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) *–1

(b) L mol–1 *–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 t1/2 = 0.693/K =

i.e. t1/2 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.