 0.3 ks

until 2.7 ks was reached. This experiment was carried out at two different temperatures which

are at 45 ᴼC and 55 ᴼC with respect to gas diffusivity. Alongside, gas diffusivity of vapour

acetone is also calculated.

Based on the two graphs of t

Lo−L against Lo – L that had been plotted, the gradient or also

known as the slopes were calculated. The data collected however shown to deviate variedly,

due to the present of errors.. A linear graph was not able to be obtained and thus to overcome

this problem the slopes was calculated taking from two points relative to the line obtained.

Next, the diffusivity of vapour acetone at different temperature was being calculated. It was

based on the data collected for T = 45 ᴼC, D equivalent to 6.12 x 10−6 m2/s while at T = 55

ᴼC, D was found to be 2.266 x 10−6 m2/s. The result has proven that as the temperature

increase, the diffusivity decreases. However, according to the principle of gas diffusion from

this experiment, supposedly the diffusivity of vapor acetone increases with increasing

temperature.

Diffusion is the movement of molecules from area of high concentration to area of

lower concentration and this is increased with increasing temperature which means

when the temperature increase the diffusion will also rising up. In the other word, when

temperature is higher, then the rate of diffusion would probably increase caused by

increasing kinetic activity of the solution. However, due to this inaccuracy, values for

gas diffusivity calculated using equation above may not explain correctly the definition of gas

diffusion.

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CONCLUSION

As a conclusion, the result for diffusivity coefficient at 45 °C is 6.12 x 10-6 m2/s and the

diffusivity coefficient at 55 °C is 2.266 x 10-6 m2/s. During the experiment, there are some

errors occur. To get accurate values of diffusivity, a few of recommendations step should be

taken. In this experiment, the results obtained are almost accurate even there are some errors

occur.

RECOMMENDATIONS

1. Some recommendations should be implements in this experiment. One of them is

insulating the glass container. It will maintain the temperature through the experiment

and the heat will not loss to the surrounding.

2. Next, the reading meter should be stabilized with the person who read the meter. The

person who read it should be at the same level to the meter to reduced parallax error.

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REFFERNCES

Journal of Physical and Chemical Reference Data. Gaseous Diffusion Coefficients.

Retrieved November 15, 2012 from http://jpcrd.aip.org/resource/1/jpcrbu/v1/i1/p3_s1?

isAuthorized=no

Gases: Graham’s Laws of Diffusion and Effusion. Graham’s Law. Retrieved

November 15, 2012 from

http://www.chem.tamu.edu/class/majors/tutorialnotefiles/graham.htm

Diffusion of Gases. Diffusion and Effusion. Retrieved November 16 2012 from

http://chem.salve.edu/chemistry/diffusion.asp

USEC. Gaseous Diffusion. RetrievedNovember 16, 2012 from

http://www.usec.com/gaseous-diffusion

Advancing the Chemical Sciences. Learn Chemistry: Diffusion of gases of ammonia

and hydrogen chloride. Retrieved November 16, 2012 from http://www.rsc.org/learn-

chemistry/wiki/TeacherExpt:Diffusion_of_gases_-_ammonia_and_hydrogen_chloride

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