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)
During Kinetic study of reaction $$\mathrm{2 A+B \rightarrow C+D}$$, the following results were obtained :
| $$\mathrm{A [M]}$$ | $$\mathrm{B [M]}$$ | initial rate of formation of $$\mathrm{D}$$ | |
|---|---|---|---|
| I | 0.1 | 0.1 | $$6.0\times10^{-3}$$ |
| II | 0.3 | 0.2 | $$7.2\times10^{-2}$$ |
| III | 0.3 | 0.4 | $$2.88\times10^{-1}$$ |
| IV | 0.4 | 0.1 | $$2.40\times10^{-2}$$ |
Based on above data, overall order of the reaction is _________.
Consider the following reaction, the rate expression of which is given below
$$\begin{aligned} & \mathrm{A}+\mathrm{B} \rightarrow \mathrm{C} \\ & \text { rate }=\mathrm{k}[\mathrm{A}]^{1 / 2}[\mathrm{~B}]^{1 / 2} \end{aligned}$$
The reaction is initiated by taking $$1 \mathrm{~M}$$ concentration of $$\mathrm{A}$$ and $$\mathrm{B}$$ each. If the rate constant $$(\mathrm{k})$$ is $$4.6 \times 10^{-2} \mathrm{~s}^{-1}$$, then the time taken for $$\mathrm{A}$$ to become $$0.1 \mathrm{~M}$$ is _________ sec. (nearest integer)
Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below.
Some details of the above reactions are listed below.
| Step | Rate constant (sec$$^{-1}$$) | Activation energy (kJ mol$$^{-1}$$) |
|---|---|---|
| 1 | $$\mathrm{k_1}$$ | 300 |
| 2 | $$\mathrm{k_2}$$ | 200 |
| 3 | $$\mathrm{k_3}$$ | $$\mathrm{Ea_3}$$ |
If the overall rate constant of the above transformation (k) is given as $$\mathrm{k=\frac{k_1 k_2}{k_3}}$$ and the overall activation energy $$(\mathrm{E}_{\mathrm{a}})$$ is $$400 \mathrm{~kJ} \mathrm{~mol} \mathrm{~m}^{-1}$$, then the value of $$\mathrm{Ea}_3$$ is ________ integer)