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Determination of Partition Coefficient

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Introduction

Diffusivityordiffusion coefficientis a proportionality constant between themolar flux due to moleculardiffusion and the gradient in the concentration of the species (or the driving force for diffusion). Diffusivity is encountered inFick's law and numerous other equations ofphysical chemistry. It is generally prescribed for a given pair of species. For a multi-component system, it is prescribed for each pair of species in the system.The higher the diffusivity (of one substance with respect to another), the faster they diffuse into each other.This coefficient has anSI unit of m2/s (length2/ time). In CGS units it was given in cm2/s.

In this experiment, agar gel is used as the diffusion medium. The gel consists of the semi-solid network of agar molecules interpenetrated by water which form the continuous phase for diffusion. The agar molecular network prevents the speed up of water molecules movement which occurs naturally such as through the convection flow of water caused by temperature difference.

Objective:

  1. To determine the D value (diffusion coefficient) at different temperature, concentration and solvent/medium.
  2. To determine the radius and volume of the particle.
  3. To determine the mass of particle and molecular weight of substance

Methodology

  1. Molten agar solution is prepared by boiling the powder in an appropriate solvent.
    1. 200 mL 2% agar in Ringer solution.
    2. 50 mL 1% agar in Ringer solution.
    3. 50 mL 2% agar in Ringer solution.
  1. 10 mL of the molten agar is poured into specified test tubes and left to solidify.
    1. 2% agar in Ringer into 14 test tubes.
    2. 1% agar in Ringer into 2 test tubes.
    3. 2% agar in distilled water into 2 test tubes.
  2. The reference mixtures is prepared for Crystal Violet and Bromothymol Blue by mixing:
    1. 5 mL of the molten 2% agar in Ringer with 5mL, 1 in 500,000 Crystal Violet solution.
    2. 5 mL of the molten 2% agar in Ringer with 5mL, 1 in 500,000 Bromothymol Blue solution.
    3. 5 mL of the molten 1% agar in Ringer with 5mL, 1 in 500,000 Crystal Violet solution.
    4. 5 mL of the molten 2% agar in distilled water with 5mL, 1 in 500,000 Crystal Violet solution.
  3. 3 mL of the following solution is filled into specified test tubes containing the solidified agar. Each test tube is covered with aluminium foil and the time is noted.
    1. 1 in 200 Crystal Violet into 4 tubes containing 2% agar in Ringer.
    2. 1 in 400 Crystal Violet into 4 tubes containing 2% agar in Ringer.
    3. 1 in 600 Crystal Violet into 4 tubes containing 2% agar in Ringer.
    4. 1 in 400 Crystal Violet into 2 tubes containing 1% agar in Ringer.
    5. 1 in 400 Crystal Violet into 2 tubes containing 2% agar in distilled water.
    6. 1 in 400 Bromothymol Blue into 2 tubes containing 2% agar in Ringer.
  4. Test tube 4(i), (ii), (iii) is kept in an incubator at 370C. The rest of the test tubes is kept at room temperature.
  5. The distance between the origin (the solution or gel interface) to the point of a known concentration (the point where the colour is equivalent to the appropriate reference mixture) is measured accurately at 900s, 1800s, 2700s, 3600s, 4500s, 322200s and 415800s.
  6. The result is recorded and tabulated.

Results

a) 1 in 200 Crystal Violet (CV) in 2% agar in Ringer at room temperature.

Tube 1

Tube 2

b) 1 in 200 CV in 2% agar in Ringer incubated at 37°C

Tube 3

Tube 4

c) 1 in 400 CV in 2% agar in Ringer at room temperature.

Tube 5

Tube 6

d) 1 in 400 CV in 2% agar in Ringer incubated at 37°C

Tube 7

Tube 8

e)1 in 600 CV in 2% agar in Ringer at room temperature.

Tube 9

Tube 10

f) 1 in 600 CV in 2% agar in Ringer incubated at 37°C

Tube 11

Tube 12

g) 1 in 400 CVin 1% agar in Ringer at room temperature.

Tube 13

Tube 14

h) 1 in 400 CV in 2% agar in distilled water at room temperature.

Tube 15

Tube 16

i) 1 in 400 Bromothymol blue in 2% agar in Ringer

Tube 17

Tube 18

Calculation

Calculations were conducted to determine:

  • the D value,
  • the radius of the molecule,
  • the volume of the particle,
  • the mass of the particle, and
  • the molecular weight of the substance

Equations used,

1. To determine the D value

*of which, x2 is y and 2.303(4)(D)(t)(log10m0-log10m) is (mx+c)

Representing the equation of straight line y=mx + c. In calculating the D value, the value of c (y-intercept) = 0, thus the new equation isy=mx.

