By what factor does the rate change in each of the following cases (assuming constant temperature) ? (a) A reaction is first order in reactant A, and [A] is doubled. (b) A reaction is second order in reactant B, and [B] is halved. (c) A reaction is second order in reactant C, and [C] is tripled.

a) 2

b) 1/4

c) 9

Explanation:

a) for a first order reaction in reactant A

r initial = k*[A initial]

then if the concentration is doubled [A final ] = 2*[A initial], then

r final = k*[A final ] = 2 * k*[A initial] = 2*r initial

then the velocity changes by a factor of 2

b) for a second order reaction in reactant B

r initial = k*[B initial]²

then if the concentration is halved: [B final ] = [B initial]/2, then

r final = k*[B final ]² = k * ([B initial]/2) ² = k * [B initial]² / 4 = r initial / 4

then the velocity changes by a factor of 1/4

c) for a second order reaction in reactant C

r initial = k*[C initial]²

then if the concentration is tripled : [C final ] = 3 * [C initial], then

r final = k*[C final ]² = k * (3*[C initial]) ² = k * [C initial]² * 9 = 9 * r initial

then the velocity changes by a factor of 9