The gas-phase reaction A(g)→2B(g)+C(g) is first order in A. Pure A at 100 kPa is allowed to react in a rigid vessel at constant temperature, and the…

Let the pressure of A that has reacted be $x$. Each mole of A gives three moles of gas, so the total pressure is $P=P_0-x+3x=P_0+2x$. At $20$ min, $160=100+2x$, so $x=30\ \mathrm{kPa}$ and $p_\mathrm{A}=70\ \mathrm{kPa}$. For first order, $k=\tfrac{1}{t}\ln(P_0/p_\mathrm{A})=\tfrac{0.357}{20}=1.785\times10^{-2}\ \mathrm{min^{-1}}$ and $t_{1/2}=0.693/k=38.8\approx39$ min: (A) is correct. (B) At one half-life $p_\mathrm{A}=50$ and $x=50$, so $P=100+2(50)=200\ \mathrm{kPa}$, not $150$ (that value comes from wrongly assuming a 1:1 mole change): wrong. (C) At completion $P=3P_0=300\ \mathrm{kPa}$: wrong. (D) $p_\mathrm{A}=100\,e^{-0.01785\times40}=49\ \mathrm{kPa}$; the value $35$ would result from assuming the pressure of A halves every $20$ min, which is the error of mistaking $20$ min for the half-life: wrong.