Consider the following first order gas phase reaction at constant temperature \(\mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})\) If the total pressure of the gases is found to be \(200\) torr after \(23 \mathrm{sec}\). and \(300\) torr upon the complete decomposition of \(\mathrm{A}\) after a very long time, then the rate constant of the given reaction is _______ \(\times 10^{-2} \mathrm{~s}^{-1}\) (nearest integer) [Given : \(\log _{10}(2)=0.301\) ]

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.