LIQUID DIFFUTION
LABORATORY REPORT
Submitted in partial fulfilment of the requirement of
BACHELOR OF ENGINEERING IN TECHNOLOGY
In
CHEMICAL ENGINEERING
In the
FACULTY OF ENGINEERING AND BUILT ENVIRONMENT
Of the
UNIVERSITY OF JOHANNESBURG
By:
SL Gumede
223129429 GROUP
2
Date: 11/03/2025
ABSTRUCT
Diffusion is a fundamental transport process that governs the movement of particles from regions
of higher concentration to lower concentration. In liquid-phase diffusion, solutes diffuse in a
solvent over time, leading to uniformity of concentration. The aim of this study was to quantify
the liquid diffusion coefficient of sodium chloride (NaCl) in distilled/deionized water using a
custom diffusion cell apparatus. The experiment involved suspending a cell in distilled water with
NaCl solutions of varying concentrations (1M, 2M, and 3M) with continuous monitoring of ionic
movement through conductivity measurements at fixed time intervals. The results provided an
insight into the role of concentration in the diffusion process and validated classical diffusion
theories, enhancing the knowledge of mass transport in electrolyte solutions.
i
DECLARATION
I solemnly declare that this report is entirely my original work. I attest that no part of this work
has been plagiarized, and I have diligently adhered to proper citation and referencing practices
for any material not of my own creation. I am fully cognizant of the university’s stringent
policies against plagiarism and affirm that this report upholds the standards of academic
integrity
Signature: ________________
ACKNOWLEGMENT
I am pleased to have been part of this amazing experiment and for being able to complete this
report. I would like to thank my group members T.O Chauke, A.S Darsot and A.G Hlophe. I
would also like to thank our Lab instructor for guiding us through the practical.
ii
Table of Contents
ABSTRUCT ................................................................................................................................................... i
DECLARATION ...........................................................................................................................................ii
ACKNOWLEGMENT ..................................................................................................................................ii
1.
INTRODUCTION ................................................................................................................................. 1
1.1
Theoretical Background ................................................................................................................. 1
1.2
Equations and Figures .................................................................................................................... 1
1.3
Objective ........................................................................................................................................ 2
2.
PROCEDURE ........................................................................................................................................ 3
3.
RESULTS AND DISCUSSIONS .......................................................................................................... 4
3.1
RESULTS ...................................................................................................................................... 4
3.2
Figures............................................................................................................................................ 4
3.3
Calculations.................................................................................................................................... 6
3.4
DISCUSSIONS .............................................................................................................................. 8
4.
CONCLUSION ...................................................................................................................................... 9
5.
RECOMENDATIONS ........................................................................................................................ 10
6.
REFERENCES .................................................................................................................................... 11
7.
APPENDIXES ..................................................................................................................................... 12
7.1
APPENDICES A ......................................................................................................................... 12
7.2
APPENDICES B .......................................................................................................................... 12
7.3
APPENDICES C .......................................................................................................................... 13
iii
1. INTRODUCTION
1.1 Theoretical Background
Diffusion is a fundamental transport process responsible for the transport of particles from regions
of greater concentration to lower concentration via random molecular motion (Cussler, 2009).
Liquid-phase diffusion involves molecules dispersing in a solvent, leading to the gradual
uniformity of concentration with time. The process is governed by Fick's laws of diffusion, which
provide a mathematical explanation of mass transfer in fluids (Crank, 1975). The diffusion
coefficient (D), the main parameter of Fick's second law, quantifies the rate of spreading of solutes
in a solvent and is subject to conditions such as temperature, viscosity, solute concentration, and
molecular size (Atkins & de Paula, 2018).
In electrolyte solutions, for instance, sodium chloride (NaCl) in water, diffusion occurs as
individual ions (Na+ and Cl-) move due to the influence of concentration gradients. Figure 1.1
illustrates this behaviore. Ion diffusion is influenced by ionic mobility, hydration effects, and
interionic interactions, and these will change the overall diffusivity of the solution (Bard &
Faulkner, 2001). Conductivity is directly connected with the migration of the charged species and
thus serves as a valuable tool for the observation of diffusion in electrolyte solutions (Levitt, 2012).
The relationship between conductance and ion concentration is described by the Nernst-Einstein
equation (Equation 1.1), which describes how the diffusion of ions relates to electric conductance
(Bockris & Reddy, 2002).
