Objective
To
determine the diffusion coefficient of crystal violet and bromothymol blue
solution through the prepared agar medium at different temperature.
Introduction
Diffusion is defined as a process of mass transfer of
molecules brought by random molecular motion from an area of high concentration
to an area of low concentration until equilibrium is achieved. It is associated
with driving forces such as concentration gradient, pressure, temperature and
electrical potential. This can be further explained by using Fick’s Law which
states that the rate of transfer of diffusing substance (amount dm in time dt)
through unit area of a section (area A) is proportional to the concentration
gradient dc/dx.
Dm=-DA (dc/dx)dt
D = diffusion
coefficient or diffusively for the solute, in unit m2s-1.
If a solution containing neutral particles with the concentration M0, is placed within a cylindrical tube next to a water column, diffusion can be stated as
M=M0 e(-x2/4Dt)
Where M is the
concentration at distance x from the intersection between water and solution
that is measured at time t. by changing the above equation to its logarithmic
form, we get
2.303 x 4D (log M0-log M) t = x2
Thus a plot of x2 against t can produce a
straight line that passes through the origin with the slope 2.303 x 4D (log M0-log
M). From here D can be calculated. If the particles in the solution are assumed
to be spherical, their size and molecular weight can be calculated by the
Stokes-Einstein equation.
D=kT/6πηa
Where
k is the Boltzmann constant 1.38 x 1023 Jk-1, T is the
temperature in Kelvin, π is the viscosity of the solvent in Nm-2s
and a is the radius of particle in M. The volume of a spherical particle is 4/3
πa3, thus its weight M is equivalent to 4/3 πa3Nρ (ρ is
density).
Diffusion for charged particles, need to include
potential gradient effect that exists between the solution and solvent.
However, this can be overcome by adding a little sodium chloride into the solvent
to prevent the formation of this potential gradient.
In this experiment, we used agar gels that contain
partially strong network of molecules that is penetrated by water. The water
molecules form a continuous phase around the gel. Thus, the molecules of
solutes can diffuse freely in the water if chemical interactions and adsorption
effects do not exist entirely. Therefore, the gel forms an appropriate support
system to be used in diffusion studies for molecules in a medium of water.
Apparatus
and Materials
8 test tubes, 500ml of
beaker, Ringer’s solution, crystal violet, agar powders and bromothymol blue.
Procedure
1. 250
ml of agar in Ringer’s solution is prepared. The agar is then divided into 6
test tubes and it is allowed to cool at room temperature.
2. An
agar is prepared in another test tube that has already being added with
1:500,00 crystal violet, this is used as the standard to measure the color
distance resulting from the crystal violet diffusion.
3. The solutions of crystal violet are prepared in distilled water in the concentration of 1:200,000, 1:400,000 and 1:600,000.
4. 5ml of each crystal violet solution is placed on the gels that was prepared and it is closed to prevent evaporation then it is stored at temperature 28°C and 37°C.
5. The distance between the interfaces 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 is obtained and this value is x in meter. The value of x after 2 hours is recorded and at suitable time distance up till 2 weeks.
7. The graph for values x2 (in M2) against time(s) is plotted for each of the concentration used. The diffusion D is calculated from the slope of the graph at temperature 28°C and 37°C.
