The equilibrium zeta adsorption isotherm for vapours indicates the amount adsorbed is finite for vapour-phase pressures approaching the saturation value, and is strongly supported by experimental measurements for a number of different vapour–solid surface systems. This isotherm assumes the adsorbate consists of differently sized molecular clusters in local equilibrium rather than the adsorbate being in layers. We use the local-equilibrium approximation and develop a method to determine the expression for chemical potential of the adsorbate in terms of the amount adsorbed, n^A(t). This allows us to apply statistical rate theory to calculate n^A(t) at five different vapour-phase pressures, x^V (≡P^V/P_sat), in terms of a parameter, r^e. Statistical rate theory indicates that r^e describes the dynamics of a given isolated system under equilibrium conditions. We consider two methods for determining the value of r^e that give the best agreement with the measurements performed at each of five values of x^V. In one method, we assume, r^e, is a function of both temperature, T, and pressure, x^V, and determine the five best-fit values of r^e. In the experiments, x^V changes by a factor of more than two, but the standard deviation in the r^e values is 6%. In the second method, we assume r^e is a function only of T; and find that the value of r^e is not changed significantly. In all cases, the calculated n^A(t) agree with the measurements.