The rate of the reaction $x + y \rightarrow \text{product}$ is $5.4 \times 10^{-2} \ mol \ dm^{-3} \ sec^{-1}$. When $[x] = 0.2 \ mol \ dm^{-3}$ and $[y] = 0.1 \ mol \ dm^{-3}$,calculate the rate constant of the reaction if it is first order in $X$ and second order in $Y$.

• A
  $18 \ mol^{-2} \ dm^6 \ sec^{-1}$
• B
  $27 \ mol^{-2} \ dm^6 \ sec^{-1}$
• C
  $32 \ mol^{-2} \ dm^6 \ sec^{-1}$
• D
  $12 \ mol^{-2} \ dm^6 \ sec^{-1}$