For the decomposition of $N_2O_5$ according to the equation $2N_2O_5(g) \to 4NO_2(g) + O_2(g)$,the reaction is of first order. After $30 \, \min$ from the start of the reaction in a closed vessel,the total pressure is $305.5 \, mm \, Hg$,and at the end of complete decomposition,the total pressure is $587.5 \, mm \, Hg$. Calculate the rate constant of the reaction.

• A
  $3.72 \times 10^{-3} \, \min^{-1}$
• B
  $3.72 \times 10^{-2} \, \min^{-1}$
• C
  $2.15 \times 10^{-3} \, s^{-1}$
• D
  $1.15 \times 10^{-4} \, s^{-1}$