The temperature $$(\mathrm{T})$$ and rate constant $$(\mathrm{k})$$ for a first order reaction $$\mathrm{R} \rightarrow \mathrm{P}$$, was found to follow the equation $$\log \mathrm{k}=-(2000) \frac{1}{\mathrm{~T}}+8.0$$. The pre-exponential factor '$$\mathrm{A}$$' and activation energy $$\mathrm{E}_{\mathrm{a}}$$, respectively are: [Given: $$\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$]

Given below a first order reaction in the gas phase

$$\mathrm{A}(\mathrm{g}) \rightarrow \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$$

If the initial pressure of the system is $$\mathrm{P}_{\mathrm{i}}$$ and the total pressure at $$\mathrm{t}$$ seconds is $$\mathrm{P}_{\mathrm{t}}$$, the rate constant $$\mathrm{k}$$ for the reaction is:

For the reaction, $$\mathrm{A}+3 \mathrm{~B} \rightarrow 2 \mathrm{C}+\mathrm{D}$$, the concentration of $$\mathrm{A}$$ changes from 0.0150 to 0.0125 in 1 minute. The rate of formation of $$\mathrm{C}$$ in $$\mathrm{mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$$ is:

The rate of appearance of bromine is related to the disappearance of bromide ion in the equation given below is:

$$\mathrm{BrO}_3^{-} \text {(aq) }+5 \mathrm{Br}^{-} \text {(aq) }+6 \mathrm{H}^{+} \rightarrow 3 \mathrm{Br}_2(\mathrm{l})+3 \mathrm{H}_2 \mathrm{O}(\mathrm{l})$$