8. The molecular weight of the crystal violet is also calculated by using the equation N and V.
Results
Table 1
System
|
Time (seconds)
|
x, M (x10-2)
|
x2, M2 ( x10-4)
|
Slope of graph
|
D, M2S-1
|
Temperature, o C
|
Average Diffusion Coefficient, D M2S-1
|
|
Crystal violet
|
||||||||
1:200
|
0
|
0.0
|
0.00
|
3.000x10-9
|
9.584 × 10-11
|
25.0
|
8.593 × 10-11
|
|
72000
|
1.5
|
2.25
|
||||||
244800
|
2.8
|
7.84
|
||||||
331200
|
3.4
|
11.56
|
||||||
676800
|
3.8
|
14.44
|
||||||
763200
|
5.1
|
26.01
|
||||||
849600
|
5.2
|
27.04
|
||||||
936000
|
5.3
|
28.09
|
||||||
1:400
|
0
|
0.0
|
0.00
|
2.500x10-9
|
8.763 ×10-11
|
25.0
|
||
72000
|
0.8
|
0.64
|
||||||
244800
|
1.8
|
3.24
|
||||||
331200
|
3.0
|
9.00
|
||||||
676800
|
3.9
|
15.21
|
||||||
763200
|
4.0
|
16.00
|
||||||
849600
|
4.8
|
23.04
|
||||||
936000
|
5.0
|
25.00
|
||||||
1:600
|
0
|
0.0
|
0.00
|
2.000x10-9
|
7.433 × 10-11
|
25.0
|
||
72000
|
0.5
|
0.25
|
||||||
244800
|
1.4
|
1.96
|
||||||
331200
|
2.5
|
6.25
|
||||||
676800
|
3.8
|
14.44
|
||||||
763200
|
4.0
|
16.00
|
||||||
849600
|
4.2
|
17.64
|
||||||
936000
|
4.3
|
18.49
|
||||||
1:200
|
0
|
0.0
|
0.00
|
3.913x10-9
|
1.250 × 10-10
|
37.0
|
1.051 × 10-10
|
|
86400
|
1.6
|
3.61
|
||||||
172800
|
3.0
|
9.00
|
||||||
259200
|
4.0
|
16.00
|
||||||
345600
|
5.3
|
28.09
|
||||||
432000
|
5.4
|
29.16
|
||||||
518400
|
5.8
|
33.64
|
||||||
604800
|
6.0
|
36.00
|
||||||
1:400
|
0
|
0.0
|
0.00
|
3.068x10-9
|
1.075 × 10-10
|
37.0
|
||
86400
|
1.1
|
1.21
|
||||||
172800
|
2.0
|
4.00
|
||||||
259200
|
3.2
|
10.24
|
||||||
345600
|
4.4
|
19.36
|
||||||
432000
|
4.6
|
21.16
|
||||||
518400
|
5.5
|
30.25
|
||||||
604800
|
5.7
|
32.49
|
||||||
1:600
|
0
|
0.0
|
0.00
|
2.22x10-9
|
8.251 × 10-11
|
37.0
|
||
86400
|
0.5
|
0.25
|
||||||
172800
|
1.4
|
1.96
|
||||||
259200
|
3.0
|
9.00
|
||||||
345600
|
4.0
|
16.00
|
||||||
432000
|
4.2
|
17.64
|
||||||
518400
|
4.3
|
18.49
|
||||||
604800
|
4.5
|
20.25
|
Graph of x2 Against Time (Crystal Violet in
Room Temperature)
Graph of x2 against Time (Crystal Violet in Water
Bath)
Table 2
System
|
Time (seconds)
|
x, M (x10-2)
|
x2, M2 (x10-4)
|
Slope of graph
|
D, M2S-1
|
Temperature, o C
|
Average Diffusion Coefficient, D M2S-1
|
|
Bromothymol blue
|
||||||||
1:200
|
0
|
0.0
|
0.00
|
2.250x10-9
|
7.188 × 10-11
|
25.0
|
7.764 × 10-11
|
|
72000
|
0.9
|
0.81
|
||||||
244800
|
2.1
|
4.41
|
||||||
331200
|
3.2
|
10.24
|
||||||
676800
|
3.3
|
10.89
|
||||||
763200
|
3.5
|
12.25
|
||||||
849600
|
4.5
|
20.25
|
||||||
936000
|
4.8
|
23.04
|
||||||
1:400
|
0
|
0.0
|
0.00
|
2.000x10-9
|
7.010 ×10-11
|
25.0
|
||
72000
|
0.7
|
0.49
|
||||||
244800
|
1.6
|
2.56
|
||||||
331200
|
2.8
|
7.84
|
||||||
676800
|
3.2
|
10.24
|
||||||
763200
|
4.1
|
16.81
|
||||||
849600
|
4.2
|
17.64
|
||||||
936000
|
4.4
|
19.36
|
||||||
1:600
|
0
|
0.0
|
0.00
|
1.818x10-9
|
6.757 × 10-11
|
25.0
|
||
72000
|
0.7
|
0.49
|
||||||
244800
|
1.6
|
2.56
|
||||||
331200
|
2.8
|
7.84
|
||||||
676800
|
3.2
|
10.24
