Question

At \(T(\mathrm{K})\), decomposition of \(A(g)\) follows first order kinetics.

\[ A(g) \rightarrow B(g) + C(g) \]
The following data is obtained for this reaction.

\[ \begin{array}{|c|c|} \hline \text{Time (s)} & \text{Total pressure (atm)} \\ \hline 0 & 0.5 \\ \hline 100 & 0.6 \\ \hline \end{array} \]
What is the rate constant (in \(\mathrm{s^{-1}}\)) for this reaction?

\[ \left(\log 1.25 = 0.097,\; \log 1.666 = 0.222\right) \]

• A. \(2.23\times10^{-3}\)
• B. \(5.11\times10^{-3}\)
• C. \(2.23\times10^{-4}\)
• D. \(5.11\times10^{-4}\)

Hint:

For gaseous first-order reactions, \[ \boxed{ k=\frac{2.303}{t}\log\left(\frac{P_0}{P_t}\right) } \] where \(P_t\) is the partial pressure of the reactant at time \(t\), not the total pressure.

Answer 1

The Correct Option is A