Academic Experts Solutions for Chapter: Chemical Kinetics & Nuclear Chemistry, Exercise 2: KVPY PROBLEMS (PREVIOUS YEARS)

The decay profiles of three radioactive species $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are given below:

These profiles imply that the decay constants ${\mathrm{k}}_{\mathrm{A}}, {\mathrm{k}}_{\mathrm{B}}$ and ${\mathrm{k}}_{\mathrm{C}}$ follow the order:

For a zero-order reaction with rate constant $\mathrm{k}$, the slope of the plot of reactant concentration against time is:

The Arrhenius plots of two reactions, $\mathrm{I}$ and $\mathrm{II}$ are shown graphically:

The graph suggests that:

The rate constant of a chemical reaction at a very high temperature will approach:

It takes $1 \mathrm{h}$ for a first-order reaction to go to $50\%$ completion. The total time required for the same reaction to reach $87.5\%$ completion will be:

In the radioactive disintegration series ${}_{90}{}^{232}\mathrm{Th}\to {}_{82}{}^{208} \mathrm{Pb},$ involving $\mathrm{\alpha }$ and $\mathrm{\beta }$ decay, the total number of $\mathrm{\alpha }$ and $\mathrm{\beta }$ particles emitted are:

${}^{227}\mathrm{Ac}$ has a half-life of $22$ years with respect to radioactive decay. The decay follows two parallel paths:

${}^{227}\mathrm{Ac}\to {}^{227}\mathrm{Th}$ and ${}^{227}\mathrm{Ac}\to {}^{223}\mathrm{Fr}$. If the percentage of the two daughter nuclides are $2.0$ and $98.0$, respectively, the decay constant (in ${\mathrm{year}}^{-1}$) for ${}^{227}\mathrm{Ac}{\to }^{227}\mathrm{Th}$ path is closest to:

Consider the following reversible first-order reaction of $\mathrm{X}$ at an initial concentration ${\left[\mathrm{X}\right]}_0$. The values of the rate constants are ${\mathrm{k}}_{\mathrm{f}}=2{\mathrm{s}}^{-1}$ and ${\mathrm{k}}_{\mathrm{b}}=1{\mathrm{s}}^{-1}$.

A plot of concentration of $\mathrm{X}$ and $\mathrm{Y}$ as function of time is: