exp_02_formal_grp_02_a2_1202036

Study of Diffusion

Mahe Rukh

Student number: 1202036

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Course Number: ChE-302

Course Title: Chemical Engineering Laboratory-II

Experiment Number: 02

Name of the Experiment: Study of Diffusion

Submitted by:

Mahe Rukh

Student Number: 1202036

Section: A2 Group Number: 02

Department of Chemical Engineering

Partners’ Student Numbers: 1202037

1202038

1202039

1202040

Date of Performance: 16/09/15

Date of Submission: 10/10/15

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Acknowledgement

I, Mahe Rukh, a student of chemical engineering department of Bangladesh University of

Engineering and Technology would like to express my profound gratitude towards my course

teacher Dr. Syeda Sultana Razia for granting me the opportunity to perform an experiment on study

of diffusion. This theorem unquestionably contributes a great deal to chemical engineering and it

has been a great experience to have been able to have insight on this theorem experimentally.

Furthermore, I would also like to acknowledge with much appreciation the crucial role of the lab

assistants and other course teachers who gave the permission to use all required equipment and

the necessary materials to complete the task. A special thanks goes to my team members who

helped to assemble the parts and gave suggestion about the task. I have to appreciate the guidance

given by my respected course teacher Dr. Syeda Sultana Razia who helped me to coordinate the

experiment and helped me to write this report.

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Table of Contents

Number of

topic

Name of topic Page number

1 Summary 1

2 Introduction 2

3 Theory 2-4

4 Experimental work

4-5

4.1 Apparatus 4

4.2 Experimental setup 4

4.3 Procedure 5

5 Observed data 5-6

6 Calculated data 7

7 Sample calculation 7-8

8 Graphical representation 9-10

9 Results 10

10 Discussions 11-12

10.1 Comment on results 11

10.2 Comment on graphs 12

11 Conclusion 12

12 Nomenclature 12-13

13 Reference 13

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List of Tables

Number of

tables

Name of tables Page number

1 Table of diffusion co-efficient and slope

obtained from graph

6

2 Table of diffusion co-efficient and

slope obtained from graph

7

List of Figures

Number of

figures

Name of figures Page number

1 Experimental setup for determining

liquid diffusivity of NaCl solution

4

2 Conductivity vs. Time for 1M NaCl

solution

9

3 Conductivity vs. Time for 4M NaCl

solution

10

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C h e m i c a l E n g i n e e r i n g L a b o r a t o r y - i i

1.0 Summary

The purpose of this experiment was to determine diffusion co-efficient of 1M and 4M NaCl solution

in deionized water. To determine diffusion co-efficient, we measured conductivity of deionized

water (in which NaCl was being diffused) at particular interval of time. And we can see from data

that conductivity increased with time in both cases due to diffusion of NaCl in water. From graph of

time vs. conductivity we measured slope and using this we determined the value of diffusion co-

efficient. It was found that the value of diffusion co-efficient for 1M and 4M solution are respectively

3.96x10-5 cm2/s and 4.574x10-5 cm2/s which deviate from literature value as several inaccuracies

were introduced during the experiment.

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2.0 Introduction

Diffusion is regarded as the motion of chemical species (on molecular or atomic level) from a region

of high concentration to a region of low concentration which results in complete homogenization of

a mixture. This phenomenon indicates vast range of applications in the field of chemical industries,

process engineering, biomedical engineering as well as in environmental protection where it forms

the basis of separation and helps in purification of materials. Consequently, mass transfer as a result

of diffusion is a fundamental part of chemical engineering. The objective of this experiment is to

determine diffusion co-efficient of NaCl solution in deionized water. The rates at which substances

spread by diffusion is called diffusion co-efficient. Diffusion co-efficient can be anticipated

theoretically or from empirical equations. It can also be found experimentally. To determine

diffusion co-efficient, we have used Fick’s law derived by Adolf Fick in 1855. According to this

law the value of diffusion co-efficient in aqueous solution depends on molecular size and

temperature and pressure. The values of diffusion co-efficients obtained from this experiment is

compared to theoretical value and reasons of discrepancies is discussed in the discussion section.

3.0 Theory

Adolf Fick was the first person to put diffusion on quantitative analysis by taking on mathematical

equation of heat conduction derived by Fourier in 1822. When concentration gradient exists within

a fluid, each species in the fluid appears to flow in such a direction to decrease concentration

gradient. This is termed as mass transfer. Rate of diffusion is given by

𝐉 = −𝐃𝛛𝐂

𝛛𝐱 … … … … … . . (𝟏)

Where

D= diffusivity, cm2/s

J= rate of transfer per unit area of section, mol/cm2.s

C= concentration of diffusing substance

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X= the space coordinate measured normal to the section

In dilute solutions D can be considered as a constant, while in others it depends highly on

concentration. If J, the amount of material diffusing, and C, the concentration, are both expressed in

terms of the same unit of quantity then it is clear from equation (1) that D is independent of this unit

and has dimensions (length)2 (time)-1, e.g. cm2 s -1

Diffusion can take place in either a gas or liquid phase or in both phases at the same time. The

negative sign in equation (1) arises because diffusion occurs in the direction opposite to that of

increasing concentration.

