Question

Consider the reaction, 2A + B → products. When concentration of B alone was doubled, the halflife did not change. When the concentration of A alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is

(a) s^–1 

(b) L mol^–1 s^–1

(c) no unit 

(d) mol L^–1s^–1 .

Answer 1

(b) : Rate = K [A]^x [B]^y 

When [B] is doubled, keeping [A] constant halflife of the reaction does not change. 

Now, for a first order reaction t_1/2  = 0.693/K = 

i.e. t_1/2 is independent of the concentration of the reactant. Hence the reaction is first order with respect to B. Now when [A] is doubled, keeping [B] constant, the rate also doubles. Hence the reaction is first order with respect to A. 

Therefore, Rate = [A]¹ [B ]¹  Therefore, order = 2. 

Now for a nth order reaction, unit of rate constant is (lit)^n–1 (mol)^1–n sec^–1 when n = 2, unit of rate constant is lit mol^–1 sec^–1.