Practical 4: Determination of Diffusion Coefficient

Date : 29 APRIL 2013

OBJECTIVE

To study the diffusion coefficient of crystal violet and bromothymol blue.

INTRODUCTION

Fick's first law suggests that the rate of diffusion in a given direction across and exchange surface are directly proportional to the concentration gradient- the steeper the concentration gradient, the faster the rate of diffusion, directly proportional to the surface area- the greater the surface area of a membrane through which diffusion is taking place, the faster the rate of diffusion this is one of the factors which limits cell size and inversely proportional to the distance- the rate of diffusion decreases rapidly with distance. Diffusion is thus effective only over short distances.

Diffusion is a process leading to equalization of substance concentrations in a system or establishing in a system an equilibrium concentration distribution that results from random migration of the system's elements. 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 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 exp ^{(-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 logarithmic form, we get

ln M =1n M₀ - x² /4Dt

or         2.303 x 4D (log₁₀ M₀ – log₁₀ M) t= x^{2 -------------------} (iii)

Thus a plot of x² against t can produce a straight line that passes through the origin with the slope 2.303 x 4D (log₁₀ M₀ – log₁₀ 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 temperature in Kelvin, π the viscosity of the solvent in Nm^-2s and a 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 = density).

It is known that molecular weight M=mN (N is Avogadro’s number 6.023 x 10²³ mol^-1).

∴ M = 4/3 πa³Nρ ------------------ (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 overcome by adding a little sodium chloride into the solvent to prevent the formation of this potential gradient.

APPARATUS

14 test tubes                      500ml beaker

Test tube rack                    electronic balance                                   

Dropper                             measuring cylinder

Glass rod                            hot plate and stirrer        

Weighing boat                   conical funnel

spatula

MATERIALS

1:200 crystal violet solution            1:200 bromothymol blue solution

1:400 crystal violet solution            1:400 bromothymol blue solution

1:600 crystal violet solution            1:600 bromothymol blue solution

1:500 000 crystal violet solution     1: 500 000 bromothymol blue solution

Jelly powders                                   ringer’s solution

Water bath

PROCEDURES

For the preparation of agar solution, 7.0g of jelly powder and 425mL of Ringer’s solution were measured and mixed in a beaker. Then, the agar solution was heated using hot plate and was stirred until homogenus and clear solution formed. The hot agar was divided into six test tubes and allowed to cool at room temperature. Agar was prepared in another test tube that has already been added with 1:500,000 crystal violet that was used as the standard to  measure the colour distance resulting from the crystal violet diffusion. Next, solutions of crystal violet was prepared in distilled water in the concentrations 1:200, 1:400 and 1:600. 5ml of each crystal violet solution was placed on the gels that was prepared. The test tubes were closed to prevent evaporation and stored at temperature 28⁰C and 37⁰C. These steps were repeated using bromothymol blue. The distance between the interface of the gel solution with the end of the crystal violet and bromothymol blue area were measured accurately everyday for two weeks as the value is x in meter.