Consider the following single step reaction in gas phase at constant temperature. \(2 \mathrm{~A}_{(\mathrm{g})}+\mathrm{B}_{(\mathrm{g})} \rightarrow \mathrm{C}_{(\mathrm{g})}\) The initial rate of the reaction is recorded as \(r_1\) when the reaction starts with \(1.5 \mathrm{~atm}\) pressure of \(\mathrm{A}\) and \(0.7 \mathrm{~atm}\) pressure of B. After some time, the rate \(r_2\) is recorded when the pressure of \(C\) becomes \(0.5 \mathrm{~atm}\). The ratio \(r_1: r_2\) is _______ \(\times 10^{-1}\). (Nearest integer)

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.