The gas-phase reaction A(g)→2B(g)+C(g) is first order in A. Starting with pure A at 200 mm Hg in a rigid vessel at constant temperature, the total…

If $x$ is the pressure of A that has reacted, then $P_A=200-x$, $P_B=2x$, $P_C=x$ and the total pressure is $P_t=200+2x$. At $20$ min, $350=200+2x$ gives $x=75$, so $P_A=125\ \mathrm{mm\,Hg}$. The first-order rate constant follows from $k=\frac1t\ln\frac{P_0}{P_A}=\frac1{20}\ln\frac{200}{125}=0.02350\ \mathrm{min^{-1}}$. At $P_t=400$, $x=100$ and $P_A=100$, which is exactly half of the initial pressure, so the time is the half-life $t_{1/2}=\ln2/k=0.6931/0.02350=29.50$ minutes. A check: the first $20$ minutes reduced A from $200$ to $125$, a factor $1.6$, and a factor of $2$ needs a little longer, consistent with $29.5$ min. Answer: $29.50$.