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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
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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 Fick’s 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, Ω
−1
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N: Number of capillaries
Cm: Change in conductivity per change in molarity (dilute solutions) Ω−1∙ L∙ mol−1
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
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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 Fick’s 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 R² = 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 C o n d u ct iv it y (S) Concentration (M)
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Table 4.1 Conductivity data for each minute during fifty minutes
t (min) k (μS) t (min) k (μS) t (min) k (μS)
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 R² = 0.9094 y = 3E-08x + 7E-05 R² = 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 C o n d u ct iv it 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 R² = 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 C o n d u ct iv it 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, Fick’s 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 Fick’s 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.
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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/dm3Cm 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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