The rate of the reaction $2A + 3B \rightarrow 2C + D$ is $6 \times 10^{-4} \text{ mol dm}^{-3} \text{ s}^{-1}$, when $[A] = [B] = 0.3 \text{ mol dm}^{-3}$. If the reaction is of first order with respect to $A$ and zeroth order with respect to $B$, find the rate constant $k$.

• A
  $1 \times 10^{-3} \text{ s}^{-1}$
• B
  $2 \times 10^{-3} \text{ s}^{-1}$
• C
  $3 \times 10^{-3} \text{ s}^{-1}$
• D
  $4 \times 10^{-3} \text{ s}^{-1}$