Thermodynamic terms:
The second shortcoming arises because Nernst law as stated above is not thermodynamically rigorous. Strictly in the thermodynamic terms, it is the activity ratio rather than concentration ratio that should be constant. In other words, the thermodynamically rigorous partition law would be stated as that the activity of a chemical species in one phase maintains a constant ratio to the activity in the other phase. This precisely defined ratio is known as thermodynamic partition coefficient or distribution coefficient (K´).
K´= {S}2/{S}1 = γ 2 [S ]2/γ 1 [S ]1= (γ 2 /γ 1) KD
or KD = γ 1 /γ 2 K '
where {S} represents the activity of the solute S and γ is its activity coefficient.
The Variation in the distribution coefficient KD can be seen due to variation in the activity coefficients in each of the phases. So long the solute concentration is very low and the activity coefficients approach unity, the value of KD is constant. The use of radiotracers for distribution studies can be very helpful to investigate the range of concentration in which the activity coefficients approach unity.
By using radiotracers, the concentration can be kept very low and the distribution of the species in the two phases can be very accurately and conveniently quantified. Using radiochemical technique, it has been observed that the distribution coefficient of gallium chloride between ethyl ether and 6 M HCl remains constant (within 5%) over a concentration range 10 -12 - 2 × 10 -3 M GaCl3. At higher concentration ranges, constant values of distribution coefficient might be expected over ranges in which the ratio of the activity coefficients remains constant. Parallel variations in the activity coefficients over extensive concentration ranges in two solvents are not likely to occur.