Objective: To determine the diffusion coefficient of crystal violet
Introduction:
Diffusion is the spontaneous movement of solutes from an area of high concentration to an area of low concentration which can be explained by Fick’s law which states that the flux of material (amount dm in time dt) across a given plane (area A) is proportional to the concentration gradient dc/dx.
dm = -DA(dc/dx) dt ---------------------- (i)
D is the diffusion coefficient or diffusivity for the solute, in unit m2s-1
If a solution containing neutral particles with the concentration Mo, is placed within a cylindrical tube next to a water column, diffusion can be stated as
M = Mo exp(-x2 / 4Dt) ---------------------- (ii)
where M is the concentration at distance x from the intersection between water and solution that is measured at time t.
By changing equation (ii) to its logarithmic form, we get
ln M = ln Mo – x2 / 4Dt or
2.303 x 4D (log10 Mo – log10M) t = x2 -------------------------------- (iii)
Thus a plot of x2 against t can produce a straight line that passes through the origin with the slope
2.303 x 4D (log10 Mo – log10M). 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 Strokes-Einstein equation.
D=kT⁄6πηa
where is the Boltzmann constant 1.38 x 1023 Jk-1, T is the temperature in Kelvin, η 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 7ra3, thus its weight is equivalent to 4/3 πa3Nρ (ρ = density).
It is known that molecular weight M = mN (N is the Avogadro’s number 6.023 x 1023 mol-1
∴M= 4⁄3 πa3Nρ ---------------------- (v)
Diffusion for charged particles, equation (iii) needs to be modified 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.
Agar gels contain a 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 the 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.
Materials:
Agar powder, Ringer’s solution, 1:500000 crystal violet solution, 1:200 crystal violet solution, 1:400 crystal violet solution, 1:600 crystal violet solution, 1:500000 bromothymol blue solution, 1:200 bromothymol blue solution, 1:400 bromothymol blue solution, 1:600 bromothymol blue solution.
Apparatus:
500 mL beaker, 5 mL pipette, glass rod, 14 test tubes with cover, hot plate
Procedures:
1. 250 mL agar in Ringer’s solution is prepared.
2. The agar is divided into six test tubes and allowed to cool at room temperature.
3. 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 color distance resulting
4. Solutions of crystal violet in distilled water in the concentrations 1:200, 1:400 and 1:600 are prepared.
5. 5mL of each crystal violet solution is placed on the gel that was prepared and it is closed to prevent evaporation and stored at temperature 28 ̊C and 37 ̊C.
6. 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.
7. The average of several measurements is obtained and this value is x in meter.
8. The value of x after 2 hours and at suitable time distances up till 2 weeks are recorded (table 1).
9. The graph for values of x2 ( in M2) against time (in hours) for each of the concentration used is plotted.
10. The diffusion coefficient D from the slope of the graph at temperature 28 ̊C and 37 ̊C is calculated. The molecular weight of the crystal violet is also calculated using the equation N and V.
