eutecticfive: June 2014

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.

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

MATERIALS

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

APPARATUS

Test tubes

Test tube caps
Test tube rack
Beaker 500 mL

Heating bath
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 28^oC

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 28^oC

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 37^oC

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 37^oC

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 28^oC 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^-1while 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,

K =Boltzmann's constant,

T = the absolute temperature.

k_B= Boltzmann's constant,

η = viscosity,

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^-1while 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^-1while at 37°C is8.0092 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

Friday 13 June 2014

EXPERIMENT 4 : DETERMINATION OF DIFFUSION COEFFICIENT