The capillaries used in the diffusion apparatus limit the diffusion to one dimension. At the lower end

the concentration is assumed constant and the concentration at the top is assumed to be effectively

zero during the experiment.

In the experiment the rate of change of moles in solution is equivalent to the rate of moles diffused

through the capillaries.

By expanding Eq. (1) we get

𝐕

𝐂𝐌

𝐝𝐤

𝐝𝐭= −𝐃

𝛑𝐝𝟐

𝟒𝐍

𝐌

𝐱

Rearranging gives

𝐃 =𝟒𝐕𝐱

𝛑𝐝𝟐 𝐍𝐌𝐂𝐌

𝐝𝐤

𝐝𝐭… … … … … … … . . (𝟐)

Where V = volume of water in diffusion vessel, L

𝒅𝒌

𝒅𝒕 = rate of conductivity change over time

CM= conductivity change per unit molar concentration change, 𝜇𝑆

𝑚𝑜𝑙𝐿⁄

d = diameter of capillaries, cm

x = length of capillaries, cm

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M = molar concentration of NaCl solution, mol/L

N = number of capillaries

4.0 Experimental Section

4.1 Apparatus:

Conductivity meter

Deionized water

Magnetic stirrer

1M and 4M solution of NaCl

Stopwatch

4.2 Experimental Setup:

Fig 01: Experimental setup for determining liquid diffusivity of NaCl solution

4.3 Experimental Procedure:

The diffusion vessel was filled with 1.1 L of de-ionized water

After that the diffusion cell was filled with NaCl solution having concetration of 1M.

The cell needs to be filled fully and any excess amount of solution should be wiped off.

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Then the cell was immersed into the distilled water till the top of the capillaries is about

5mm below the surface of water.

The conductivity meter and the magnetic stirrer were switched on in the next step.

After 10 minutes, the conductivity reading was recorded. At intervals of 5 minutes

reading were recorded for 40 minutes

The procedure described above was repeated for 4M NaCl solution.

5.0 Observed data

Volume of water, V =1.1 L

Length of capillaries, x = 0.5 cm

Diameters of capillaries, d = 0.1 cm

Number of capillaries, N = 97

Molar concentration of NaCl solution=1M and 4M

Electrical conductivity change per unit molar concentration change, Cm= 4.1x105 mol/L

Table:01- Table of observed data from conductivity meter

Number of

observation

Reading from conductivity meter

1 M NaCl 4 M NaCl

Time (s) EC (µS) Time (min) EC (µS)

1 300 157.4 300 709.2

2 600 179.1 600 834.4

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3 900 191.6 900 894.4

4 1200 199.8 1200 937.2

5 1500 207.2 1500 968.2

6 1800 212.8 1800 997.5

7 2100 217.3 2100 1018

8 2400 220.7 2400 1038

6.0 Calculated data

Table 02: Table of diffusion co-efficient and slope obtained from graph

Concentration of

NaCl solution Obtained slope,

𝑑𝑘

𝑑𝑡

(From graph)

Conductivity

change per unit

molar conc., CM

µS/(mol/L)

Diffusion coefficient of NaCl

(cm2

s)

Experimental Theoretical

1M 0.0225

4.1x105

3.96 × 10−5 1.611×10-5

4M 0.1093 4.576 × 10−5 -

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7.0 Sample Calculation

7.1 Determination of diffusivity

1M NaCl solution:

From figure-02

Slope = dk

dt= 0.028 µS/min

Now, D = 𝟒𝑽𝑿

𝛑𝐝𝟐𝐍𝐌𝐂𝒎

𝐝𝐤

𝐝𝐭

= 4×.0011×0.005

π×(0.001)2×97×1×410000 × 0.0225

= 3.96× 10-5 cm2/s

4M NaCl solution:

From figure-03

Slope = dk

dt= 0.1039 µS/min

Now, D = 𝟒𝐕𝐗

𝛑𝐝𝟐𝐍𝐌𝑪𝒎

𝐝𝐤

𝐝𝐭

= 4×.0011×0.005

π×(0.001)2×97×4×410000 × 0.1039

= 4.576× 10-5 cm2/s

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8.0 Graphical representation:

Fig 02: Conductivity vs. Time for 1M NaCl solution.

y = 0.0225x + 170.29

0

50

100

150

200

250

0 500 1000 1500 2000 2500 3000

Conduct

ivit

y o

f 1M

solu

tion(µ

S)

Time(s)

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Fig 03: Conductivity vs. Time for 4M NaCl solution.

9.0 Results:

Diffusion co-efficient for 1M NaCl solution = 3.96x10-5 cm2/s

Diffusion co-efficient for 1M NaCl solution= 4.576 x10-5 cm2/s

10.0 Discussions:

10.1 Comment on result:

We see from the experiment that the diffusivity values obtained deviates from the theoretical value

1.611x10-5 cm2/s. the possible reasons for this deviation and solutions are depicted below:

y = 0.1093x + 791.4

0

200

400

600

800

1000

1200

0 500 1000 1500 2000 2500 3000

Conduct

ivit

y o

f 4M

solu

tion(µ

S)

Time(s)

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The presence of air bubbles under the capillaries can hinder the rate of diffusion. Air bubble

can be formed if the walls of capillary tubes are wet or if the solution is poured too slowly

or wrongly in the diffusion tube.

