AIIMS 2019 Chemistry Rate Laws MCQ Question

To derive the rate constant $k$ for the reaction $A(g) \rightarrow 2B(g) + C(g)$, we substitute $P = \frac{P_t + P_0}{2}$ into the rate equation $k = \frac{2.303}{t} \log \left( \frac{P_0}{P_0 - P} \right)$. This substitution leads to option B: $k = \frac{2.303}{t} \log \left( \frac{2P_0}{2P_0 - P_t} \right)$, which correctly accounts for the stoichiometry of the reaction and the changes in pressure.

Options A and C are incorrect because they misrepresent the relationship between $P_0$, $P_t$, and $P$, leading to invalid logarithmic expressions that do not accurately reflect the system's behavior. Understanding these relationships is crucial for correctly applying the integrated rate laws in chemical kinetics.