EXPERIMENT 4 :
DETERMINATION OF DIFFUSION COEFFICIENT
INTRODUCTION
Fick's first law states that the flux of material (amount dn in time dt ) across a given plane (area A) is proportional to the concentration gradient dc/dx.Fick's first law relates the diffusive flux to the concentration under the assumption of steady state. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient, or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low concentration across a concentration gradient.
Fick's first law states that the flux of material (amount dn in time dt ) across a given plane (area A) is proportional to the concentration gradient dc/dx.Fick's first law relates the diffusive flux to the concentration under the assumption of steady state. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient, or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low concentration across a concentration gradient.
Meanwhile Fick's Second Law
predicts how diffusion causes the concentration to change with time. Fick's laws of
diffusion describe diffusion and can be used to solve for the diffusion
coefficient, D. They were derived by Adolf Fick in 1855.
OBJECTIVE
To determine the diffusion coefficient by using the graph
To determine the diffusion coefficient by using the graph
MATERIALS
Agar powder
Agar powder
Ringer's solution 250ml
Crystal violet 1:500000, 1:200, 1:400, 1:600
Bromothymol blue 1:500000, 1:200, 1:400, 1:600
Crystal violet 1:500000, 1:200, 1:400, 1:600
Bromothymol blue 1:500000, 1:200, 1:400, 1:600
APPARATUS
Test tubes
Test tubes
Test tube caps
Test tube rack
Beaker 500 mL
Test tube rack
Beaker 500 mL
Heating bath
Glass rod
Measuring cylinder
Glass rod
Measuring cylinder
EXPERIMENT PROCEDURE
1. 250ml agar is prepared in
Ringer's solution.
2. The agar is divided into six
test tubes and is allowed to cool at room temperature.
3. The agar is prepared in
another test tube that has already been added with 1:500000 crystal
violet, this will be used as the standard to measure the colour distance
resulting from the crystal violet diffusion.
4. 5ml of each crystal violet
solution is placed on the gels that was prepared and is closed to prevent
evaporation and is stored at temperature 28 degree celcius and 37 degree
celcius.
5. The distance between the
interface of this gel solution with the end of the crystal violet area that has
color equivalent to the standard is measured accurately.
6. The average of several
measurements are obtained, this value is x in meter.
7. The values of x after 2 hours
and at suitable time distances up till 2 weeks are recorded.
8. The graph for values of x2 (in
M2) against time (in seconds) for each of the concentration used is
plotted.
9. The diffusion coefficient D
from the slope of the graph at temperature 28 and 37 degree celcius are
calculated.
10. The molecular weight of the
