Embibe Experts Solutions for Chapter: Chemical Kinetics, Exercise 5: Exercise 5

The specific rate constant of a first order reaction depends upon the,

The reaction, $\mathrm{X}+2\mathrm{Y}+\mathrm{Z}\to \mathrm{N}$, occurs by the following mechanism

$\left(\mathrm{i}\right) \mathrm{X}+\mathrm{Y}\rightleftharpoons \mathrm{M};$ very rapid equilibrium.

$\left(\mathrm{ii}\right) \mathrm{M}+\mathrm{Z}\to \mathrm{P};$ slow.

$\left(\mathrm{iii}\right) \mathrm{P}+\mathrm{Y}\to \mathrm{N};$ very fast.

What is the rate law for this reaction?

The rate constant is numerically the same for three reactions of first, second and third-order, respectively. Which of the following is correct?

Two substances $\mathrm{A}\left({\mathrm{t}}_{1/2}=5\right.\min )$ and $\mathrm{B}\left({\mathrm{t}}_{1/2}=15\right.\min )$ are taken in such a way that initially, $\left[\mathrm{A}\right]=4\left[\mathrm{B}\right] .$ The time after which both the concentrations will be equal is: (Assume that the reaction is first order)

If for a reaction in which $\mathrm{A}\left(\mathrm{g}\right)$ converts to $\mathrm{B}\left(\mathrm{g}\right)$ the reaction carried out at constant $\mathrm{V}\&\mathrm{T}$ results into the following graph.

The reaction of hydrogen and iodine monochloride is given as:

${\mathrm{H}}_{2 \left(\mathrm{g}\right)}+2{\mathrm{ICl}}_{ \left(\mathrm{g}\right)}⟶2{\mathrm{HCl}}_{ \left(\mathrm{g}\right)}+{\mathrm{I}}_{2 \left(\mathrm{g}\right)}$

The reaction is of a first-order, with respect to ${\mathrm{H}}_{2 \left(\mathrm{g}\right)}$ and ${\mathrm{ICl}}_{ \left(\mathrm{g}\right)},$ following mechanisms were proposed.

Mechanism $\mathrm{A}:$

${\mathrm{H}}_{2 \left(\mathrm{g}\right)}+2\mathrm{ICl}{ }_{\left(\mathrm{g}\right)}⟶2{\mathrm{HCl}}_{ \left(\mathrm{g}\right)}+{\mathrm{I}}_{2 \left(\mathrm{g}\right)}$

Mechanism $\mathrm{B}:$

${\mathrm{H}}_{2 \left(\mathrm{g}\right)}+{\mathrm{ICl}}_{ \left(\mathrm{g}\right)}⟶{\mathrm{HI}}_{ \left(\mathrm{g}\right)};$ slow

$\mathrm{HI}{ }_{\left(\mathrm{g}\right)}+{\mathrm{ICl}}_{ \left(\mathrm{g}\right)}⟶\mathrm{HCl}{ }_{\left(\mathrm{g}\right)}+{\mathrm{I}}_{2 \left(\mathrm{g}\right)};$ fast

Which of the above mechanism(s) can be consistent with the given information about the reaction?

The bromination of acetone that occurs in acid solution is represented by the equation ${\mathrm{CH}}_3{\mathrm{COCH}}_3\left(\mathrm{aq}\right)+{\mathrm{Br}}_2\left(\mathrm{aq}\right)\to {\mathrm{CH}}_3{\mathrm{COCH}}_2\mathrm{Br}\left(\mathrm{aq}\right)+{\mathrm{H}}^{+}\left(\mathrm{aq}\right)+{\mathrm{Br}}^{-}\left(\mathrm{aq}\right)$
These kinetic data were obtained for given reaction concentrations.
                                   Initial concentrations, $\mathrm{M}$

                          Initial Rate, disappearance of ${\mathrm{Br}}_2, \mathrm{M} {\mathrm{s}}^{-1}$
                                             $$\begin{gathered} 5.7\times {10}^{-5} \\ 5.7\times {10}^{-5} \\ 1.2\times {10}^{-4} \\ 3.1\times {10}^{-4} \end{gathered}$$                     

Based on these data, the rate of reaction is :                        

The reaction ${\mathrm{N}}_2{\mathrm{O}}_5 \left(\mathrm{in} {\mathrm{CCl}}_4\right)\to 2{\mathrm{NO}}_2+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)$ is first order in ${\mathrm{N}}_2{\mathrm{O}}_5$ with rate constant $6.2\times {10}^{-4} {\mathrm{s}}^{-1}$. What is the value of rate of reaction when $\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]=1.25 \mathrm{mol} {\mathrm{L}}^{-1}$ ?