Saturday, 1 June 2013

PRACTICAL 4: DETERMINATION OF DIFFUSION COEFFICIENT

OBJECTIVE :
To determine the value of diffusion coefficient, D.

THEORY :
Diffusion, which is the spontaneous movement of solutes from an area of high concentration to an area of low concentration 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.
                                  dc
            dm  =   - DA        dt      ----------- (i)
                                  dx
D is the diffusion coefficient or diffusivity for the solute, in unit m²sֿ¹.
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 eksp (-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 logarithm form, we get
               ln M  =  ln M0 – x2/ 4Dt
or  2.303 x 4 D ( log10 M0 – log10 M) t = x2 ---------- (iii)
Thus aplot of x² against t can produce a straight line that passes through the origin with the slope 2.303 x 4D (log 10 M0–log 10 M). From here, D can be counted.
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
It is known that molecular weight M=mN (N is Avogadro’s number 6.02 x 1023 mol-1 ).
M = 4/3πa3N ρ ---------- (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 prevented by adding a little sodium chloride into the solvent to avoid 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 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:                                                               APPARATUS:
Agar powder                                                                    500 mL beaker
Ringer’s solution                                                               5 mL pipette
1 : 500000 crystal violet solution                                       Glass rod
1 : 200 crystal violet solution                                             14 test tubes with covers
1 : 400 crystal violet solution                                             Hot plate
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



EXPERIMENTAL PROCEDURES :
1)      7g of agar powder was weighed and mixed with 420ml of Ringer solution in the 500mL beaker..
2)      The mixture in the beaker was stirred and boiled on a hot plate until a transparent yellowish solution was obtained.
3)      About 20ml of the agar solution was pour into each 6 test tubes. The test tubes were then put in the fridge to let them cool.
4)      An agar test tube which contained 5ml of 1:500,000 crystal violet was being prepared and it was used as a standard system to measure the distance of the colour as a result of the diffusion of crystal violet.
5)      After the agar solutions in the test tubes solidifying, 5ml of each 1:200, 1:400, 1:600 crystal violet solution were pour into each test tubes.
6)      The test tubes were closed immediately to prevent the vaporization of the solutions.
7)      Three test tubes were put in room temperature,28 ºC while another three were put in 37ºC water bath.
8)      The distance between the agar surface and the end of crystal violet where that area has the same color as in the indicator was measured accurately.
9)      Average of the readings were obtained, this value is x in meter.
10)  The x values were recorded after 2 hours and at appropriate intervals for 1 weeks.
11)  Procedures 3 to 10 were repeated for bromothymol blue solutions.
12)  Graph of x² values ( in m²) versus time ( in hours) was potted.
The diffusion coefficient , D was determined from the graph gradient for both   28 ºC and 37 ºC ; the molecular mass of crystal violet and bromothymol blue  were also determined by using N and V equation.

RESULTS

Crystal violets at room temperature (28°C)

Crystal violets in water bath (37°C)

Bromothymol blue at room temperature (28°C)

Bromothymol blue in water bath (37°C)
At concentration 1:200
Gradient          = 2.303x4D(log10Ma-log10 M)
(14-6)x10-4         =2.437x10-9 = 2.303x4D(log10Ma-log10 M)
(6.2-2.4)(86400)
2.437x10-9               = 2.303x4D[log10(1/200)-log10(1/500 000)]
D                     = 7.785 x10-11 m2s-1

At concentration 1:400
Gradient          = 2.303x4D(log10Ma-log10 M)
(12-6)x10-4         =1.929x10-9 = 2.303x4D(log10Ma-log10 M)
(6.6-3)(86400)
1.929x10-9               = 2.303x4D[log10(1/400)-log10(1/500 000)]
D                     = 6.762x10-11 m2s-1

At concentration 1:600
Gradient          = 2.303x4D(log10Ma-log10 M)
(5.2-1.2)x10-4         =1.157x10-9 = 2.303x4D(log10Ma-log10 M)
(6-2)(86400)
1.157x10-9               = 2.303x4D[log10(1/600)-log10(1/500 000)]
D                     = 4.3x10-11 m2s-1
Average diffusion coefficient: 6.282x10-11 m2s-1 

At concentration 1:200
Gradient          = 2.303x4D(log10Ma-log10 M)
(25-10)x10-4         =4.34x10-9 = 2.303x4D(log10Ma-log10 M)
(5.8-1.8)(86400)
4.34x10-9                   = 2.303x4D[log10(1/200)-log10(1/500 000)]
D                     = 13.865x10-11 m2s-1

At concentration 1:400
Gradient          = 2.303x4D(log10Ma-log10 M)
(12-5)x10-4         =2.7x10-9 = 2.303x4D(log10Ma-log10 M)
(5-2)(86400)
2.7x10-9                       = 2.303x4D[log10(1/400)-log10(1/500 000)]
D                     =9.464 x10-11 m2s-1

At concentration 1:600
Gradient          = 2.303x4D(log10Ma-log10 M)
(10-1)x10-4         =2.604x10-9 = 2.303x4D(log10Ma-log10 M)
(5-1)(86400)
2.604x10-9               = 2.303x4D[log10(1/600)-log10(1/500 000)]
D                     = 9.678x10-11 m2s-1

