COURSE NUMBER ChE 302

TITLE STUDY OF DIFFUSION

EXPERIMENT NO 02

DATE OF PERFORMANCE 15/01/2014

DATE OF SUBMISSION 22/01/2014

SUBMITTED TO

DR.MD.EASIR ARAFAT KHAN

ASSISTANT PROFESSOR

DEPARTMENT OF CHEMICAL ENGINEERING

BUET,DHAKA-1000,BANGLADESH

SUBMITTED BY

KAMONASHIS SARKAR (TENDUL)

STUDENT ID 1002008(L-3/T-1)

GROUP NUMBER 02 (A1)

PARTNERS STUDENT ID 1002006,1002007,1002009,1002010

CHEMICAL ENGINEERING DEPARTMENT

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

Summary

The main objective of this experiment is to determine the liquid diffusion co-efficient of NaCl solution in

distilled water by using the concept of mass transfer.Mass transfer is the net movement of mass from one

location, usually meaning a stream, phase, fraction or component, to another. Mass transfer occurs in

many processes, such as absorption, evaporation, adsorption, drying, precipitation, membrane filtration,

and distillation.The phrase is commonly used in engineering for physical processes that involve diffusive

and convective transport of chemical species within physical systems. Mass transfer takes place in either a

gas phase or a liquid phase or in both simultaneously. Mass transfer is a result of diffusion. Diffusion is

the phenomenon of material transport by atomic motion. The driving force of diffusion process is the

concentration gradient of the component. Diffusivity is one of the most important fluid properties.

Diffusion is of great importance in Fluid flow and mass transfer operations such as chemical process plant

design, catalyst design in chemical industry, formation of alloys etc.

Experimental setup

Figure1 Schematic diagram for liquid diffusivity measurement

Diffuser

Conductivity

meter

Capillaries

Conductivity

Probe

Magnetic

stirrer

Stirrer bar

Observed data

Volume of water, V = 1.1 Liter

Length of capillaries, x = 0.5 cm

Diameter of capillaries, d = 0.1 cm

Numbers of capillaries, N = 97

Table1 Observed data for determining diffusivity of NaCl solution.

Observation

number

Time (seconds)

1M NaCl solution 4M NaCl solution

Conductivity, k (µS) Conductivity, k (µS)

01 0 0.70 11.29

02 300 83.42 641.60

03 600 100.60 758.90

04 900 114.20 845.60

05 1200 124.20 892.50

06 1500 133.20 940.50

07 1800 141.20 980.30

08 2100 148.60 1013.00

09 2400 155.60 1045.00

Calculated data

Observation

number

Concentration

of NaCl

solution

,M(mol/L)

Rate of conductivity change

over

time(slope),dk/dt(µs/sec)

Electrical conductivity

change per unit molar

concentration

change,Cm(µs/mol/L)

Diffusivity

,D(cm2/sec)

01 1 0.0331 85543.96 2.79×10-4

02 4 0.1804 85543.96 3.81×10-4

Graphs

y = 0.0331x + 80.381 for 1M NaCl solution

0

20

40

60

80

100

120

140

160

180

0 500 1000 1500 2000 2500 3000

Con

du

ctiv

ity,µ

s

Time,sec

Graph-1(Conductivity vs time)

y = 0.1804x + 646.12 for 4M NaCl solution

0

200

400

600

800

1000

1200

0 500 1000 1500 2000 2500 3000

Con

du

ctiv

ity,µ

s

Time,sec

Graph2(Conductivity vs time)

Graph3 Determination of conductivity change over time

y = 0.0331x + 80.381

for 1M solution

y = 0.1804x + 646.12 for 4M solution

0

200

400

600

800

1000

1200

0 500 1000 1500 2000 2500 3000

Co

nd

uct

ivit

y,µ

s

Time,sec

Graph3(Conductivity vs time)

Sample calculation

Determination of electrical conductivity change per unit molar concntration change

Water was 500ml and 2ml 1M NaCl solution was added,then we can write

V1S1=V2S2 V1=Volume of NaCl solution=2ml

S2=(V1S1/V2) S1=Concentration of NaCl solution

=1M

S2=(2×1)/502 V2=Volume of solution=502ml

S2=3.98×10-3M S2=Concentration of solution=?

Water was 500ml and 4ml 1M NaCl solution was added,then we can write

V1S1=V3S3 V1=Volume of NaCl solution=2ml

S3=(V1S1/V3) S1=Concentration of NaCl solution

=4M

S3=(4×1)/504 V3=Volume of solution=502ml

S3=7.94×10-3M S3=Concentration of solution=?

