MEASUREMENT OF THE DIFFUSION COEFFICIENT

MEASUREMENT OF THE DIFFUSION COEFFICIENT WITH THE CLACK APPARATUS

Description of the experimental apparatus
Phaenomenon observation
Quantitative analysis

DESCRIPTION OF THE EXPERIMENTAL APPARATUS

fig. 1(1.8 K)

There are several methods to make the measurement of the diffusion coefficient for liquid solutions.
The simplest apparatus, used till today, is the one set up by Clack on 1921

The apparatus consists of a very thin vertical glass capillary which ends at the two extremities whith expantions as reservoir.

fig. 2(2.0 K)

The lower reservoir is filled with the more dense solution, the upper with the less dense one ( usually the more diluite or pure solvent) to have no disturbance from gravity .
In both the reservoir the solutions are agitated to mantain a uniform solute concentration. Both the recipients have to be sufficiently big because the little mass transport has not to sensibly alter the concentration.

PHAENOMENON OBSERVATION

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What does it happen filling the cell?

It forms a sharp interface in the capillary between the two solutions with a sudden variation of concentration.
The variation of concentration becomes smaller because of the diffusion.
After some time we have a stationary state inside the capillary with a flux of the deffundent substance so small that we can consider constants in time the concentrations in the various points. talmente piccolo che le concentrazioni alle varie altezze

(2.8 K)

Animation

QUANTITATIVE ANALYSIS

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After reaching a stationary state, the flux of diffusing substance depends only on the concentration gradient which is constant in time.

(*)

This means that the concentration difference between two points, whose distance Dx is fixed, is a constant independently of the position of the two points along the capillary.

Upon reaching a stationary state, the flux of diffusing substance depends only on the constant concentration gradient

and the concentration in the capillary shows a linear profile.

The procedure is as follows: measurement of the small concentration variations in the superior reservoir, determination of the flux of the diffusing substance J=dc/dT and derivation of the diffusion coefficient using the First Fick's law equation (italian), with the constant concentration gradient obtained by (*).