At $300 \mathrm{~K}$, a gaseous reaction $\mathrm{A} \longrightarrow \mathrm{B}+\mathrm{C}$ was found to follow first order kinetics. Starting with pure $A$, the total pressure at the end of $20 \mathrm{~min}$ was $100 \mathrm{~mm}$ of $\mathrm{Hg}$. The total pressure after the completion of the reaction is $180 \mathrm{~mm}$ of $\mathrm{Hg}$. The partial pressure of $A$ (in $\mathrm{mm}$ of $\mathrm{Hg}$ ) is

• A

  90
• B

  180
• Correct answer
  C

  80
• D

  100

Solution

At the end of the reaction, A completely converted into products, so the pressure of the products after completion of the reaction $=\mathrm{P}_{\mathrm{i}}$ Partial pressure of $\mathrm{A}, \mathrm{P}_{\mathrm{A}}=\mathrm{p}_{\mathrm{i}}-\mathrm{x}$ $$ \begin{aligned} &=(180-100) \mathrm{atm} \\ &=80 \mathrm{~atm} \end{aligned} $$

Hence, the correct answer is option: 'C'.