Rate of reaction is r₁=k[A]^a[B]^b . If the concentration of A is doubled and B is halved the new rate is r₂ , What is the value of r₂ r₁ ?

Step-by-step solution

The rate law for this reaction is r = k[A]^a[B]^b . When the concentration of A is doubled and B halved, the rate becomes: r₂ = k(2[A])^a ( 1 2 [B] )^b = k 2^a[A]^a 2^ -b [B]^b = 2^ a-b k[A]^a[B]^b The ratio of rates is therefore: r₂ r₁ = 2^ a-b k[A]^a[B]^b k[A]^a[B]^b = 2^ a-b The final answer is C .