Question

For a reaction, 1/2 A -> 2B rate of disappearance of A is related to the rate of appearance of B by the expression

a) - (d[A])/dt = 1/2 (d[B])/dt

b) - (d[A])/dt = 4 (d[B])/dt

c) - (d[A])/dt = (d[B])/dt

d) - (d[A])/dt = 1/4 (d[B])/dt

Solution

Reaction : 1/2 A -> 2B

Rate of disappearance of 'A' = - (d[A])/dt

Rate of appearance of 'B' =  (d[B])/dt

Rate of reaction in terms of A is -2(d[A])/dt

Rate of reaction in terms of B is (d[B])/(2dt)

So

- (2d[A])/dt = 1/2 (d[B])/dt

=> - (d[A])/dt = 1/4 (d[B])/dt

Therefore, option (d) is correct.