Water was 500ml and 6ml 1M NaCl solution was added,then we can write

V1S1=V4S4 V1=Volume of NaCl solution=2ml

S4=(V1S1/V4) S1=Concentration of NaCl solution

=1M

S4=(6×1)/506 V4=Volume of solution=502ml

S4=11.86×10-3M S4=Concentration of solution=?

From conductivity meter we have measured conductivity(K).

when S2=3.98×10-3

M then K2=400.9 µs

when S3=7.94×10-3

M then K3=741 µs

when S4=11.86×10-3

M then K4=1075 µs

Now electrical conductivity change per unit molar conductivity change(C)

C1=(K3-K2)/(S3-S2) =(741-400.9)/((7.94-3.98)×10-3) =85883.84 (µs/mol/L)

C2=(K4-K3)/(S4-S3) =(1075-741)/((11.86-7.94)×10-3) =85204.08 (µs/mol/L)

Cm=(C1+C2)/2 =(85883.84+85204.08)/2 =85543.96 (µs/mol/L)

Here

Diffusivity, D=

Wher V=Volume of water in diffusion vessel,(mol/L).

x=Length of capillaries,(cm).

d=Capillaries diameter,(cm).

N=Number of capillaries.

M=Molar concentration of NaCl solution,(mol/L).

CM=The electrical conductivity change per unit molar concentration

change,(µs/mol/L).

=Rate of conductivity change over time,(µs/sec).

For 1M NaCl solution

D=

D=2.79×10-4

cm2/s

For 4M NaCl solution

D=

D=3.81×10-4

cm2/s

Results and Discussions

In this experiment for different values of concentration we have obtained the following results:

For 1M NaCl solution the value of diffusivity is 2.79×10-4

cm2/s

For 4M NaCl solution the value of diffusivity is 3.81×10-4

cm2/s

Diffusion coefficient is inversely proportional to concentration and directly proportional to the

slope of conductivity vs. time graph. As we use the more concentrated solution, the slope of the

graph also increases Now here we have two plots (concentration vs time).Both the plots are

y=mx+c types state line.Their slopes are

For 1M NaCl solution the value of slope is 0.0331 (µs/sec)

For 4M NaCl solution the value of slope is 0.1804 (µs/sec)

Actually diffusivity needs to be constant for both case and the statelines needs to be parallel for

satisfying this condition.But in reality are not parallel and even they intersect each other at a

certain point on the graph paper.Thats why there are some ups and downs in the results we

have.Behind this result there are some following reasons which are listed below:

a) Trapped air bubbles in the capillaries which can hinder mass transfer.

b) Incomplete filling of the cell could create a trapped air pocket.

c) Overfilling of the cell, resulting in NaCl spilling out into the water when the cell is placed in

the diffusion vessel.

d) As the 4M NaCl solution was not freshly prepared, its concentration may not be precisely

equal to 4M.

e) In order to keep the external concentration of salt as low as possible, and in order to get

conductivity readings that reflect the total amount of salt in the tank, we have to keep fluids

in the tank well-mixed. To keep the fluids well-mixed a magnetic stirrer were used.The rate

of stirring should be kept low enough to prevent the fluid flow out of the capillaries.

f) Conductivity vs. time graph for 1M and 4M solutions should be parallel to each other. But

from our experiment it is seen that the lines for 1M and 4M solutions intersect each other. We

were supposed to use dematerialized water. Initial conductivity reading for 1M solution were

found higher than it should be for completely dematerialized water which means the 1M

solution we have used were contaminated. May be this contamination were responsible for

the change in the relationship graph between conductivity and time.

g) Fick’s first law holds good when concentration is constant(steady state) and when it varies

with time then fick’s second law appears to satisfy the condition.The second law is

But when steady state condition applies to fick’s second law it becomes

fick’s first law that is

where c=concentration, D=diffusivity , x=X-direction, j=diffusion flux.

These two law can describe the reason of deviation from ideal condition.

List of References

Mc Cab, Smith , Harriott Unit Operation of Chemical Engineering, Sixth edition

Cussler E.L., Diffusion-Mass transfer in fluid systems, third edition

Holman J.P., Heat Transfer, Ninth edition, McGraw-Hill

http://en.wikipedia.org/wiki/Mass_transfer

http://wiki.answers.com/Q/What_are_the_factors_affecting_the_rate_of_diffusion

http://classof1.com/homework_answers/chemical_engineering/ficks_law/