Average diffusion coefficient: 11.002x10-11 m2s-1 

At concentration 1:200
Gradient          = 2.303x4D(log10Ma-log10 M)
(12-4)x10-4         =2.205x10-9 = 2.303x4D(log10Ma-log10 M)
(5.8-1.6)(86400)
2.205x10-9               = 2.303x4D[log10(1/200)-log10(1/500 000)]
D                     = 7.044x10-11 m2s-1

At concentration 1:400
Gradient          = 2.303x4D(log10Ma-log10 M)
(8-4)x10-4         =1.781x10-9 = 2.303x4D(log10Ma-log10 M)
(4.4-1.8)(86400)
1.781x10-9               = 2.303x4D[log10(1/400)-log10(1/500 000)]
D                     =6.243 x10-11 m2s-1

At concentration 1:600
Gradient          = 2.303x4D(log10Ma-log10 M)
(7.6-2)x10-4         =1.62x10-9 = 2.303x4D(log10Ma-log10 M)
(6.4-2.4)(86400)
1.62x10-9                   = 2.303x4D[log10(1/600)-log10(1/500 000)]
D                     = 6.021x10-11 m2s-1

Average diffusion coefficient: 6.436x10-11 m2s-1 

At concentration 1:200
Gradient          = 2.303x4D(log10Ma-log10 M)
(16-6)x10-4         =2.894x10-9 = 2.303x4D(log10Ma-log10 M)
(5.4-1.4)(86400)
2.894x10-9               = 2.303x4D[log10(1/200)-log10(1/500 000)]
D                     =9.245 x10-11 m2s-1

At concentration 1:400
Gradient          = 2.303x4D(log10Ma-log10 M)
(15-5)x10-4         =2.63x10-9 = 2.303x4D(log10Ma-log10 M)
(6-1.6)(86400)
2.63x10-9                   = 2.303x4D[log10(1/400)-log10(1/500 000)]
D                     =9.219x10-11 m2s-1

At concentration 1:600
Gradient          = 2.303x4D(log10Ma-log10 M)
(11-3)x10-4         =2.205x10-9 = 2.303x4D(log10Ma-log10 M)
(6-1.8)(86400)
2.205x10-9               = 2.303x4D[log10(1/600)-log10(1/500 000)]
D                     = 8.195x10-11 m2s-1

Average diffusion coefficient: 8.886x10-11 m2s-1 

Discussion
Agar diffusion refers to the movement of molecules through the matrix that is formed by the gelling of agar. When performed under controlled conditions, the degree of the molecule's movement can be related to the concentration of the molecule. Agar will be the inert medium that we are using to investigate diffusion through. Agar is extracted from seaweed and after dissolving it in hot water it cools to form a 'solid' jelly. The agar that will be used will be made alkaline by adding small amounts of sodium hydroxide

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-1 while bromothymol blue solution with molecular formula C27H28Br2O5S has molecular weight of 624.38 g mol−1.  Molecular weight is how much mass each particle has or how heavy it is. The heavier the particle, the slower it is going to move ii solidified agar solution, assuming energy of the system remains constant.

For a given concentration gradient, a molecule's rate of diffusion is inversely proportional to its frictional coefficient, which depends on both size and shape. Assuming that the particle has a constant shape,  a sphere, then rate of diffusion is inversely proportional to the radius or diameter of the diffusing molecule. Assuming particle density doesn’t change, particle mass is proportional to the cube of particle radius. Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molecular weight

Rate1 / Rate2 = square root of (Mass2 / Mass 1)
As the experiment is done in two different temperature of 28oC water bath and 37oC room temperature, the higher the temperature gives higher rate of diffusion. As the temperature increases, the amount of energy available for diffusion is increased. There would be increase in molecules' speed (kinetic energy). 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
                       (D = kT/9 and 9 =6пŋa)
Where D is the diffusion constant, K is Boltzmann's constant, T is the absolute temperature.
kB is Boltzmann's constant, η is viscosity, a is the radius of the spherical particle.

The concentration also varies for each crystal violet and bromothymol blue solution. For higher concentration of solution gives higher rate of diffusion. When a substance is diffusing between two compartments, the greater the concentration difference between the two compartments, the faster the substance will diffuse (faster rate of diffusion). diffusion will occur from areas of high concentration to low concentration. Fick's First Law states that the flux, J, of a component of concentration, C, across a membrane of unit area, in a predefined plane, is proportional to the concentration differential across that plane), and is expressed by:

Where J – Flux, D – diffusion coefficient, δC/δx – concentration gradient

(C is concentration and x is distance of movement perpendicular to the membrane surface )

Crystal violet diffuse faster than bromothymol blue solution. The diffusion coefficient value calculated from the experiment for crystal violet has higher value compared  to the value of diffusion coefficient for bromothymol blue solution. 

CONCLUSION
The diffusion coefficient of crystal violet at 28oC is 6.282x10-11 m2s-1 while at 37oC is 11.002x10-11 m2s-1. diffusion coefficient of bromothymol blue at 28oC is 6.436x10-11 m2s-1  while at 37oC is 8.886x10-11 m2s-1 the factor that influence the ratof diffusion is concentration, temperature and molecular weight since the surface area, Permeability is kept constant. diffusion rate is faster in the concentration of diffusing molecules 1:200> 1:400> 1:600.


REFERENCE









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