(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.