crystal violet is calculated using the equation N and V.
11. Steps 3 until step 10
are repeated by using bromothymol blue.
RESULT
a) Crystal Violet solution at 28oC
System
|
Time (s)
|
x (m)
|
X2
(x10-4 m2)
|
Slope of graph
|
D
(m2s-1)
|
Temperature (oC)
|
Average Diffusion Coefficient, D
(x10-10 m2s-1)
|
Crystal violet solution
with dilution 1:200
|
86400 (Day 1)
|
0.014
|
1.96
|
4 x 10-9
|
1.2779 x 10-10
|
28
|
|
172800 (Day 2)
|
0.017
|
2.89
|
28
|
||||
259200 (Day 3)
|
0.022
|
4.84
|
28
|
||||
345600 (Day 4)
|
0.028
|
7.84
|
28
|
||||
432000 (Day 5)
|
0.039
|
15.21
|
28
|
||||
518400 (Day 6)
|
0.042
|
17.64
|
28
|
||||
604800 (Day 7)
|
0.046
|
21.16
|
28
|
||||
|
|
||||||
Crystal violet solution
with dilution 1:400
|
86400 (Day 1)
|
0.012
|
1.44
|
3 x 10-9
|
1.1150 x 10 -10
|
28
|
1.4171
|
172800 (Day 2)
|
0.014
|
1.96
|
28
|
||||
259200 (Day 3)
|
0.020
|
4.00
|
28
|
||||
345600 (Day 4)
|
0.025
|
6.25
|
28
|
||||
432000 (Day 5)
|
0.032
|
10.24
|
28
|
||||
518400 (Day 6)
|
0.035
|
12.25
|
28
|
||||
604800 (Day 7)
|
0.036
|
12.96
|
28
|
||||
|
|
||||||
Crystal violet solution
with dilution 1:600
|
86400 (Day 1)
|
0.005
|
0.25
|
5 x 10-9
|
1.8583 x 10-10
|
28
|
|
172800 (Day 2)
|
0.006
|
0.36
|
28
|
||||
259200 (Day 3)
|
0.007
|
0.49
|
28
|
||||
345600 (Day 4)
|
0.008
|
0.64
|
28
|
||||
432000 (Day 5)
|
0.015
|
2.25
|
28
|
||||
518400 (Day 6)
|
0.020
|
4.00
|
28
|
||||
604800 (Day 7)
|
0.026
|
6.76
|
28
|
b) Bromothymol blue solution at 28oC
System
|
Time (s)
|
x (m)
|
X2
(x10-4 m2)
|
Slope of graph
|
D
(m2s-1)
|
Temperature (oC)
|
Average Diffusion Coefficient, D
(x10-11 m2s-1)
|
Bromothymol blue solution
with dilution 1:200
|
86400 (Day 1)
|
0.013
|
1.69
|
2 x 10-9
|
6.3894 x 10-11
|
28
|
|
172800 (Day 2)
|
0.015
|
2.25
|
28
|
||||
259200 (Day 3)
|
0.017
|
2.89
|
28
|
||||
345600 (Day 4)
|
0.020
|
4.00
|
28
|
||||
432000 (Day 5)
|
0.031
|
9.61
|
28
|
||||
518400 (Day 6)
|
0.033
|
10.89
|
28
|
||||
604800 (Day 7)
|
0.037
|
13.69
|
28
|
||||
|
|
||||||
Bromothymol blue solution
with dilution 1:400
|
86400 (Day 1)
|
0.011
|
1.21
|
3 x 10-9
|
1.0516 x 10 -10
|
28
|
8.1128
|
172800 (Day 2)
|
0.012
|
1.44
|
28
|
||||
259200 (Day 3)
|
0.013
|
1.69
|
28
|
||||
345600 (Day 4)
|
0.015
|
2.25
|
28
|
||||
432000 (Day 5)
|
0.027
|
7.29
|
28
|
||||
518400 (Day 6)
|
0.030
|
9.00
|
28
|
||||
604800 (Day 7)
|
0.039
|
15.21
|
28
|
||||
|
|
||||||
Bromothymol blue solution
with dilution 1:600
|
86400 (Day 1)
|
0.003
|
0.09
|
0.00002
|
7.4331 x 10 -11
|
28
|
|
172800 (Day 2)
|
0.005
|
0.25
|
28
|
||||
259200 (Day 3)
|
0.007
|
0.49
|
28
|
||||
345600 (Day 4)
|
0.010
|
1.00
|
28
|
||||
432000 (Day 5)
|
0.025
|
6.25
|
28
|
||||
518400 (Day 6)
|
0.029
|
8.41
|
28
|
||||
604800 (Day 7)
|
0.035
|
12.25
|
28
|
c) Crystal Violet solution at 37oC
System
|
Time (s)
|
x (m)
|
X2
(x10-4 m2)
|
Slope of graph
|
D
(m2s-1)
|
Temperature (oC)
|