Understanding the liquid diffusivity of substances is very important in industries that deal with
gases, oil and polymers and other fluid based production. In gas and oil industries the diffusion
coefficient aids in comprehending the mass transfer mechanisms between the gas, oil, and aqueous
phases in increased oil recovery and CO2 sequestration. This information is crucial for maximizing
these procedures' efficacy and design. In polymer industries the longevity and durability of
polymer structures used in industrial applications can be greatly impacted by the diffusion of
liquids into and through polymers. For example, knowing the diffusion coefficient improves barrier
qualities and chemical resistance in fiber-reinforced polymers (FRP) used in chemically harsh
situations.
1.2 Equations and Figures
−4𝑉𝑥
𝐷 = 𝜋𝑑2 𝑁𝑀𝐶
𝑑𝑘
𝑚 𝑑𝑡
(Equation 1.1 Stokes-Einstein equation)
Figure 1.1 (https://atlas-scientific.com/blog/how-do-ions-increase-conductivity/)
1.3 Objective
The objective of this study is to determine the liquid diffusion coefficient of NaCl in
distilled/deionized water using a particular diffusion cell apparatus. The process involves
immersing a cell containing a known concentration of NaCl solution (1 M, 2 M, and 3 M) in
distilled water. Uniform mixing is guaranteed by a magnetic stirrer, and the continuously measured
ionic flow at fixed time intervals is done with a conductivity meter. Here, it is assumed that since
the lower end of the diffusion cell has a comparatively fixed concentration, the upper end would
have an effectively zero concentration, thus creating a very well-defined gradient of concentration.
By observing the evolution of conductivity with respect to time, which reflects the ionic diffusion,
the effective diffusion coefficient can be derived from the intrinsic relationship between
conductivity and diffusivity (Lee et al., 2012).
In the following sections, ionic diffusion theory, sequential experimental procedures, and
interpretation of resulting conductivity data will be discussed. This study not only confirms current
established diffusion theories but also details how ionic mobility varies as a function of NaCl
concentration in dilute water systems. Such findings are essential for optimization of industrial
processes as well as research protocols in which controlled mass transport is needed.
2
2. PROCEDURE
The liquid diffusion coefficient apparatus was utilized to determine the diffusivity of NaCl solution
in distilled water. A known concentration of NaCl solution was placed in a diffusion cell immersed
in distilled water. The experiment employed a magnetic stirrer and a conductivity meter to monitor
the progress of diffusion over time. The diffusion vessel was filled with 1L of distilled/de-ionized
water. The conductivity probe's BNC connector was connected to the socket on the conductivity
meter. The magnetic stirrer's main cable was plugged into the electrical supply, ensuring the correct
supply voltage. The conductivity meter and the magnetic stirrer were switched on. The following
NaCl solutions were prepared (1 M, 2 M and 4 M NaCl solution). The magnetic stirrer was
maintained at a range of 250-300 rpm.
The diffusion cell was filled with 1 M NaCl solution, ensuring the capillary tubes were in place.
The cell was carefully immersed in the distilled water, with the top of the capillaries positioned
about 5 mm below the water level. The conductivity meter and the magnetic stirrer were switched
on. After 5 minutes, the conductivity reading was recorded, and readings were taken at 5-minute
intervals for 20 minutes. Steps were repeated for the 2 M and 4 M NaCl solutions.
Apparatus
Figure 2.1: Liquid Diffusion Coefficients Apparatus (CELCHA2 Practical manual)
3
3. RESULTS AND DISCUSSIONS
3.1 RESULTS
Assumptions:
• The concentration at the lower end was taken to be constant, while the concentration at the
top end was effectively zero.
