Concept of Rate of disappearance

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.