PRACTICAL 4 : DETERMINATION DIFFUSION COEFFICENT

PRACTICAL 4 : DETERMINATION OF A DIFFUSION COEFFICIENT 

INTRODUCTION:

Introduction:

            Diffusion is a process where the spontaneous movement of certain molecules from a high concentration gradient to a low concentration gradient. This phenomenon can be explained by Fick’s law of diffusion. Fick’s law state that the flowing of a substance (amount, dm in time, dt) through certain dimensions (area A) is directly proportional to concentration gradient dc/dx.

dm = -DA(dc/dx)dt

 where D is the diffusion coefficient or diffusion force for solute that has unit as m²sֿ¹.

            If a solution which have neutral molecules with concentration, Mo, put in a slim tube next to a water tube, diffusion can be stated as

M = M0 eksp (-x²/ 4 Dt)

where M is the concentration at x distance from the level between water and solution that measured at time t.

            By changing equation (II) to logarithm form, we can obtain

ln M = (ln M0 )(-x²/4Dt)

or 2.303 x 4D (log ₁₀ M₀ –log ₁₀ M) t = x² …….(III)

            Thus, one x² versus t graph can produce a straight line which cross the origin with its gradient 2.303 x 4D (log ₁₀ M₀–log ₁₀ M). From here, D can be counted.

            If the molecules in the solution are assumed to be a sphere shape, then the size and mass of the molecules can be counted from Stokes-Einstein equation.

D = kT/6пŋa

(D =kT/9 and 9 = 6пŋa)

where k is the Boltzmann constant 1.38 x 10²³ Jk^-1 , T is the temperature in Kelvin, ŋ is the viscosity of the solute, in Nm-2s and a half diameter of molecule in M. The volume for that certain sphere molecule is 4/3пa³, thus the mass of M is equal to 4/3пa³р where p is the density of the molecule.

As we know that the molecular mass of M = mN, where N is the Avogadro’s number 6.02 x 10²³ mol^-1  .

M = 4/3пa³Nр

Diffusion for molecules with charges, equation (III) has to be changed to insert the gradient force effect that exists between the solution and the solvent. However, this can be overcome by adding a little of sodium chloride into the solvent to prevent the forming of this gradient force.

Agar gel contains a semi-solid molecular net that can be interfering by water molecules. The water molecules will form a continuous phase in the agar gel. By this, the solute molecules can be diffused freely in the water, if not there will be no chemical interaction and diffusion occur. Thus, these agar gels provide a suitable supportive system that can be used in the experiment for diffusion of certain molecules in a aqueous medium

APPARATUS :

1.  Test tubes
2.  pestle and mortar
3.  stirrer
4.  beaker
5.  electronic heater
6.  test tube holder
7.  test tube 
8. stoppers
9.  measuring cylinders.

PROCEDURES:

1.      7g of agar powder was weighed and mixed with 450ml of Ringer solution.

2.      The mixture in step 1 was stirred and boiled on a hot plate until transparent yellowish solution.

3.      20ml of the agar solution was pour into each 6 test tubes. The test tubes ware 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 for standardize the colour distance that cause by the diffusion of crystal violet.

5.      After the agar solutions in the test tubes were become solidify, 5ml of 1:200, 1:400, 1:600 crystal violet solution were pour into each test tubes and 3 test tubes were to be put in room temperature while another 3 were been put in 37ºc water bath.

6.      The test tubes were been closed immediately to prevent the vaporization of the solutions.

7.      Step 2 to 6 was repeated for Bromothymol Blue solutions.

DISCUSSION:

            Diffusion is a passive process by which a concentration difference is reduced by a spontaneous flow of matter. The solute will spontaneously diffuse from a region of high chemical potential to a region of low chemical potential. This means that it is from a region of high concentration to a region of low concentration; in which the solvent molecules move in the reverse direction. The expression which relates the flow of material to the concentration gradient is referred to as Fick’s first law equation.

                      dm = -DA(dc/dx)dt ………….(I)This equation states that the amount of dm substance diffuse in the direction (x) at time (dt) go through an area (A) is proportional with the concentration gradient (dc/dx) in the area. While D is the diffusion coefficient(or diffusivity). The negative sign indicates that the flux is in the direction of decreasing concentration. Fick’s first law equation describes the diffusion process under conditions of steady state; that is the concentration gradient does not change with time.In this experiment, the diffusion particles are neutral with Mo concentration, the agar medium is considered homogenous and with constant concentration, hence the diffusion can be expressed as 

