Kinetics of Some Complex Reactions

For a parallel first order reaction ${\mathrm{E}}_{\mathrm{a}}\left(\mathrm{kJ}/\mathrm{mol}\right)$ is:

If reaction starts with pure $\mathrm{A}$, then at any stage of reaction, mole $\%$ of $\mathrm{B}$ in product is $40\%$. Then activation energy for overall reaction is:

A substance undergoes first order decomposition involving two parallel first order reactions as :






${\mathrm{k}}_1=1.25\mathrm{ }\times \mathrm{ }{10}^{-4}\mathrm{ }{\mathrm{s}}^{-1}$

${\mathrm{k}}_2=3.80\mathrm{ }\times \mathrm{ }{10}^{-5}\mathrm{ }{\mathrm{s}}^{-1}$

The mole percentage of $\mathrm{B}$ in the products is approximately :

For a hypothetical elementary following reaction,

 Where $\frac{{\mathrm{K}}_1}{{\mathrm{K}}_2}=\frac{1}{2}$

initially, only $2$ moles of $\mathrm{A}$ are present. Find the total no. of moles of  $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ at the end of $75\%$ reaction.

A compound dissociates by two parallel reactions through the first-order path at a fixed temperature:

 $\text{A}\left(\text{g}\right)\stackrel{{\text{ k}}_1\mathrm{(}{\text{min}}^{-1}\mathrm{)} }{\to }2\text{B}\left(\text{g}\right){\text{k}}_1=6\text{.}93\times 10^{-3}{\text{ min}}^{-1}$

$\text{A}\left(\text{g}\right)\stackrel{{\text{ k}}_2\mathrm{(}{\text{min}}^{-1}\mathrm{)} }{\to }\text{C}\left(\text{g}\right){\text{k}}_2=6\text{.}93\times 10^{-3}{\text{ min}}^{-1}$

In a $1$$\mathrm{litre}$ closed vessel, the reaction is started with pure $\text{'}\mathrm{A}\text{'}$, with $1$$\mathrm{mole}$ of $\mathrm{A}$ with initial pressure of $2 \mathrm{atm}$. What is the pressure (in $\mathrm{atm}$) developed in the container after $50$ minutes from the start of the experiment?

The concentration of $\mathrm{C}$ after $5$ hours is

The initial rate of consumption of $\mathrm{A}$ and the sum of the initial rate of formation of $\mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ are respectively, taking$\left[\mathrm{A}\right]=0.25 \mathrm{M}$, equal to

Cotyledons are also called-

Ozone depletion takes place as
$2{\mathrm{O}}_3\left(\mathrm{g}\right)\to 3{\mathrm{O}}_2\left(\mathrm{g}\right)$
Step-1 ${\text{O}}_{\text{3}}\text{(g)}\stackrel{\text{K}}{\leftrightarrow }{\text{O}}_{\text{2}}\text{(g)}\text{+}\text{[O]}$
Step-2 ${\text{O}}_{\text{3}}\text{(g)}\text{+}\text{[O]}\stackrel{\text{k}}{\to }{\text{2O}}_{\text{2}}\text{(g)}\text{(slow)}$
Order of the reaction will be

Bicyclohexane was found to undergo two parallel first order rearrangements. At 730 K, the first order rate constant for the formation of cyclohexane was measured as $1.26\times {10}^{-4}\mathrm{ }{\mathrm{s}}^{-1}$, and for the formation of methyl cyclopentene, the rate constant was $3.8\times {10}^{-5}\mathrm{ }{\mathrm{s}}^{-1}$. What is the percentage distribution of the rearrangement products?

