Q7(d). Second-order rate law with unequal concentrations; units of k

(i) Consider a second-order reaction A + B → P, where the initial concentration of A is ‘a’ mol dm⁻³ and that of B is ‘b’ mol dm⁻³. After time ‘t’, x mol dm⁻³ of A and x mol dm⁻³ of B react to form x mol dm⁻³ of the product P. Show that the second-order rate constant for this reaction will be given by k₂ = [1/((a − b)t)] ln[b(a − x)/a(b − x)] with the assumption that a > b. What will be the unit of k₂? (Consider time in seconds.) (ii) Determine the units of the rate constants for zeroth-order and 5/2-order reactions. Assume that concentrations are expressed in mol dm⁻³ and time in seconds.