|
||||||
763200
|
4.1
|
16.81
|
||||||
849600
|
4.2
|
17.64
|
||||||
936000
|
4.4
|
19.36
|
||||||
1:200
|
0
|
0.0
|
0.00
|
3.158x10-9
|
1.009 × 10-10
|
37.0
|
9.517 × 10-11
|
|
72000
|
1.5
|
2.25
|
||||||
244800
|
2.2
|
4.84
|
||||||
331200
|
3.7
|
13.69
|
||||||
676800
|
3.9
|
15.21
|
||||||
763200
|
4.1
|
16.81
|
||||||
849600
|
5.7
|
32.49
|
||||||
936000
|
5.9
|
34.81
|
||||||
1:400
|
0
|
0.0
|
0.00
|
2.763x10-9
|
9.685 × 10-11
|
37.0
|
||
72000
|
1.3
|
1.69
|
||||||
244800
|
2.0
|
4.00
|
||||||
331200
|
2.8
|
7.84
|
||||||
676800
|
4.0
|
16.00
|
||||||
763200
|
4.2
|
17.64
|
||||||
849600
|
5.0
|
25.00
|
||||||
936000
|
5.6
|
31.36
|
||||||
1:600
|
0
|
0.0
|
0.00
|
2.361x10-9
|
8.755 × 10-11
|
37.0
|
||
72000
|
1.1
|
1.21
|
||||||
244800
|
1.5
|
2.25
|
||||||
331200
|
3.0
|
9.00
|
||||||
676800
|
3.8
|
14.44
|
||||||
763200
|
4.2
|
17.64
|
||||||
849600
|
4.6
|
21.16
|
||||||
936000
|
4.8
|
23.04
|
||||||
Graph of x2 Against Time (Bromothymol
Blue in Room Termperature)
Graph of x2 Against
Time (Bromothymol Blue in Water Bath)
From
equation: 2.303 x 4D (log 10 Mo – log 10 M) t = X²
Hence the gradient of
the graph = 2.303 x 4D (log 10 Mo - log 10 M)
1. Crystal violet system with dilution 1:200 (25ºC)
Gradient = 3.000×10-9 m2/sec
M = 1:500000 Mo = 1:200
= 1 /
500000 = 1 / 200
= 2.000 x
10-6 =
5.000 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) =
3.000 x 10-9 m2/sec
2.303x4D [log 10 (5.000x10-3)-log 10 (2.000x10-6)]
= 3.000×10-9 m2/sec
D = 9.584×10-11 m2/sec
2. Crystal violet system with dilution 1:400 (25ºC)
Gradient =2.500×10-9 m2/sec
M = 1:500000 Mo = 1:400
= 1 /
500000 = 1 / 400
= 2.000
x 10-6 = 2.500 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 2.500×10-9
m2/sec
2.303x4D [log 10 (2.500x10-3)-log 10 (2.000x10-6)]
= 2.500×10-9 m2/sec
D = 8.763×10-11 m2/sec
3. Crystal violet system with dilution 1:600 (25ºC)
Gradient =2.000×10-9 m2/sec
Gradient =2.000×10-9 m2/sec
M = 1:500000 Mo = 1:600
= 1 /
500000 = 1 / 600
= 2.000
x 10-6 = 1.667 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 2.000×10-9
m2/sec
2.303x4D [log 10 (1.667x10-3)-log 10 (2.000x10-6
)] = 2.000×10-9
m2/sec
D = 7.433×10-11 m2/sec
Average of Diffusion Coefficient, m²/sec for
Crystal violet system at 25ºC
= (9.584×10-11
m2/sec + 8.763×10-11 m2/sec + 7.433×10-11
m2/sec) / 3
= 8.593 ×10-11 cm2/sec
4. Crystal violet system with dilution 1:200 (37ºC)
Gradient =3.913×10-9 m2/sec
M= 1:500000 Mo = 1:200
= 1 /
500000 = 1 / 200
= 2.000 x
10-6 =
5.000 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 3.913×10-9
m2/sec
2.303x4D [log 10 (5.000
x 10-3)-log 10 (2.000 x 10-6)] = 3.913×10-9
m2/sec
D=1.250×10-10 m2/sec
5.
Crystal violet system with dilution 1:400 (37ºC)
Gradient =3.068×10-9 m2/sec
M = 1:500000 Mo = 1:400
= 1 /
500000 = 1 / 400
= 2.000
x 10-6 = 2.500 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 3.068×10-9
m2/sec
2.303x4D [log 10 (2.500x10-3)-log 10 (2.000x10-6)]
= 3.068×10-9 m2/sec
D = 1.075 ×10-10 m2/sec
6.
