In this paper , we discuss that the result of mathematical exercises of first differentiating and second differentiating the mixing entropy of ideal gases with respect to extent of reaction at constant pressure and temperature. The minimum value of reaction free energy is ver ified indirectly in chemical equilbirium. On the basis of the relative formula of reaction mixing entropy Δ_rS_(mix)=0, it is derived to deduce and illustrate the fact that the suitable cond ition of reaction equation is |ν_2|<|ν|≤|ν_1| and ν<0, but only |ν_2|<|ν| of reactant is established.