Average Diffusion Coefficient, D
(x10-10 m2s-1)
|
Crystal violet solution
with dilution 1:200
|
86400 (Day 1)
|
0.011
|
1.21
|
5 x 10-9
|
1.5974 x 10-10
|
37
|
|
172800 (Day 2)
|
0.015
|
2.25
|
37
|
||||
259200 (Day 3)
|
0.025
|
6.25
|
37
|
||||
345600 (Day 4)
|
0.030
|
9.00
|
37
|
||||
432000 (Day 5)
|
0.040
|
16.00
|
37
|
||||
518400 (Day 6)
|
0.045
|
20.25
|
37
|
||||
604800 (Day 7)
|
0.052
|
27.04
|
37
|
||||
|
|
||||||
Crystal violet solution
with dilution 1:400
|
86400 (Day 1)
|
0.010
|
1.00
|
5 x 10-9
|
1.7526 x 10 -10
|
37
|
1.2406
|
172800 (Day 2)
|
0.013
|
1.69
|
37
|
||||
259200 (Day 3)
|
0.025
|
6.25
|
37
|
||||
345600 (Day 4)
|
0.029
|
8.41
|
37
|
||||
432000 (Day 5)
|
0.039
|
15.21
|
37
|
||||
518400 (Day 6)
|
0.043
|
18.49
|
37
|
||||
604800 (Day 7)
|
0.052
|
27.04
|
37
|
||||
|
|
||||||
Crystal violet solution
with dilution 1:600
|
86400 (Day 1)
|
0.005
|
0.25
|
0.00001
|
3.7166 x 10 -11
|
37
|
|
172800 (Day 2)
|
0.006
|
0.36
|
37
|
||||
259200 (Day 3)
|
0.007
|
0.49
|
37
|
||||
345600 (Day 4)
|
0.008
|
0.64
|
37
|
||||
432000 (Day 5)
|
0.012
|
1.44
|
37
|
||||
518400 (Day 6)
|
0.020
|
4.00
|
37
|
||||
604800 (Day 7)
|
0.026
|
6.76
|
37
|
d) Bromothymol blue solution at 37oC
System
|
Time (s)
|
x (m)
|
X2
(x10-4 m2)
|
Slope of graph
|
D
(m2s-1)
|
Temperature (oC)
|
Average Diffusion Coefficient, D
(x10-11 m2s-1)
|
Bromothymol blue solution
with dilution 1:200
|
86400 (Day 1)
|
0.010
|
1.00
|
3 x 10-9
|
9.5841 x 10-11
|
37
|
|
172800 (Day 2)
|
0.012
|
1.44
|
37
|
||||
259200 (Day 3)
|
0.017
|
2.89
|
37
|
||||
345600 (Day 4)
|
0.020
|
4.00
|
37
|
||||
432000 (Day 5)
|
0.034
|
11.56
|
37
|
||||
518400 (Day 6)
|
0.036
|
12.96
|
37
|
||||
604800 (Day 7)
|
0.041
|
16.81
|
37
|
||||
|
|
||||||
Bromothymol blue solution
with dilution 1:400
|
86400 (Day 1)
|
0.008
|
0.64
|
2 x 10-9
|
7.0105 x 10 -11
|
37
|
8.0092
|
172800 (Day 2)
|
0.010
|
1.00
|
37
|
||||
259200 (Day 3)
|
0.015
|
2.25
|
37
|
||||
345600 (Day 4)
|
0.018
|
3.24
|
37
|
||||
432000 (Day 5)
|
0.028
|
7.84
|
37
|
||||
518400 (Day 6)
|
0.030
|
9.00
|
37
|
||||
604800 (Day 7)
|
0.035
|
12.25
|
37
|
||||
|
|
||||||
Bromothymol blue solution
with dilution 1:600
|
86400 (Day 1)
|
0.002
|
0.04
|
2 x 10-9
|
7.4331 x 10 -11
|
37
|
|
172800 (Day 2)
|
0.004
|
0.16
|
37
|
||||
259200 (Day 3)
|
0.010
|
1.00
|
37
|
||||
345600 (Day 4)
|
0.016
|
2.56
|
37
|
||||
432000 (Day 5)
|
0.021
|
4.41
|
37
|
||||
518400 (Day 6)
|
0.024
|
5.76
|
37
|
||||
604800 (Day 7)
|
0.031
|
9.61
|
37
|
DISCUSSION
Diffusion is a passive process by which the net movement of a substance from a region of high concentration to a region of low concentration. This is also referred to as the movement of a substance down a concentration gradient. A gradient is the change in the value of a quantity (e.g., concentration, pressure, temperature) with the change in another variable .