Crystal violet system with dilution 1:600 (37ºC)
Gradient = 2.220×10-9 m2/sec
M = 1:500000 Mo = 1:600
= 1 /
500000 = 1 / 600
= 2.000
x 10-6
= 1.667 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 2.220×10-9
m2/sec
2.303x4D [log 10 (1.667x10-3)-log 10 (2.000x10-6
)] = 2.220×10-9 m2/sec
D = 8.251×10-11 m2/sec
Average
of Diffusion Coefficient, m²/sec for Crystal violet system at 37ºC
= (1.250×10-10 m2/sec
+ 1.075×10-10 m2/sec +8.251×10-11 m2/sec)
/ 3
= 1.051×10-10 m2/sec
7. Bromotymol blue system with dilution 1:200 (25ºC)
7. Bromotymol blue system with dilution 1:200 (25ºC)
Gradient = 2.250×10-9 m2/sec
M = 1:500000 Mo = 1:200
= 1 / 500000 = 1 / 200
= 2.000 x 10-6 = 5.000 x
10-3
2.303 x 4D (log 10 Mo – log 10
M) = 2.250×10-9 m2/sec
2.303x4D
[log 10 (5.000x10-3)-log 10 (2.000x10-6)]
= 2.250×10-9 m2/sec
D = 7.188×10-11 m2/sec
8. Bromotymol blue system with dilution 1:400 (25ºC)
Gradient = 2.409×10-9
m2/sec
M = 1:500000 Mo = 1:400
= 1 /
500000 = 1 / 400
= 2.000 x
10-6 =
2.500 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 2.000×10-9
m2/sec
2.303x4D [log 10 (2.500x10-3)-log 10 (2.000x10-6
)] = 2.000×10-9 m2/sec
D= 7.010×10-11 m2/sec
9. Bromotymol blue system with dilution
1:600 (25ºC)
Gradient =1.818×10-9
m2/sec
M = 1:500000 Mo = 1:600
= 1 /
500000 = 1 / 600
= 2.000
x 10-6
= 1.667 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 1.818×10-9
m2/sec
2.303x4D [log 10 (1.667x10-3)-log 10 (2.000x10-6
)] = 1.818×10-9 m2/sec
D = 6.757×10-11 m2/sec
Average
of Diffusion Coefficient, m²/sec for Bromotymol blue system at 25ºC
= (7.188×10-11 m2/sec
+ 9.347×10-11 m2/sec
+6.757×10-11 m2/sec) / 3
= 7.764×10-11 m2/sec
10. Bromotymol blue system with dilution 1:200 (37ºC)
Gradient = 3.158×10-9 m2/sec
M = 1:500000 Mo = 1:200
= 1 /
500000 = 1 / 200
= 2.000 x
10-6 =
5.000 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 3.158×10-9
m2/sec
2.303x4D
[log 10 (5.000x10-3)-log 10 (2.000x10-6
)] = 3.158×10-9
m2/sec
D = 1.009×10-10 m2/sec
11.
Bromotymol blue system with dilution 1:400 (37ºC)
Gradient =2.763×10-9 m2/sec
M = 1:500000 Mo = 1:400
= 1 /
500000 = 1 / 400
= 2.000
x 10-6 = 2.500 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 2.763×10-9
m2/sec
2.303x4D [log 10 (2.500x10-3)-log 10 (2.000x10-6)]
= 2.763×10-9
m2/sec
D = 9.685×10-11 m2/sec
12. Bromotymol blue system with
dilution 1:600 (37ºC)
Gradient =2.361×10-9 m2/sec
M = 1:500000 Ma = 1:600
= 1 /
500000 = 1 / 600
= 2.000x
10-6 =
1.667 x 10-3
2.303 x 4D (log 10 Mo – log 10 M) = 2.361×10-9
m2/sec
2.303x4D [log 10 (1.667x10-3)-log 10 (2.000x10-6
6 = 2.361×10-9 m2/sec
D = 8.775×10-11 m2/sec
Average
of Diffusion Coefficient, m²/sec for Bromotymol blue system at 37ºC
= (1.009×10-10 m2/sec
+9.685×10-11m2/sec +8.775×10-11 m2/sec)
/ 3
= 9.517×10-11 m2/sec
M = 4/3 πa3Nρ
where M= molecular weight,
a3 = radius of particle
N= Avogadro’s number (6.023×10-23mol-1)
ρ = density
Bromothymol blue:
M = 4/3 πa3Nρ
density of bromothymol blue: 1.25g/cm3
Molecular weight of bromothymol blue: 624.38g/mol
624.38 gmol-1 = 4/3 π aBB
3 (6.023×1023mol-1) (1.25 gcm-3)
aBB = 5.828 × 10-8cm
= 5.828 × 10-10m
Crystal Violet:
Density of Crystal Violet : 1.19g cm-3
Molecular weight of Crystal Violet : 407.98 gmol-1
407.98 gmol-1 = 4/3 π aCV
3 (6.023×1023mol-1) (1.19g cm-3)
aCV = 5.141 × 10-8cm
= 5.141 × 10-10m
Discussion
In
the experiment, diffusion has occur at crystal violet and bromothymol blue. It
is a process of mass transfer of the substrate molecule by random molecular
motion associated with forces including concentration gradient until
equilibrium is achieved. The molecules
move from region of higher concentration to region of lower concentration. The
region of lower concentration will increase in concentration whereas the region
of higher concentration will decrease in concentration. The
change of concentration will stop when the equilibrium is achieved. The diffusion driving force included is the concentration gradient.
