1

1. NOMENCLATURE

Symbol Definition Units(SI)

Volume of water in outer vessel L

Length of capillaries cm

Diameter of capillaries cm

Number of capillaries

Molarity of salt solution in diffusion cell mole/dm3

Change in conductivity per change in molarity

Rate of change of conductivity with time

mass transfer rate into bulk liquid mole/sec

X Distance through which diffusion occurs cm

2

2. INTRODUCTION

Mass transfer occurs when two solutions have different concentrations. In other words,

mass transfer takes place when there is a concentration gradient of the diffusing component.

Concentration gradient is the driving force for mass transfer and the mass transfer that

continue until the concentrations are equal each other. Because when the concentrations are

equal there is no driving force [1]. Convective mass transfer and diffusional mass transfer are

two different kinds of mass transfer. Former one occurs due to bulk motion and it occurs fast.

Latter one is the diffusion and there is no bulk motion, because of that diffusion is a slow

process. In diffusion when species B is stationary-solvent and species A (solute) moves

through high concentration to low concentration. The diffusion flux of species A into

stationary B is expressed by Ficks Law of Diffusion:

(1)

Where J: diffusion flux across unit area to the x-direction, mol/cm2 s

DAB: diffusivity, cm2/s

: Concentration gradient (mol/cm

3)/cm

A: the cross sectional area perpendicular to direction of diffusion, cm2

: Mass transfer rate into bulk liquid, mole/sec

C: Concentration, mole/cm2

X: Distance through which diffusion occurs, cm

The negative sign indicates that flow is from high to low concentration.

(2)

Where;

: Rate of change of conductivity with time, 1 sec1

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N: Number of capillaries

Cm: Change in conductivity per change in molarity (dilute solutions) 1 L mol1

By combining equations 1 and 2 :

(

)

(3)

Where;

V: Volume of water in outer vessel, L

From Equation 3 diffusivity coefficient may be obtained as:

(4)

Where;

d: diameter of capillaries, cm

The assumptions that are made to derive the equation are;

and molarity is constant.

The slope obtained from the plot of conductivity as function of time can be used to calculate

the diffusivity. The importance of diffusion coefficient DAB is that, it explains the tendency of

diffusion of species A in B. It is a function of temperature and pressure.

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3. EXPERIMENTAL METHOD

In this experiment, equipment and chemicals which are used to determine the diffusion

coefficient of KCl solution are listed below and Figure 3.1 represents experimental setup.

Equipments :

Diffusion cell,

Acrylic vessel or diffuser vessel,

Conductivity meter,

Magnetic stirred,

Stop watch

Chemicals:

Distilled water

0.001 M, 0.002M, 0.004M, 0.006M and 1 M KCL solution

Figure 3.1: Experimental setup [2]

After washing the acrylic vessel and the diffusion with distilled water clearly in the

case of obtaining accurate data, the acrylic vessel is filled with 1 liter distilled water. There

are numerous small glass capillary pipes at the top of honeycomb otherwise it would not be a

diffusion. After adding 1M KCl solution into diffusion cell that is prepared, magnetic stirrer

bar is placed on the bottom of the acrylic vessel and the vessel is located on the battery

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operated stirrer. After the conductivity meter is connected to the vessel, it is switched on and

immediately after the first data is recorded. Conductivities are recorded in every 1 minute and

experiment lasts 50 minutes. While obtaining conductivities, conductivity versus time graph is

plotted on a graph paper in this way it can be determined when process reaches steady state.

In the second part of the experiment, 0.001, 0.002, 0.004, 0.006 molar of KCl

solutions are prepared and their conductivities are measured time independently to plot

conductivity versus molarity graph to get Cm.

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4. RESULTS

In this experiment, in order to find liquid diffusion coefficient, conductivity data

recorded in every minutes during 50 minutes while diffusion takes place. For calculation Eqn

1 is used; however, in the equation, there is an unknown term which is Cm.

To find this term, calibration curve is plotted by measuring the conductivity data of the

KCl in solutions which have different concentrations; such as, 0.001, 0.002, 0.004 and 0.006

M. It is shown below in Figure 4.1.Since Cm is equal to slope of this graph, it can be found

from the calibration curve as 0.1336 S/M.