                      M = Mo eksp ^(x²/4Dt)  ………….(II)

Change the equation II to logarithm form, we have

                      ln M = ln Mo – (x²/4Dt)

                      2.303 x 4D (log ₁₀ Mo- log ₁₀ M) t = x² ………….(III)

Therefore, when a graph x² against time t is plotted, a straight line is obtained with the gradient of 2.303 

x 4D (log ₁₀ Mo- log ₁₀ M) . From here D can be calculated. We can know the both 28ºC and 37 ºC 

system, the rate of diffusion from the result that is 1:200 > 1:400 > 1:600.M is the system with the dilution 1:500,000. It acts as a constant system during the experiment. When Mo is increased, (log ₁₀ Mo- log ₁₀  M) will increased. This causes the concentration gradient become larger, therefore the driving force for the occurrence of diffusion would be larger and the diffusion process will become faster.

         Other than that, the size of the solute particles also influences the diffusion rate. In this experiment,

 the diffusion rate in Bromothymol Blue system is faster than Crystal Violet system. Thus we can

conclude that the size particle of Bromothymol Blue molecules is smaller than the size particle of Crystal 

Violet molecules.The diffusion rate at 37ºC is higher than at 28ºC. This can be explained by the Stokes-Einstein equation—the relationship between the the radius of the drug molecules and its diffusion coefficient 

(assuming spherical particles or molecules)  in which the particles are spherical.

                         D = kT/6пŋa

                       (D = kT/9 and 9 =6пŋa)

     From this equation, we know that D, the diffusion coefficient is directly proportional to the T, 

temperature. This is because when the temperature is increased, the particles gain more energy and 

become more active, hence they can diffuse more rapidly into the agar medium.

   Stokes-Einsteins equation also shows the influence of the viscosity of the medium, ŋ , on the diffusion 

coefficient. Besides that, the agar gel also can influence the rate of diffusion. When the concentration of 

gel substance is increase, the size of the hole will decrease and the diffusion rate will decrease too as the 

hole size same with the size of the diffuse molecule. Moreover, 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 be 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.

   There were errors in answer for bromothymol blue system in 37 ºC where the diffusion rate observed 

was lower than in 28 ºC . That was because of the way everyone observed the length of the diffused 

solution into agar was not same, causing inaccurate of results being recorded.

QUESTION:

1) From the trial value for Crystal Violet system D   , estimate the value of D   by using the following equation:

                        D_{28ºC      =}      T_28ºC

                       D_37ºC     =     T_37ºC

Where n₁ and n₂ are viscosity of water at 28ºC and 37ºC.Is the calculated value of D_37ºC value the same as the value from the experiment? Give some explanation if it is different. Is there any difference between the calculated molecular weight with the real molecular weight?

          

      The D_37ºC value is 5.497 x10^-11 cm²/s while the trial value is  5.631 x10^-11 cm²/s .There is a difference between these two values, where it is less of 1.34 x10^-12   cm²/s of D_37ºC value from the trial value. This is because there are some errors occurred during the trial. For example, parallax error occurred when reading the measurements, the temperature at the room is not constant at 28 ºC and the viscosity of agar in the test tube is not uniform.

2) Between Crystal Violet and Bromothymol Blue, which will diffuse much faster? Explain it if there are some differences in the diffusion coefficients.

Bromothymol Blue will diffuse faster than Crystal Violet as the diffusion coefficient of Bromothymol Blue is larger than diffusion coefficient of Crystal Violet. The smaller size of molecule, the easier it needs to penetrate through agar.

CONCLUSION:

Diffusion coefficient, D for Crystal Violet system at 28ºC is 5.338 x10^-11 cm²/s while at 37ºC is
5.497 x10 ^-11 cm²/s. The diffusion coefficient, D for Bromothymol Blue system at 28ºC is 4.06x10^-11 cm²s^-1..while at 37ºC is 4.181 x10^-11 cm²/s. The temperature and concentration of diffusing molecules are the main factors for this experiment. In both 28ºC and 37ºC system, diffusion rate is faster in the concentration of diffusing molecules 1:200> 1:400> 1:600.

REFERENCES:

A.T.Florence and D.Attwood. (1998). Physicochemical Principals of Pharmacy, 3^rd Edition. Macmillan Press Ltd.