This
experiment is carried out to determine the diffusion coefficient of the crystal
violet and bromothymol blue. The controlled variables in this experiment are
the size of the particles and also the temperature. The temperature is
set at 28oC and 37 oC. Viscosity
and concentration of agar gel may also affect the
rate of diffusion.
From the equation
ln M = ln Mo –x2/4Dt or 2.303 x 4D (log10 Mo – log10 M) t = x2
By
plotting a graph of x2 versus t , we will get a straight line
that passes through the origin with the slope 2.303
x 4D (log10 Mo – log10 M). From here D ( diffusion coefficient ) can be
calculated. Hence, we know that the both 28ºC and 37 ºC system, the rate of
diffusion is 1:200 > 1:400 > 1:600.
M is the system with dilution 1: 500,000 which
acts as standard during the experiment. When Mo increases, (log10 Mo – log10 M)
also increase, causing the concentration gradient to be bigger, then the
driving force for the occurrence of diffusion would be bigger, and diffusion
becomes faster and favorable.
In the experiment, crystal violet diffuse faster than
bromothymol blue solution. Crystal violet with molecular formula C25N3H30Cl
has molecular weight of 407.979 g mol-1 while bromothymol blue
solution with molecular formula C27H28Br2O5S
has molecular weight of 624.38 g mol−1. The bromothymol blue is heavier than
crystal violet. The heavier the
particle is, the
slower it is going to move to solidified agar solution. Assuming energy of the system remains constant. Thus,
supposedly, in each experiment, D, the diffusion coefficient for
bromothymol blue is smaller than crystal violet.
When carried out this
experiment, test tube is placed in two
different temperature. One of the test tube is put in the
water bath at the temperature of 37°C and the other is located in the lab at room
temperature 28°C The
rate of diffusion is faster when the temperature is higher. As the
temperature increases, the amount of energy available for diffusion is
increased. There would be increase in kinetic energy. This will provide them energy to free from the
intermolecular attractive forces and thus making them easier to escape and
enter the agar. So the molecules
move faster and there will be more spontaneous spreading of the material which
means that diffusion occurs quicker. Thus the rate of diffusion will be faster
as the temperature increases. From Stokes-Einstein
equation:
D = kT/6пŋa
Where
D = the diffusion
constant,
a =the radius of the
spherical particle.
From the equation, the diffusion coefficient, D is also influenced by particle
size, viscosity, radius of particle and temperature.
The viscosity of the
solution in the hole also can influence the diffusion rate. When the
crystallinity of the gel medium is increased, the diffusion rate will decrease.
The larger the volume fraction of crystalline material, the slower the movement
of diffusion molecules. This can happened because crystalline regions of the
gel medium represent an impenetrable barrier to the movement of solute
particles where it have to circumnavigate through it.
In this experiment, some errors may arise
and causing inaccuracy to the final result.
1. The test tubes
which contain agar solution did not be closed immediately after added crystal
violet solution causing it to evaporate.
2. The
measurement is taken by different people day by day, so
the x value taken is from personal judgement and estimation. Thus, it lead to the inconsistency and
inaccuracy of the readings.
3. The level of
eyes of observer did not parallel to the ruler or measuring scale that cause
parallax errors.
CONCLUSSION
As obtained from this
experiment data it is calculated that crystal
violet diffusion coefficient at 28°C
is 1.4171 x 10-10 m2s-1 while at 37°C is 1.2406 x 10-10
m2s-1. Otherwise, for bromothymol blue, diffusion coefficient
at 28°C is 8.1128 x 10-11 m2s-1 while at 37°C is 8.0092 x 10-11
m2s-2. Some factor do affect this value. Firstly,
crystal violet diffuse quicker compare to the bromothymol as it have smaller
molecular mass. Temparature also play a role in diffusion as it will increase
the rate when the temperature was to be increased too. Besides, other factor
that affect rate of diffusion is the concentration of the crsytal violet and
bromothymol used whereas the concentration increasese as more diluted
ones' were used.
REFERENCES
- http://urila.tripod.com/mole.htm
- http://en.wikipedia.org/wiki/Molecular_mass
- http://www.pojman.com/mg_materials/Diffusion/Diffusion.html