The rate law for a reaction is given by the equation:Rate = k [A]^m [B]^nwhere Rate is the reaction rate, k is the rate constant, [A] and [B] are the concentrations of the reactants, and m and n are the reaction orders with respect to each reactant.In this case, the reaction is between nitrogen dioxide NO2 and hydrogen gas H2 . The problem states that the reaction rate is directly proportional to the concentration of nitrogen dioxide and the square of the concentration of hydrogen gas. This means that the reaction order with respect to nitrogen dioxide m is 1, and the reaction order with respect to hydrogen gas n is 2.Therefore, the rate law for this reaction can be expressed as:Rate = k [NO2]^1 [H2]^2or simply:Rate = k [NO2][H2]^2