Based on 2 equations to find the slope of the line, m;

and

D value is calculated as such,

Modified to,

2. To determine the radius of the molecule

The radius is calculated as such,

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

a) 1 in 200 Crystal Violet (CV) in 2% agar in Ringer at room temperature.

Tube 1

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

Tube 2

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

b) 1 in 200 CV in 2% agar in Ringer incubated at 37°C

Tube 3

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

Tube 4

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

c) 1 in 400 CV in 2% agar in Ringer at room temperature.

Tube 5

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

Tube 6

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

d) 1 in 400 CV in 2% agar in Ringer incubated at 37°C

Tube 7

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

Tube 8

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

e) 1 in 600 CV in 2% agar in Ringer at room temperature.

Tube 9

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

Tube 10

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

f) 1 in 600 CV in 2% agar in Ringer incubated at 37°C

Tube 11

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

Tube 12

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

g) 1 in 400 CV in 1% agar in Ringer at room temperature.

Tube 13

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

Tube 14

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

h) 1 in 400 CV in 2% agar in distilled water at room temperature.

Tube 15

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

Tube 16

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

i) 1 in 400 Bromothymol blue in 2% agar in Ringerat room temperature.

Tube 17

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

Tube 18

1. Determining D value

2. Determining the radius of the molecule

3. To determine the volume of the particle

4. To determine the mass of the particle

5. To determine the molecular weight of the substance

Summary of the calculated values

Conditions

1 in 200 Crystal Violet (CV) in 2% agar in Ringer at room temperature

Tube no

Distance travelled (m)

D-value

Radius (m)

Volume (ml)

Mass (g)

Molec ular weight (g/mol)

1

0.037

1.03 × 10ˉ¹â°

2.06× 10ˉ¹²

3.66× 10ˉ³âµ

3.66× 10ˉ³âµ

2.20 × 10ˉ¹¹

2

0.033

8.35 × 10ˉ¹¹

2.54 × 10ˉ¹²

6.86 × 10ˉ³âµ

6.86 × 10ˉ³âµ

4.13 × 10ˉ¹¹

Conditions

1 in 200 CV in 2% agar in Ringer incubated at 37°C.

3

0.050

1.91 × 10ˉ¹â°

1.19 × 10ˉ¹²

7.06 × 10ˉ³â¶

7.06 × 10ˉ³â¶

4.25 × 10ˉ¹²

4

0.050

1.91 × 10ˉ¹â°

1.19 × 10ˉ¹²

7.06 × 10ˉ³â¶

7.06 × 10ˉ³â¶

4.25 × 10ˉ¹²

             

Conditions

1 in 400 CV in 2% agar in Ringer at room temperature.

Tube no

Distance travelled (m)

D-value

Radius (m)

Volume (ml)

Mass (g)

Molec ular weight (g/mol)

5

0.033

9.12 × 10ˉ¹¹

2.32 × 10ˉ¹²

5.23 × 10ˉ³âµ

5.23 × 10ˉ³âµ

3.15 × 10ˉ¹¹

6

0.033

9.12 × 10ˉ¹¹

2.32 × 10ˉ¹²

5.23 × 10ˉ³âµ

5.23 × 10ˉ³âµ

3.15 × 10ˉ¹¹

Conditions

1 in 400 CV in 2% agar in Ringer incubated at 37°C.

7

0.045

1.71 × 10ˉ¹â°

1.33 × 10ˉ¹²

9.85 × 10ˉ³â¶

9.85 × 10ˉ³â¶

5.93 × 10ˉ¹²

8

0.045

1.71 × 10ˉ¹â°

1.33 × 10ˉ¹²

9.85 × 10ˉ³â¶

9.85 × 10ˉ³â¶

5.93 × 10ˉ¹²

             

Conditions:

1 in 600 CV in 2% agar in Ringer at room temperature.

Tube no

Distance travelled (m)

D-value

Radius (m)

Volume (ml)

Mass (g)

Molec ular weight (g/mol)

9

0.030

8.05 × 10ˉ¹¹

2.63 × 10ˉ¹²

7.62 × 10ˉ³âµ

7.62 × 10ˉ³âµ

4.59 × 10ˉ¹¹

10

0.030

8.03 × 10ˉ¹¹

2.64 × 10ˉ¹²

7.71 × 10ˉ³âµ

7.71 × 10ˉ³âµ

4.64 × 10ˉ¹¹

Conditions

1 in 600 CV in 2% agar in Ringer incubated at 37°C.

