If concentration of reactant ' A ' is increased by 10 times, rate of reaction increases 100 times. What is order of reaction if rate law is r = k [ A ]^x

Step-by-step solution

Given the rate law r = k[A]^x , the initial rate is r₁ = k[A]₁^x . When the concentration increases tenfold to [A]₂ = 10[A]₁ , the rate becomes r₂ = 100r₁ = k(10[A]₁)^x = k 10^x [A]₁^x . Dividing the second expression by the first yields: r₂ r₁ = k 10^x [A]₁^x k[A]₁^x = 10^x Since r₂ r₁ = 100 = 10^2 , it follows that 10^x = 10^2 , so x = 2 . The reaction is second order with respect to A. The correct choice is C .