No air bubble formation must be ensured by filling diffusion cell slowly and using porous

plate can ensure solute and solvent pass spontaneously

the solution not being stirred well the concentration of the solution can be greater near the

diffusion surface than the other regions. Hence accurate values of conductivity will not be

achieved.

This problem can be dealt by using more than one conductivity sensors at various depths of

the solution and averaging the values obtained from them.

It is assumed that convection occurred during this experiment which can substantially affect

the accuracy of this experiment. The rotation of magnetic stirrer can be one probable reason

which introduces convection in solution.

Diffusivity is dependent on temperature. In the experiment temperature was assumed

constant. Constant temperature cannot be ensured as the apparatus was exposed to

surroundings.

If the experiment was done in an enclosed surrounding, we could assure constant temperature

of water bath and diffusion cell. Minimum contact with the surrounding should be checked.

The vessel not being thoroughly cleaned it contained sodium chloride residue at the walls

which added to the conductivity of the solution during the experiment.

No Accumulation of sodium chloride on the wall of the vessel should be made sure by

thoroughgoing cleaning of apparatus.

Evaporation of water from vessel is not unlikely which can reduce the volume of water

present in the vessel and affecting the value of diffusion co-efficient in turn which we assume

happened during the experiment

A lid or cover can be used to minimize this problem.

There was steep concentration gradient between two solutions. And any delay in starting the

stopwatch can add to error.

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10.2 Comment on graphs:

The conductivity data recorded at t=0s were very low. As a result, those points are not plotted

on the graphs.

From the graphs we could see the conductivity in both cases increased with time which is

in accordance the fact that availability of ions increases as more time passes by.

The slope found for 4M solution from graph was steeper than 1M solution which indicates

when concentration of NaCl solution increases, there will be more ions available in the

solution of diffusion vessel. So, the conductivity also increases.

11.0 Conclusion:

The value achieved from our experiment is of order 10-5cm2/s which is close to literature value.so

the process followed in this experiment can be used effectively to find out diffusion co-efficient for

various liquids. However, this procedure is only valid for solutes which dissociate in water

completely. It was seen that the co-efficient we found was approximately 100% greater than the

theoretical value which is due to various errors introduced during experiment. And in literature value

the effect of hydration was neglected. The effect of hydration increases the value of co-efficient

gained experimentally. One should keep in mind for any slight error introduced, magnitude of

diffusion co-efficient can deviate in large amount. Therefore, the application may have large

consequence in real situations. Hence the experimented should be performed in meticulously.

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12.0 Nomenclature:

Symbol Definition Unit

J Diffusion flux across unit area mol

cm2s

D Diffusivity cm2

s

𝛛𝐂

𝛛𝐱

Concentration gradient in the

x-direction

molcm3⁄

cm

V Volume of water L

X Length of capillaries cm

N Number of capillaries

M Molar concentration of NaCl

solution

mol/L

Cm Electrical conductivity

change per unit molar

concentration change

𝛍𝐒

𝐦𝐨𝐥𝐋⁄

𝐝𝐤

𝐝𝐭

Rate of conductivity change

over time

d Diameter of capillaries cm

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13.0 References:

Measurement of Liquid Diffusion Coefficient Biology Essay,UKESSAYS, Retrieved from

http://www.ukessays.com/essays/biology/measurement-of-liquid-diffusion-coefficient-

biology-essay.php

Liquid diffusion co-efficient, UEMK2411 Chemical Engineering Lab I Manual, Retrieved

from

http://www.utar.edu.my/fes/file/UEMK2411%20ChemEng%20Lab%20I%20Manual-

200905-2.pdf

Mass transfer by Diffusion, Institute of Chemical Engineering, Polish Academy of Sciences,

Retrieved from

http://www.eolss.net/sample-chapters/c06/e6-34-01-07.pdf

http://www.utar.edu.my/fes/file/UEMK2411%20ChemEng%20Lab%20I%20Manual-200905-2.pdf

http://www.utar.edu.my/fes/file/UEMK2411%20ChemEng%20Lab%20I%20Manual-200905-2.pdf

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Marking Scheme: Formal Report

Name: Mahe Rukh

Student number: 1202036

Section and % marks allocated Marks

Summary (5%)

Introduction (10%)

Theory (10%)

Experimental Work (10%)

Observed Data (5%)

Calculated Data (5%)

Sample Calculation (5%)

Graphs (10%)

Results and Discussion (10%)

Conclusion (5%)

References and Nomenclature (5%)

Writing Quality and Style (10%)

Overall Presentation (10%)

Total (100%)

Study of Diffusion

C h e m i c a l E n g i n e e r i n g L a b o r a t o r y - I I

exp_02_formal_grp_02_a2_1202036

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