11. This experiment is repeated using bromothymol blue. However, sufficient alkali has to be added into this solution to obtain the color completely from the dye.
Table 1:
System
|
Time (hours)
|
x (M)
|
x2 (M2)
|
Slope of graph
|
D (M2Hr-1)
|
Temperature ( ̊C)
|
Average Diffusion Coefficient D
|
RESULTS:
a.) Crystal
Violet in 28 0C
System
|
Time (day)
|
X
(10-2m)
|
X2 (10-4m2)
|
Temp (0C)
|
1
|
1.8
|
3.24
|
28
|
|
2
|
2.4
|
5.76
|
28
|
|
(a)
crystal violet with dilution 1:200
|
3
|
2.8
|
7.84
|
28
|
4
|
3.5
|
12.25
|
28
|
|
5
|
3.8
|
14.44
|
28
|
|
6
|
4.3
|
18.49
|
28
|
|
7
|
4.5
|
20.25
|
28
|
|
1
|
1.7
|
2.89
|
28
|
|
2
|
2.0
|
4.00
|
28
|
|
(b)
crystal violet with dilution 1:400
|
3
|
2.5
|
6.25
|
28
|
4
|
3.3
|
10.89
|
28
|
|
5
|
3.5
|
12.25
|
28
|
|
6
|
4.0
|
16.00
|
28
|
|
7
|
4.3
|
18.49
|
28
|
|
1
|
1.4
|
1.96
|
28
|
|
2
|
1.6
|
2.56
|
28
|
|
(c)
crystal violet with dilution 1:600
|
3
|
1.9
|
3.61
|
28
|
4
|
2.2
|
4.84
|
28
|
|
5
|
2.3
|
5.76
|
28
|
|
6
|
2.5
|
6.25
|
28
|
|
7
|
3.0
|
9.00
|
28
|
b)Crystal
violet in 370C
System
|
Time (day)
|
X
(10-2m)
|
X2 (10-4m2)
|
Temp (0C)
|
1
|
2.0
|
4.00
|
37
|
|
2
|
2.4
|
5.76
|
37
|
|
(a)
crystal violet with dilution 1:200
|
3
|
3.0
|
9.00
|
37
|
4
|
3.8
|
14.44
|
37
|
|
5
|
4.1
|
16.81
|
37
|
|
6
|
4.5
|
20.25
|
37
|
|
7
|
5.0
|
25.00
|
37
|
|
1
|
1.9
|
3.61
|
37
|
|
2
|
2.3
|
5.29
|
37
|
|
(b)
crystal violet with dilution 1:400
|
3
|
2.6
|
6.76
|
37
|
4
|
3.7
|
13.69
|
37
|
|
5
|
3.9
|
15.21
|
37
|
|
6
|
4.2
|
17.64
|
37
|
|
7
|
4.5
|
20.25
|
37
|
|
1
|
1.5
|
2.25
|
37
|
|
2
|
1.7
|
2.89
|
37
|
|
(c)
crystal violet with dilution 1:600
|
3
|
2.0
|
3.61
|
37
|
4
|
2.3
|
5.29
|
37
|
|
5
|
2.4
|
5.76
|
37
|
|
6
|
2.7
|
7.29
|
37
|
|
7
|
3.2
|
10.24
|
37
|
c) Bromothymol
blue in 280C
System
|
Time (day)
|
X
(10-2m)
|
X2 (10-4m2)
|
Temp (0C)
|
1
|
1.2
|
1.44
|
28
|
|
2
|
1.5
|
2.25
|
28
|
|
(a)
Bromothymol Blue with dilution 1:200
|
3
|
2.2
|
4.84
|
28
|
4
|
2.7
|
7.29
|
28
|
|
5
|
3.4
|
11.56
|
28
|
|
6
|
3.7
|
13.69
|
28
|
|
7
|
4.0
|
16.00
|
28
|
|
1
|
1.6
|
2.56
|
28
|
|
2
|
2.0
|
4.00
|
28
|
|
(b)
Bromothymol Blue with dilution 1:400
|
3
|
2.1
|
4.41
|
28
|
4
|
2.6
|
6.76
|
28
|
|
5
|
2.8
|
7.84
|
28
|
|
6
|
3.3
|
10.89
|
28
|
|
7
|
3.8
|
14.44
|
28
|
|
1
|
1.4
|
1.96
|
28
|
|
2
|
1.6
|
2.56
|
28
|
|
(c)
Bromothymol Blue with dilution 1:600
|
3
|
1.8
|
3.24
|
28
|
4
|
2.0
|
4.00
|
28
|
|
5
|
2.7
|
7.29
|
28
|
|
6
|
3.0
|
9.00
|
28
|
|
7
|
3.3
|
10.89
|
28
|
d)
Bromothmoyl blue in 37 0C
System
|
Time (hour)
|
X
(10-2m)
|
X2 (10-4m2)
|
Temp (0C)
|
1
|
1.8
|
3.24
|
37
|
|
2
|
2.2
|
4.84
|
37
|
|
(a)
Bromothymol Blue with dilution 1:200
|
3
|
2.5
|
6.25
|
37
|
4
|
3.0
|
9.00
|
37
|
|
5
|
3.7
|
13.69
|
37
|
|
6
|
4.0
|
16.00
|
37
|
|
7
|
4.4
|
19.36
|
37
|
|
1
|
1.6
|
2.56
|
37
|
|
2
|
2.2
|
4.84
|
37
|
|
(b)
Bromothymol Blue with dilution 1:400
|
3
|
2.5
|
6.25
|
37
|
4
|
3.0
|
9.00
|
37
|
|
5
|
3.1
|
9.61
|
37
|
|
6
|
3.6
|
12.96
|
37
|
|
7
|
4.0
|
16.00
|
37
|
|
1
|
1.8
|
3.24
|
37
|
|
2
|
2.5
|
6.25
|
37
|
|
(c)
Bromothymol Blue with dilution 1:600
|
3
|
2.8
|
7.84
|
37
|
4
|
3.0
|
9.00
|
37
|
|
5
|
3.3
|
10.89
|
37
|
|
6
|
3.5
|
12.25
|
37
|
|
7
|
3.6
|
12.96
|
37
|
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