Salt Effects on Second-Order Ionic Reactions

5 SALT EFFECTS ON SECOND-ORDER IONIC REACTIONS 

The application of TST to account for the effects on the rate constants of reactions involving ions is one of its notable successes. We shall make use of a previously derived equation [Eq. (9-28)] to relate changes in the rate constant to the activity coefficients  

The Debye-Hiickel formula for the activity coefficient of an ion was developed by a consideration of ion atmosphere effects.10 It starts with an electrostatic expression for the free energy of interaction for one ion with one mole of others  

From the difference between the reference solution (taken as the ideal one governed by Raoult s law) and the one with ions, the expression for the activity coefficient for a single ion is 

As it happens, the product Ba is near unity. In particular, it is about one in water if a (the interaction distance) is 3 X 10 10 m. This is not an unreasonable distance. Even if a is somewhat different, the simplification that Ba is nearly unity is a fair approximation, and one that is often made. This is allowed because Ba occurs as a multiplier of fju in the denominator of Eq. (9-39), where this product is invariably less than the unity to which it is added. And the equations for the activity coefficients are in any event reliable only at low ionic strength. For these reasons, and because of the resulting simplification, we shall approximate the expression for the activity coefficient as 

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