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(B) For the reaction: $A_{(g)} \rightarrow B_{(g)} + C_{(g)}$At $t = 0$: Pressure of $A = P_{i}$,$B = 0$,$C = 0$.At $t = t$: Pressure of $A = P_{i} -

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$k = \frac{2.303}{t} 	imes \log_{10} \frac{P_{i}}{2P_{i} - P}$

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(B) For the reaction: $A_{(g)} \rightarrow B_{(g)} + C_{(g)}$At $t = 0$: Pressure of $A = P_{i}$,$B = 0$,$C = 0$.At $t = t$: Pressure of $A = P_{i} - x$,$B = x$,$C = x$.Total pressure $P = (P_{i} - x) + x + x = P_{i} + x$.Therefore,$x = P - P_{i}$.The pressure of $A$ at time $t$ is $P_{A} = P_{i} - x = P_{i} - (P - P_{i}) = 2P_{i} - P$.For a first-order reaction,the integrated rate law is $k = \frac{2.303}{t} \log_{10} \frac{P_{i}}{P_{A}}$.Substituting $P_{A}$,we get $k = \frac{2.303}{t} \log_{10} \frac{P_{i}}{2P_{i} - P}$.

Which of the following represents the integrated rate law equation for the gas-phase first-order reaction,$A_{(g)} \rightarrow B_{(g)} + C_{(g)}$? If $P_{i}$ is the initial pressure of $A$ and $P$ is the total pressure of the reaction mixture at time $t$.

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