Figure 4.1 Concentration versus conductivity graph

After finding Cm, by Ficks law can be used to calculate difussivity. In the equation

(4), there is dk/dt term; therefore, it is needed to plot conductivity versus time graph. This is

the reason for recording conductivity datum in every minute during the 50 minutes. Recorded

datum are shown below in Table 4.1.

y = 0.1336x + 1E-05 R = 0.9995

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Co

nd

uct

ivit

y (S

)

Concentration (M)

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Table 4.1 Conductivity data for each minute during fifty minutes

t (min) k (S) t (min) k (S) t (min) k (S)

0 5.6 17 100.4 34 136.8

1 37.3 18 102.9 35 138.3

2 44.3 19 105.5 36 140.4

3 50.6 20 107.0 37 142.4

4 55.7 21 108.0 38 144.2

5 59.7 22 110.6 39 145.4

6 64.6 23 113.4 40 147.3

7 68.7 24 115.6 41 148.9

8 72.7 25 118.1 42 150.6

9 76.4 26 120.2 43 152.3

10 79.7 27 122.4 44 153.9

11 83.1 28 124.8 45 155.9

12 86.7 29 126.6 46 157.3

13 89.5 30 128.8 47 159.0

14 92.4 31 130.7 48 160.6

15 95.2 32 132.7 49 162.2

16 98.0 33 134.6 50 163.6

When the graph is plotted, it can be seen that, until a specific point, curve has same

slope; however, after that point a refraction is shown up. Because of this result, the graph is

plotted for the first 20 minutes, then for last 30 minutes and finally for all 50 minutes,

seperately and three different slopes are observed.

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Conductivity of first 20 minutes are shown by blue line and last 30 minutes are shown

by the red one in Figure 4.2.

Figure 4.2 Conductivity versus time graph for the first and the second set of data

For the first set of data, dk/dt is found from solpe as 7x10-8

S/s and for other datum it

is found as 3x10-8

S/s. These difference is resulted from, the rapid increase of conductivity

until saturation. When saturation is reached, the red part of the graph is more linear, stable,

and accurate. Accordingly, to verify that, a new graph is plotted by using all datum. It is

shown in Figure 4.3.

y = 7E-08x + 3E-05 R = 0.9094

y = 3E-08x + 7E-05 R = 0.9953

0

0.00002

0.00004

0.00006

0.00008

0.0001

0.00012

0.00014

0.00016

0.00018

0 500 1000 1500 2000 2500 3000 3500

Co

nd

uct

ivit

y (S

)

Time (s)

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Figure 4.3 Conductivity versus time graph for all datum

In this graph, slope is found as 4 x10-8

S/s . It is close to the second slope of

Figure 4.2; in other words, after saturation point, which is expected.

By using these datum, diffusivity is calculated as 16.57 x 10-7

, 5.41 x 10-7

, 7.22 x 10-7

dm2

/s, respectively. When it is compared to the literature value that is 1.891*10-7

dm2

/s,

errors are found as 777%, 186%, 282% [3]. Possible reasons of this error is discussed in

discussion and recommendation parts; moreover, sample calculation of these results is shown

in the Appendices.

y = 4E-08x + 5E-05 R = 0.9456

0

0.00002

0.00004

0.00006

0.00008

0.0001

0.00012

0.00014

0.00016

0.00018

0.0002

0 500 1000 1500 2000 2500 3000 3500

Co

nd

uct

ivit

y (S

)

Time (s)

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5. DISCUSSION

In the experiment, the aim is to determine the diffusion coefficient of solution of KCl.

In order to reach the goal, conductivity data are recorded for 50 minutes by using conductivity

meter while the solution is diffusing from the diffusion cell to distilled water. During the

experiment, magnetic stirrer is used to mix the solution and obtain uniform mixture. The

graph of conductivity versus time is plotted and slope of the graph gives rate of change of

conductivity with time that is used to find diffusion coefficient value. After certain value,

slope of the graph shows rapid change; therefore, to reach more realistic value, the graph is

examined as three parts that are before the certain value, after the certain value and whole

values. As a result of calculation, diffusion coefficient of the second part is more accurate

than first and whole part. The reason is that at certain value, the solution reach saturation

point; therefore, it becomes more stable and linear. Thus, in error calculation, second part is

taken into consideration.

