Wednesday 29 May 2013

PRACTICAL 4: DETERMINATION OF DIFFUSION COEFFICIENT


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)


Calculations
    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
  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)
      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 πa3
where M= molecular weight,
 a3 = radius of particle
N= Avogadro’s number (6.023×10-23mol-1)
ρ = density

Bromothymol blue:

M = 4/3 πa3
density of bromothymol blue: 1.25g/cm3
Molecular weight of bromothymol blue: 624.38g/mol

624.38 gmol-1 = 4/3 π aBB (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 (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.

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

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


1. Patrick J. Sinki, Yashveer Singh, Martin Physical Pharmacy and Pharmaceutical Sciences, Lippincott Williams and Wilkins, 2011, Baltimor, MD


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