After obtaining the trend on conductivity vs time for the 1M, 2M and 4M in the graphs Figure 3.1,
𝑑𝑘
figure 3.2 and figure 3.3 from the liner equation 𝑑𝑡 was obtained as the gradient. The diffusivity
for each solution of NaCl was obtained using equation 1.1 and the results are illustrated by figure
3.4 for diffusivity coefficient vs concentration
3.2 Figures
Graphs of results
Time(s) Conductivity (mS)
1M NaCl Solution
0.000
295.000
350.000
300.000
311.000
600.000
324.000
340.000
900.000
335.000
y = 0.0407x + 297.4
1 200.000
344.000
330.000
320.000
310.000
300.000
290.000
0.000
200.000
400.000
600.000
800.000 1 000.000 1 200.000 1 400.000
Time(s)
Figure 3.1 (1M NaCl solution)
4
Time(s) Conductivity (mS)
2M NaCl Solution
0.000
355.000
700.000
300.000
474.000
600.000
524.000
600.000
900.000
559.000
500.000
1 200.000
586.000
400.000
y = 0.1823x + 390.2
300.000
200.000
100.000
0.000
0.000
200.000 400.000 600.000 800.000 1 000.000 1 200.000 1 400.000
Time(s)
Figure 3.2 (2M NaCl solution)
Time(s) Conductivity (mS)
4M NaCl Solution
0.000
539.000
590.000
300.000
557.000
600.000
567.000
580.000
900.000
y =577.000
0.0347x + 543.4
1 200.000
581.000
570.000
560.000
550.000
540.000
530.000
0.000
200.000
400.000
600.000
800.000 1 000.000 1 200.000 1 400.000
Time(s)
Figure 3.3 (4M NaCl solutions)
5
3.3 Calculations
−4𝑉𝑥 𝑑𝑘
𝜋𝑑2 𝑁𝑀𝐶𝑚 𝑑𝑡
−4(1)(0.045)
𝐷=
(0.0407)
𝜋(0.1)2 (121)(1)(0.112)
𝐷 = −0.0385𝑐𝑚2 /𝑠
𝐷=
Gradients obtained:
𝑑𝑘
𝑑𝑡
𝑑𝑘
𝑑𝑡
𝑑𝑘
𝑑𝑡
(1M NaCl solution) = 0.0407 𝑐𝑚2 /𝑠
(2M NaCl solution) = 0.1823 𝑐𝑚2 /𝑠 (calculation on Appendices C)
(4M NaCl solution) = 0.0347 𝑐𝑚2 /𝑠 (calculation on Appendices C)
Table 3.1 (Diffusivity coefficient obtained from calculations in Appendices 2)
1M NaCl solution
2M NaCl solution
4M NaCl solution
-D (cm2/s)
0.0172
0.0385
0.00366
Figure 3.4 (diffusivity vs concentration of NaCl)
6
Data obtained from literature
Figure 3.5 (Obtained from Mills, R., 1955. A remeasurement of the self-diffusion coefficients
of sodium ion in aqueous sodium chloride solutions. Journal of the American Chemical
Society, 77(23), pp.1551.)
7
3.4 DISCUSSIONS
After the experiment was done and calculations were complete, different values were obtained for
each NaCl solution. I was observed that conductivity is direcly propotional to the number of ions
in the distilled water. This is illustrated in figures 3.1, 3.2 and 3.3 It was observed that when the
concentration of NaCl was increased from 1M to 2M the diffusivity coefficient seemed to increase
from 0.0172 cm2/s to 0.0385 cm2/s but when it was changed to 4M concentration the diffusivity
coefficient dropped to 0.00366 cm2/s as illustrated in figure 3.4. This finding aligns with the data
found from literature (figure 3.5) where it was observed that as the consecration of NaCl increased
the diffusivity coefficient also increased but at a certain concentration it starts to drop down. The
initial increase at low moderate concentration (1M to 2M) is due to the increasing number of Na +
and Cl-. Diffusion is driven by concentration gradients, a higher number of Na+ and Cl- ions in
solution results in a higher effective diffusivity (Atkins & de Paula, 2018). The drop at very high
concentrations (4M) is due to an increase in viscosity at higher concentrations of NaCl which
effects ion mobility. According to Stokes-Einstein diffusivity is inversely proportional to viscosity,
which tells us that when viscosity of the solution increased due to higher concentration of NaCl
the diffusivity must decrease (Cussler, 2009). This can also be due to the fact that as concentration
increases beyond a certain threshold, interactions between ions become more pronounced. The
strong electrostatic attraction between Na+ and Cl- results in the formation of temporary ion pairs
or clusters, which decreases the number of freely moving ions available for diffusion (Bockris &
Reddy, 2002). Consequently, this leads to a reduction in the effective diffusion coefficient.
8
4. CONCLUSION
The experiment was successful in determining the liquid diffusion coefficient of NaCl in distilled
water solutions at different concentrations. The results revealed that as the concentration
increased from 1M to 2M, the diffusivity coefficient increased from 0.0172 cm²/s to 0.0385
cm²/s. At a higher concentration of 4M, the diffusivity coefficient plummeted to 0.00366 cm²/s.