Moreover, conductivity data are taken from KCl solution for different concentrations

that are 0.001, 0.002, 0.004 and 0.006 M solutions. The graph of conductivity versus

concentration is plotted by using these data. Change in conductivity per change in molarity is

found as 0.1336 S/M. using the slope of best line.

Using three different slope values of the graph of conductivity versus time and the

value that is found from different concentrations, diffusion coefficient values are calculated as

16.57*10-7

, 5.41*10-7

and 7.22*10-7

dm2

/s. While slope of rate of change of conductivity with

time is taken into consideration for second part, error is calculated as 186%. This error shows

experimental value is not close enough to the literature value. One reason can be that

concentration value at the top of capillaries assumed as zero although it is not exactly zero.

Other reason is that the temperature at the time experiment is done may be different than the

value at literature. Furthermore, the conductivity data that is recorded for each 60 seconds

changes rapidly; therefore, data are not exact values. This can be causes an error too.

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6. CONCLUSION

The main aim of this experiment is determining the diffusion coefficient of KCl solution

at room temperature. In order to determination, Ficks Law of diffusion is used.After

equipments and chemicals are supplied , electrical conductivity of the solution is measured at

intervals of 60 seconds and total time is 3000 seconds. Purpose of the using of KCL solution

is to increase ions in water so that conductivity can be measured by conductivity meter. After

collecting data, conductivity versus time graph is plotted. After plotting graph, calibration is

made to calculate Cm. Calibration made with 0.001 M, 0.002 M, 0.004 M and 0.006 M of KCl

solutions. By using Ficks Law, the diffusion coefficients are found as 16.57*10-7 , 5.41*10-7

and 7.22*10-7

dm2

/s for 3 different dk/dt ( rate of change of conductivity with time ). When

these values are compared with the literature value which is 1.891*10-7

dm2

/s error is

calculated as 186%.

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7. RECOMMANDATION

The glass hook and honeycomb are filled with the solution should not have air bubbles

trapped.

Be sure glass diffusion cell outer surface is clean from salt before located the water.

Always check and rectify any leak.

Do not use any coarse or abrasive cleaners on glass components.

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8. REFERENCES

[1] Crooks, J. E. (1989). Measurement of diffusion coefficients. (Master's thesis, King's

College) Retrieved from http://www.qi.fcen.uba.ar/materias/fq1/FQpdfs/No

realizadas/Difusion Micrometro/difusionCKOOKS.pdf

[2] Experiment 39 liquid diffusion coefficient. (2013). Manuscript submitted for publication,

Chemical Engineering, Retrieved from

http://www.metu.edu.tr/~zculfaz/ChE320_files/Exp39_Measueremnt of Liquid

Diff Coeff_2013.pdf

[3] Lobo, V., Riberio, A. C., & Verissimo, L. M. (1998). Diffusion coefficients in aqueous

solutions of potassium chloride at high and low concentrations.Journal of

Molecular Liquids, 139-149. Retrieved from

https://estudogeral.sib.uc.pt/bitstream/10316/5282/1/filef165a90a02bd4844afe

291aad5da3cf4.pdf

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9. APPENDICES

Sample Calculation

V=1dm3

x=0.045 dm

d=0.01 dm

N=121

M=1 mol/dm3

Cm is found from graph 3.2 as 0.1336 S/M.

dk/dt values are determined for 3 different part. These are found as 7x10-8

, 3x10-8

and 4x10-8

S/s, respectively. After that DAB values determined according to equation written above.

DAB1 =16.57*10-7

dm2 /s

DAB2 = 5.41*10-7

dm2

/s

DAB3 = 7.22*10-7

dm2

/s

From using literature data DAB=1.89*10-7

dm2/s , errors are calculated for each DAB.

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