Question

The rate of reaction, 2NO + C l 2 → 2 N O C l is doubled when concentration of C l 2 is doubled and quadrapules when concentration of both NO is doubled. by what factor will the rate increase if both concentration of no and cl2 are doupled

• A. 2
• B. 4
• C. 8
• D. 16

Answer 1

Answer: (C)

8

Answer 2

The rate law is given by: Rate = $k[\text{NO}]^x[\text{Cl}_2]^y$. When $[\text{Cl}_2]$ is doubled, the rate doubles: $2 = 2^y \Rightarrow y = 1$. When $[\text{NO}]$ is doubled, the rate quadruples: $4 = 2^x \Rightarrow x = 2$. So, the rate law is: Rate = $k[\text{NO}]^2[\text{Cl}_2]$. If both concentrations are doubled: New Rate = $k(2[\text{NO}])^2(2[\text{Cl}_2]) = k(4[\text{NO}]^2)(2[\text{Cl}_2]) = 8 k[\text{NO}]^2[\text{Cl}_2] = 8 \times \text{Rate}$. The rate increases by a factor of 8.