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 $t$.

• A
  $k = 2.303 \times \log_{10} \frac{P_{i}}{2P_{i} - P}$
• B
  $k = \frac{2.303}{t} \times \log_{10} \frac{P_{i}}{2P_{i} - P}$
• C
  $k = \frac{1}{t} \ln \frac{2P_{i} - P}{P_{i}}$
• D
  $k = \frac{2.303}{t} \times \log_{10} \frac{P_{i} - P}{P_{i}}$