Two substances $\mathrm{R}$ and $\mathrm{S}$ decompose in a solution independently, both following first order kinetics. The rate constant of $\mathrm{R}$ is twice that of $\mathrm{S}.$ In an experiment, the solution initially contained $0.5$ millimoles of $\mathrm{R}$ and $0.25$ millimoles of $\mathrm{S}.$ The molarities of $\mathrm{R}$ and $\mathrm{S}$ will be equal just at the end of time equal to:

Consider the reaction: ${\mathrm{Cl}}_2\left(\mathrm{aq}\right)+{\mathrm{H}}_2\mathrm{S}\left(\mathrm{aq}\right)\to \mathrm{S}\left(\mathrm{s}\right)+2{\mathrm{H}}^{+}\left(\mathrm{aq}\right)+2{\mathrm{Cl}}^{-}\left(\mathrm{aq}\right)$

The rate equation for this reaction is:

$\mathrm{Rate}=\mathrm{K}\left[{\mathrm{Cl}}_2\right]\left[{\mathrm{H}}_2\mathrm{S}\right]$

Which of these mechanisms is/are consistent with this rate equation?

$\begin{array}{l}\left(\mathrm{A}\right) {\mathrm{Cl}}_2+{\mathrm{H}}_2\mathrm{S}\to {\mathrm{H}}^{+}+{\mathrm{Cl}}^{-}+{\mathrm{Cl}}^{+}+{\mathrm{HS}}^{-}\left(\mathrm{slow}\right) \\ {\mathrm{Cl}}^{+}+{\mathrm{HS}}^{-}\to {\mathrm{H}}^{+}+{\mathrm{Cl}}^{-}+\mathrm{S} \left(\mathrm{fast}\right)\end{array}$

$\begin{array}{ll}\left(\mathrm{B}\right) {\mathrm{H}}_2\mathrm{S}\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{HS}}^{-}& (\mathrm{fast} \mathrm{equilibrium}) \\ {\mathrm{Cl}}_2+{\mathrm{HS}}^{-}\to 2{\mathrm{Cl}}^{-}+{\mathrm{H}}^{+}+\mathrm{S}& \mathrm{ }\left(\mathrm{slow}\right)\mathrm{ }\end{array}$

For a second-order reaction of the type: $\begin{array}{c}a\\ 2A\\ a-x\end{array}\to \underset{\mathrm{x}/2}{\mathrm{products},}$

the rate law is given by:

$\mathrm{rate} \mathit{=}\mathit{-}\mathit{ }\frac{\mathit{1}}{\mathit{2}}\mathit{ }\frac{d\mathit{(}a\mathit{-}x\mathit{)}}{dt}\mathit{ }\mathit{=}\mathit{+}\frac{d\mathit{(}x\mathit{/}\mathit{2}\mathit{)}}{dt}\mathit{ }\mathit{=}\mathit{ }{k}_{\mathit{2}}\mathit{ }\mathit{(}a\mathit{-}x{\mathit{)}}^{\mathit{2}}$

The Integrated rate law will be:

From the following data for the reaction between $\mathrm{A}$ and $\mathrm{B}$ :

If the pre-exponential factor is $\mathrm{a}\times {10}^{17}$, find the value of $\text{'}\mathrm{a}\text{'}$ up to the nearest integer.

The decomposition of ${\mathrm{PH}}_3$ at $950 \mathrm{K}$ according to $4{\mathrm{PH}}_3\left(\mathrm{g}\right)\to {\mathrm{P}}_4\left(\mathrm{g}\right)+6{\mathrm{H}}_2\left(\mathrm{g}\right)$ is a first-order reaction. The following measurements were made on a system containing only ${\mathrm{PH}}_3$ initially.

Calculate the rate constant in ${\min }^{-1}$ .