Consider a [[Global reaction]] $\ce{A->products}$ Let us say the detail reaction steps are $\ce{A + A <=>[k_f][k_b] A^* + A}\tag{1}$ $\ce{A^* ->[k_{f'}] Products}\tag{2}$ Writing the rate equation $\frac{dC_A}{dt} = -k_fC_A^2 + k_bC_AC_A* \tag{3}$ $\frac{dC_A*}{dt} = k_fC_A^2 - k_bC_AC_A* - k_f'C_A*$ By [[Detailed chemistry#1. Steady State approximation|steady state approximation]]: $\frac{dC_A*}{dt}=0$ $k_fC_A^2 - k_bC_AC_A* - k_f'C_A*=0$ $$$C_A* = \frac{k_fC_A^2}{k_bC_A+k_f'} \tag{4}$ substituting (4) in overall reaction rate equation (3) $\frac{dC_A}{dt} = -k_fC_A^2 + k_bC_A\frac{k_fC_A^2}{k_bC_A+k_f'}$ $\frac{dC_A}{dt} = -\frac{k_f'k_fC_A^2}{k_bC_A+k_f'}$ $\frac{dC_A}{dt} = -\frac{k_fC_A^2}{\frac{k_b}{k_f'}C_A+1}$ At high pressures the bi-molecular reactions are fast so $k_b$ is large and the reaction approximates to $\frac{dC_A}{dt} = -\frac{k_fC_A}{\frac{k_b}{k_f'}}$ which is first order At low pressures $k_b$ is small and the reaction behaves as second order