The gas-phase reaction A(g)→ 2B(g)+C(g) is first order in A and is carried out in a rigid vessel at constant temperature, starting with pure A at 100…

Let $p_A$ be the partial pressure of $\mathrm{A}$ and let $x$ be the pressure of $\mathrm{A}$ that has reacted. At constant volume and temperature, $p_A=100-x$ while the total pressure is $P_t=(100-x)+2x+x=100+2x$. After $30\ \mathrm{min}$, $250=100+2x$ gives $x=75$, so $p_A=25\ \mathrm{kPa}$. Because the reaction is first order in $\mathrm{A}$, $p_A$ decays exponentially, and $p_A$ fell from $100$ to $25$, a factor of $4$, in $30\ \mathrm{min}$. That is two half-lives, so $t_{1/2}=15\ \mathrm{min}$. At $60\ \mathrm{min}$ there have been four half-lives and $p_A=100/16=6.25\ \mathrm{kPa}$, so $x=93.75$ and $P_t=100+2(93.75)=287.5\ \mathrm{kPa}$. Option (B) is the pressure at $45\ \mathrm{min}$, and (C) is the limit as $t\to\infty$.