Question

For the reaction \[\ce{aA + bB + cC -> Products}\], 

following conclusions have been derived on the basis of experimental studies:

1. The rate of reaction remains unchanged on doubling the concentration of A.
2. The rate of reaction becomes half on doubling the concentration of B.
3. The rate of reaction increases 8 times on doubling the concentration of C.

Derive the rate law of the reaction and determine its order.

Answer 1

We are given the experimentally observed effects of concentration changes on the rate of the reaction

\[\ce{aA + bB + cC -> Products}\]

Doubling [A] does not change the rate → Order with respect to A = 0

Doubling [B] halves the rate → Order with respect to B = –1

Doubling [C] increases rate 8 times → Order with respect to C = 3 (since 2³ = 8)

The rate law can be written as

Rate = k[A]^m[B]ⁿ[C]^p

Rate = k[B]⁻¹[C]³

The overall order of the reaction is the sum of the exponents in the rate law

Order = 0 + (−1) + 3 = 2​