In ideal solutions, molarity [], mol/l is used as the unit of concentration. If the dissolution is real, it is necessary to use activities. It is only necessary to substitute the molar concentration for the activity in the equations.\\ Let the reaction be elementary, $aA+bB\rightleftharpoons cC+dD$, the speed of the direct reaction as a function of activities is given by the equation, $r_d=k_da_{A}^{a}a_{B}^{b}$ and the rate of the reverse reaction by, $r_i=k_ia_{C}^{c}a_{D}^{d}$.

Equating both speeds, the equilibrium constant as a function of activities is obtained, $r_d=r_i$: $$k_da_{A}^{a}a_{B}^{b}=k_ia_{C}^{c} a_{D}^{d}$$ Solving for: $$\frac{k_d}{k_i}=\frac{a_{C}^{c}a_{D}^{d}}{ a_{A}^{a}a_{B}^{b}}=K_e$$ In 1929, it was observed that the equations of $r_d$ and $r_i$ were not correct and needed a correction factor, And, dependent on temperature, pressure and concentrations. The speeds that fit the experimental data are: $$r_d=kYa_{A}^{a}a_{B}^{b}\;\;\;\;\;\;\;\; r_i=kYa_{C}^{c}a_{D}^{d}$$ By equating $r_d$ to $r_i$, the Y factor disappears and we get $Ke=\frac{k_d}{k_i again }$.

To finish, we will write the kinetic equation of the elementary reaction $aA+bB\rightarrow P$, assuming that the solution is real. $$r=kYa_{A}^{a}a_{B}^{b}\;\;\;\Rightarrow \;\;\; r=kY\gamma_{A}^{a}[A]^a\gamma_{B}^{b}[B]^b$$ Expression that can be written as: $r=k_{ap} [A]^a[B]^b$, where, $k_{ap}=kY\gamma_{A}^{a}\gamma_{B}^{b}[B]^b$.