This is in line with literature reports, which indicate that diffusivity increases with concentration
initially due to an increased number Na+ and Cl- ions for diffusion. However, above a certain
concentration, diffusivity is reduced as a result of higher viscosity and more intense interionic
interactions. At high concentrations of NaCl, the enhancement of viscosity decelerates the
mobility of ions, reducing diffusion efficiency, as the Stokes-Einstein equation forecasts. In
addition, enhanced electrostatic interactions also lead to the formation of ion pairs and clusters,
reducing the number of freely moving ions available for diffusion. These combined effects result
in the observed decrease in the diffusion coefficient at 4M concentration. Overall, the experiment
was quite enlightening on how NaCl concentration influences diffusion behavior and how
conductivity is directly proportional to concentration.
9
5. RECOMENDATIONS
For a more accurate conclusion for this experiment the duration of the experiment should be
increased, instead of 20 minutes the readings should extend to 40-60 minutes this will provide a
more detailed analysis of the diffusion coefficient. Instead of collecting data in intervals of 5
minutes’ data can be collected after 1 minutes this will also give more precise data to work with.
During the experiment temperature difference between the solutions was not considered and
diffusion is also impacted by temperature. The temperature for each solution (1M, 2M and 4M)
should have been measured and kept constant to ensure accurate results. The sample size could
have been increased where we would have the concentration of the solutions differ by 0.5M
extending from 0.5M to 6M, this would also give us more details on the trend of conductivity vs
time.
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6. REFERENCES
Atkins, P., & de Paula, J. (2018). Atkins' Physical Chemistry (11th ed.). Oxford University
Press.
Bard, A. J., & Faulkner, L. R. (2001). Electrochemical Methods: Fundamentals and
Applications (2nd ed.). Wiley.
Bockris, J. O’M., & Reddy, A. K. N. (2002). Modern Electrochemistry 1: Ionics (2nd ed.).
Springer.
Cussler, E. L. (2009). Diffusion: Mass Transfer in Fluid Systems (3rd ed.). Cambridge
University Press.
Crank, J. (1975). The Mathematics of Diffusion (2nd ed.). Oxford University Press.
Levitt, D. G. (2012). Conductivity and Diffusion in Electrolyte Solutions. Springer.
Mills, R., 1955. A remeasurement of the self-diffusion coefficients of sodium ion in aqueous
sodium chloride solutions. Journal of the American Chemical Society, 77(23), pp.1551
Lee, I.M., Shiroma, E.J., Lobelo, F., Puska, P., Blair, S.N. and Katzmarzyk, P.T., 2012.
11
7. APPENDIXES
7.1 APPENDICES A
𝑉 = volume of water in diffusion vessel, L (1L)
𝑥 = lenght of capillaries, cm (0.045cm)
𝑑 = capillaries diameter, cm (0.1cm)
𝑁 = number of capillaries (121)
𝑀 = molar concentration of NaCl solution, mol/L or M (1M, 2M and 4M)
𝐶m = conductivity change per unit molar concentration change, µS/mol.L (0.112 µS/mol.L)
k =conductivity µS t = time, s
𝑑𝑘
= rate of change in conductivity over time
𝑑𝑡
NaCl = sodium chloride (table salt)
7.2 APPENDICES B
(Equation 1.1) this will be used to calculate diffusivity coefficient foe each concentration.
Calculation of diffusivity coefficient for 2M:
−4𝑉𝑥
𝑑𝑘
𝐷 = 𝜋𝑑2𝑁𝑀𝐶𝑀 𝑑𝑡
−4(1)(0.045)
𝐷=
𝜋(0.1)2(121)(2)(0.112) (0.1823)
𝐷 = −0.00366𝑐𝑚2/𝑠
12
Calculation of diffusivity coefficient for 4M:
−4𝑉𝑥
𝑑𝑘
𝐷 = 𝜋𝑑2𝑁𝑀𝐶𝑀 𝑑𝑡
−4(1)(0.045)
𝐷 = 𝜋 (0.1)2(121)(4)(0.112) (0.0347)
𝐷 = −0.0172𝑐𝑚2/𝑠
7.3 APPENDICES C
Time, t
1 M NaCl Solution
(s)
Conductivity, k (µS)
2 M NaCl Solution
Conductivity, k(µS)
4 M NaCl Solution
Conductivity, k(µS)
0
295
355
539
300
311
474
557
600
324
524
567
900
335
559
577
1200
344
586
581
13