There are a few
factors that affect the diffusion coefficient. One of the factor is
temperature, as stated in the Stokes-Einstein equation, where D = kT/6πηa.The diffusion coefficient for
both bromothymol blue and crystal violet in 37°C is higher than the diffusion coefficient in
room temperature, 25°C. This is because in higher temperature, more energy is supplied to
the molecules. As a result the kinetic energy of the molecules increases. This
will help the molecules to overcome intermolecular force and move more rapidly
from region of higher concentration to region of lower concentration.
From
the Stokes-Einstein equation, another factor that influence the diffusion
coefficient is the radius of the particle. The radius of the particle is
inversely proportional to the diffusion coefficient. The radius of bromothymol
blue molecule, 5.828 × 10-10m is larger than the radius of crystal violet
molecule, 5.141 × 10-10m. Due to its larger radius, the molecule would diffuse
harder between the limited space of agar particles than crystal violet
particle. This causes bromothymol blue have lower rate of diffusion and lower diffusion
coefficient than crystal violet at both
temperature. Besides that, the molecular weight of bromothymol blue,
624.38 g/mol is also higher than crystal violet, which is 407.98g/mol. The rate of diffusion of a substance is affected by its
molecular weight. As the molecular weight increases, the rate of diffusion is
generally low. This is because the larger the size of a particle, a greater amount of
force, in this case, thermal energy is required to move the particle. Thus smaller, lighter molecules could diffuse
faster than larger, heavier ones.
A
few errors has occur during the experiment. For example, parallax error. When we
measure the crystal violet solution and bromothymol solution, we may take the
wrong reading as the eye level is not perpendicular to the meniscus. Besides
that, this error also occur while taking the result, which is to measure the
length of agar which the two solution has diffused with a ruler. When boiling the agar
powder and Ringer’s solution, the boiling process should only be stopped when
the solution become clear solution. The solution also should be stirred
continuously to prevent coagulation.
Questions
Between the crystal violet
and bromothymol blue, which diffuse quicker? Explain if there are any
differences in the diffusion coefficient values?
From the result, the average of diffusion coefficient (D) of crystal violet at 28C and 37C are higher than the average coefficient of bromothymol blue at 28C and 37C. The average of diffusion coefficient of crystal violet at 28C is 8.593 x 10-11 while at 37C is 1.051 x 10-10. The average of diffusion coefficient of bromothymol blue at 28C is 7.764 x 10-11 while at 37C is 9.517 x 10-11.
From the result, the average of diffusion coefficient (D) of crystal violet at 28C and 37C are higher than the average coefficient of bromothymol blue at 28C and 37C. The average of diffusion coefficient of crystal violet at 28C is 8.593 x 10-11 while at 37C is 1.051 x 10-10. The average of diffusion coefficient of bromothymol blue at 28C is 7.764 x 10-11 while at 37C is 9.517 x 10-11.
Crystal
violet is diffuse faster than bromothymol blue. This is because crystal violet
has smaller particle when compared with bromothymol blue. The smaller the
molecular weight, the smaller the size of the particle, the faster will be the
diffusion rate of a substance. Thus, crystal violet has a larger value of D as
compared to bromothymol blue.
Conclusions
Conclusions
The
diffusion coefficient of crystal violet is 8.593
×10-11m2/sec in 25°C and 1.051×10-10 m2/sec
at 37°C.
The diffusion coefficient of bromothymol blue in 25°C is 7.764×10-11
m2/sec and 9.517×10-11 m2/sec at 37°C.
The
diffusion coefficient would be higher in high temperature, low molecular weight
and small size of particles, and high concentration
gradient. The objectives are verified.
References
3. Alexander
Ken Libranza, The Effect of Molecular
Weight on the Rate of Diffusion of Substances, March 6, 2012 retrieved from http://www.academia.edu/1776814/The_Effect_of_Molecular_Weight_on_the_Rate_of_Diffusion_of_Substances
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