Standard States Based on Henrys Law

Because the activities of solutes in dilute solutions can be more closely approximated with Henry s Law than with Raoult s Law, they are traditionally treated separately and use standard states different than those we have so far encountered. There are two variations of usage here, both of the variable pressure type, one required when using mole fractions, and another when using molalities. 

We derived equation (12.12) from equation (12.10) simply by saying that 7 could be introduced to take care of deviations from Raoult s Law. Deviations from Henry s Law are similarly accounted for by introducing 7// instead of 7/ , thus 

Studies of aqueous solutes traditionally use molalities, which implies use of still another standard state. To develop this subject we will resort to using Euler s theorem, which makes the derivation less than completely intuitive, but basically we are just looking for the relationship between p and m, the solute molality, in the dilute solution region where Henry s Law is obeyed. 

Partial differentiation of equation (12.12) with respect to the number of moles of the second component, n-i, gives 

We wish to consider first solutions in which the solute obeys Henry s Law, and it can be shown that in these solutions the solvent must obey Raoult s Law, i.e., 7 = 1. If we also assume that ri2 is so much smaller than ni that it may be neglected in the (ni + n2 term, then 

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