Based on an approximate model of the collisions of electrons with molecules in a binary gas mixture, analytic formulas are obtained which yield quantitative estimates of the impact ionization constant for a mixture of argon with ethane or n-hexane. It is shown that the electric field dependence of the ionization constant varies nonmonotonicly with increasing the admixture percentage in argon. This is due to the simultaneous effect of two factors: the variation of the average electron energy and the transformation of the electron energy spectrum.