(d/dt)[A] = -k[A][B]

In the simple theory of reaction rates, k is actually constant. This means that if the concentration of A is doubled keeping the concentration of B unchanged, then the reaction rate doubles, and vice versa. At a molecular level, the assumption of this simple theory is that each individual reaction between molecules takes place essentially uninfluenced by the presence of all the other molecules. This is similar to the assumptions underlying the equations of an ideal gas.

The simple theory of reaction rates can be derived from the absolute rate theory given in the 'Kinetics' section of this course by assuming that the Gibbs free energy of each solvated ion of type i varies with concentration in exactly the same way as the Gibbs free energy of an ideal gas, i.e.:

G_i(c) = G_i(c₀)+kT ln(c/c₀)

This assumption is not true when the reacting molecules interact with solvated molecules in addition to the ones taking part. This is most noticeable when the molecules have an electric charge, because the electrostatic interaction is long-range. In studies of the rates of reaction involving ions in aqueous solution, Brønsted and Bjerrum found that at high concentrations k is not in fact constant but changes progressively with increasing concentration, usually in a downwards direction (decreasing). This change of reaction constant is known as the primary salt effect.

When the reaction constant decreases with increasing concentration, this does not mean that the reaction rate (d/dt)[A] slows down for increasing concentrations, which would be contrary to le Chatelier's principle. It just means that the reaction rate increases with concentration slower than proportionally.

The Brønsted-Bjerrum law for the change of rate constant of a reaction involving two ions A and B is given by:

k =   k_o10^{2 A z_A z_B I ½}

For reactions in water, A is a constant equal to 0.509 kg^½.mol^-½, z_A and z_B are the charges on the two ions and I is the ionic strength, defined by:

I   =   ½Sm_iz_i²

For a 1-1 electrolyte like NaCl, the ionic strength is equal to the molality, i.e. for 1 M NaCl, I = 1 M. The ionic strength of a 1-2 electrolyte is 3m and of a 2-2 electrolyte is 4m. Take care, I is only an S.I. quantity if it is taken to have the units of mol.kg^-1, which is not strictly allowed in the equations that I enters into.

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