Chemical Kinetics Part 2

The incorrect option is option D, which gives the rate constant.Let the initial partial pressure of A be $p_0$ and its partial pressure at time $t$ be $p_t$.For the reaction $A(g) \longrightarrow 2B(g) + C(g)$, if $x$ is the decrease in pressure of A, then $p_A=p_0-x$, $p_B=2x$, and $p_C=x$.At $t=\infty$, all A has reacted, so total pressure $=2p_0+p_0=3p_0$.Given $3p_0=240\ \text{mm Hg}$, we get $p_0=80\ \text{mm Hg}$.So option B is true.At $t=10\ \text{min}$, total pressure is $p_t+2(p_0-p_t)+(p_0-p_t)=3p_0-2p_t$.Thus $160=3(80)-2p_t=240-2p_t$, giving $p_t=40\ \text{mm Hg}$.So option A is true.A first-order reaction reaches completion only as $t\to\infty$, so it never goes to completion in finite time; option C is true.For a first-order reaction, $k=\frac{1}{t}\ln\frac{p_0}{p_t}$.Therefore $k=\frac{1}{10}\ln\frac{80}{40}=\frac{\ln 2}{10}=\frac{0.693}{10}=0.0693\ \text{min}^{-1}$.Option D states $1.693\ \text{min}^{-1}$, which is incorrect.Hence the correct choice is option D.