Question

For a chemical reaction, A + 2B → C + D, the rate of reaction increases three times, when concentration of A only is increased to nine times. While when concentration of B only is increased 2 times, then rate of reaction also becomes 2 times. The order of this reaction is

• A. 3
• B. 3/2
• C. 1/2
• D. None of these

Answer 1

Answer: (B)

(2) 3/2

Answer 2

Let the rate law be Rate = k[A]^x[B]^y. When [A] is increased 9 times (and [B] is constant), the rate increases 3 times. $R_1 = k[A]^x[B]^y$ $R_2 = k[9A]^x[B]^y = 9^x R_1$ Given $R_2 = 3 R_1$, so $9^x = 3 \Rightarrow (3^2)^x = 3^1 \Rightarrow 2x = 1 \Rightarrow x = 1/2$.

When [B] is increased 2 times (and [A] is constant), the rate becomes 2 times. $R_1 = k[A]^x[B]^y$ $R_3 = k[A]^x[2B]^y = 2^y R_1$ Given $R_3 = 2 R_1$, so $2^y = 2 \Rightarrow y = 1$.

The overall order of the reaction is x + y = 1/2 + 1 = 3/2.