It is shown that the replacement of difference equations of cluster size distribution, in the standard way in classical nucleation theory, by differential equation gives erroneous cluster size distribution in the case of cluster scavenging by an aerosol. The condition for the value of vapor pressure is found. The condition is that the effect of vapor distribution around an aerosol particle of given size on nucleation can be ignored. The cluster balance equations of ion-induced nucleation at low vapor pressure, in the case of ion recombination and in the presence of an aerosol are presented.