11

0.040

1.35 × 10ˉ¹â°

1.68 × 10ˉ¹²

1.99 × 10ˉ³â¶

1.99 × 10ˉ³â¶

1.20 × 10ˉ¹²

12

0.040

1.35 × 10ˉ¹â°

1.68 × 10ˉ¹²

1.99 × 10ˉ³â¶

1.99 × 10ˉ³â¶

1.20 × 10ˉ¹²

             

Conditions:

1 in 400 CV in 1% agar in Ringer at room temperature.

Tube no

Distance travelled (m)

D-value

Radius (m)

Volume (ml)

Mass (g)

Molec ular weight (g/mol)

13

0.044

1.63 × 10ˉ¹â°

1.30 × 10ˉ¹²

9.20 × 10ˉ³âµ

9.20 × 10ˉ³âµ

5.54 × 10ˉ¹²

14

0.040

1.35 × 10ˉ¹â°

1.57 × 10ˉ¹²

1.62 × 10ˉ³âµ

1.62 × 10ˉ³âµ

9.75 × 10ˉ¹²

             

Conditions:

1 in 400 CV in 2% agar in distilled water at room temperature.

Tube no

Distance travelled (m)

D-value

Radius (m)

Volume (ml)

Mass (g)

Molec ular weight (g/mol)

15

0.043

1.56 × 10ˉ¹â°

1.36 × 10ˉ¹²

1.05 × 10ˉ³âµ

1.05 × 10ˉ³âµ

6.32 × 10ˉ¹²

16

0.039

1.23 × 10ˉ¹â°

1.72 × 10ˉ¹²

2.13 × 10ˉ³âµ

2.13 × 10ˉ³âµ

1.28 × 10ˉ¹¹

             

Conditions:

1 in 400 Bromothymol blue in 2% agar in Ringer at room temperature.

Tube no

Distance travelled (m)

D-value

Radius (m)

Volume (ml)

Mass (g)

Molec ular weight (g/mol)

17

0.057

2.73 × 10ˉ¹â°

7.75 × 10ˉ¹³

1.95 × 10ˉ³â¶

1.95 × 10ˉ³â¶

1.17 × 10ˉ¹²

18

0.058

2.83 × 10ˉ¹â°

7.48 × 10ˉ¹³

1.75 × 10ˉ³â¶

1.75 × 10ˉ³â¶

1.05 × 10ˉ¹²

             

Discussion

Holistically, the main objectives for this experiment are to figure out the process of diffusion and to determine the diffusion coefficient. Diffusion can be defined as the movement of particles or small molecules from a region of higher concentration to a region of lower concentration until equilibrium is reached. This process does not use energy and the temperature and pressure are in fixed condition.

Based on this experiment, various ratios of crystal violet and bromothymol blue are used with different percentage of agar. Some of the test tubes are also being tested with different temperature. This are some of the factors that we are needed to test. Based on the graph that have been plotted, when the temperature and the pressure are kept as constant variables, the rate of diffusion increases as the concentration gradient increases for both crystal violet and bromothymol blue.

The results obtained are following the Fick’s Law which stated that the relocation of diffusing substance rate through unit area of a section is proportional to the concentration gradient. Besides that, when the concentration of the agars are kept constant, the temperature will play its part as the manipulative variable. This part of experiment takes the effect as the kinetic energy of the molecules rise when the temperature increases. Thus, the particles or molecules will be strong enough to overcome either the intermolecular forces or the Van Der Waal forces in shorter period of time and which caused the higher concentration region to move to the lower concentration region a little bit faster.

Conclusion

To conclude, the rate of diffusion can be affected by several factors such as different in concentration, size of particle, volatility of solvent or medium and temperature. For the fixed percentage concentration of agar in Ringer, the higher the concentration of Crystal Violet, the higher the D value, so higher diffusion rate. While in higher temperature, D value is higher, therefore rate of diffusion higher at higher temperature. When we fixed the concentration of Crystal Violet, D value is higher at lower percentage of agar in Ringer solution which means the rate of diffusion higher at lower percentage of agar. Besides that, in a fixed concentration of Crystal Violet and percentage of agar, higher D value for agar in distilled water than agar in Ringer. Finally, Bromothymol Blue has higher D value than Crystal Violet when same concentration is used in the same percentage of agar which means Bromothymol Blue diffuse faster than Crystal Violet.

References

  1. Attwood, D., & Florence, A. T. (2008). Physical pharmacy. London: Pharmaceutical Press.
  1. Bentley, A. C., & Rawlins, E. A. (1977). Bentley's textbook of pharmaceutics. London: Baillière Tindall.
  1. DIFFUSION COEFFICIENT. (n.d.). Retrieved from http://www.thermopedia.com/content/696/
  1. http://chemwiki.ucdavis.edu/Physical_Chemistry/Kinetics/Complex_Reactions/Ionic_Mobility_and_El

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