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 $\mathrm{r}_1$ 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 $\mathrm{r}_1: \mathrm{r}_2$ is _________ $\times 10^{-1}$. (Nearest integer)

<p>$$2 \mathrm{~A}(\mathrm{~g})+\mathrm{B}(\mathrm{g}) \rightarrow \mathrm{C}(\mathrm{g})$$</p> <p>As this is single step reaction,</p> <p>$\mathrm{r}=\mathrm{k}_{\mathrm{f}}[\mathrm{A}]^2[\mathrm{~B}]^2$</p> <p>$$\begin{array}{lllll} & 2 \mathrm{~A}(\mathrm{~g})+ & \mathrm{B}(\mathrm{g}) \rightarrow & \mathrm{C}(\mathrm{g}) \\ \mathrm{t}=0 & 1.5 & 0.7 & 0 \\ \mathrm{t}=\mathrm{t}^{\prime} & 1.5-2 \mathrm{x} \quad & 0.7-\mathrm{x} & \mathrm{x} \end{array}$$</p> <p>$$\begin{aligned} & \Rightarrow x=0.5 \mathrm{~atm} \\ & \mathrm{r}_1=\mathrm{k}_{\mathrm{f}}(1.5)^2(0.7) \\ & \mathrm{r}_2=\mathrm{k}_{\mathrm{f}}(0.5)^2(0.2) \\ & \frac{r_1}{r_2}=\frac{9 \times 7}{2}=31.5 \\ & =315 \times 10^{-1} \end{aligned}$$</p>