A substance undergoes first order decomposition involving two parallel first order reactions as :






${\mathrm{k}}_1=1.25\mathrm{ }\times \mathrm{ }{10}^{-4}\mathrm{ }{\mathrm{s}}^{-1}$

${\mathrm{k}}_2=3.80\mathrm{ }\times \mathrm{ }{10}^{-5}\mathrm{ }{\mathrm{s}}^{-1}$

The mole percentage of $\mathrm{B}$ in the products is approximately :

For a $\mathrm{I}\mathrm{s}\mathrm{t}$ order decomposition of $\mathrm{A}$ as given








Therefore rate constant $\left(\mathrm{K}\right)$ for the overall decomposition of $\mathrm{A}$ is

For reaction $\mathrm{R}\mathrm{X}+{\mathrm{O}\mathrm{H}}^{-}\to \mathrm{R}\mathrm{O}\mathrm{H}+{\mathrm{X}}^{-}$, Rate expression is $\mathrm{R}=4.7\times {10}^{-5}\left[\mathrm{R}\mathrm{X}\right]\left[{\mathrm{O}\mathrm{H}}^{-}\right]+2.4\times \mathrm{ }{10}^{-5}\left[\mathrm{R}\mathrm{X}\right]$. What $\mathrm{\%}$ of reactant react by $S{N}^2$ mechanism when $\left[\mathrm{O}{\mathrm{H}}^{-}\right]=0.001$ molar -

If $\mathrm{\prime }\mathrm{a}\mathrm{\prime }$ is the initial concentration of the reactant, the half-life period of the reaction of ${\mathrm{n}}^{\mathrm{th}}$ order is proportional to which of the following?

Find out the time required to decompose half of the substance for ${\mathrm{n}}^{\mathrm{th}}$order reaction is inversely proportional to: 

$\mathrm{A}$ decomposes as:



the rate of appearance of $\mathrm{B}$, taking $4 \mathrm{M}$ concentration of $\mathrm{A}$, is equal to:

The forward rate constant for the reversible gaseous reaction ${\text{C}}_2{\text{H}}_6\rightleftharpoons 2{\text{CH}}_3$ is $\text{3.14}\times 10^{+2}{s}^{-1}$ at $200 \mathrm{K}$. What is the rate constant for the backward reaction at this temperature, if ${10}^{-5}$ moles of ${\mathrm{CH}}_3$ and $100 \mathrm{mol} \mathrm{of} {\mathrm{C}}_2{\mathrm{H}}_6$ are present in $10 \mathrm{L}$ vessel at equilibrium? 

Consider the following case of a competing $1^{\mathrm{st}}$ order reaction:



The reaction starts at $\mathrm{t}=0$ with only $\mathrm{A}$. $\mathrm{C}$ is equal to $\mathrm{D}$ at all times. The time in which all three concentrations will be equal is given by:

A substance undergoes first order decomposition. The decomposition follows two parallel first order reactions as,



$\mathrm{k}1 = 1.26 \mathrm{x} {10}^{-4} {\sec }^{-1}$ and  ${\mathrm{k}}_2 = 3.8 \mathrm{x} {10}^{-4} \sec -1$

Thus the percentage distribution of $\mathrm{B}$ and $\mathrm{C}$ are:

The equilibrium between two isomers $\mathrm{A} \mathrm{and} \mathrm{B}$ studies as $\text{A}\underset{{\text{k}}_2}{\overset{{\text{k}}_1}{\rightleftharpoons }}\text{B}$, Starting with non equilibrium mixture of concentrations $[\mathrm{A}{]}_{\circ }=\mathrm{a}$ molar and$[\mathrm{B}{]}_{\circ }=\mathrm{b}$molar. It was found that $\mathrm{x}$molar concentration of $\mathrm{A}$had reacted at time t (i) Find an expression for reaction Rate $\left(\frac{\text{dx}}{\text{dt}}\right)$

(ii)  Find integrated rate equation as $2.303 \log$ $\frac{\text{p}}{\text{p}-\text{x}}=\left({\text{k}}_1+{\text{k}}_2\right)\text{ t}$ where $\text{p}=\frac{{\text{k}}_1\text{a}-{\text{k}}_2\text{b}}{{\text{k}}_1+{\text{k}}_2}$

(iii)  After$69.3 \min , \mathrm{x} = \mathrm{p}/2$calculate ${\mathrm{k}}_1 \mathrm{and} {\mathrm{k}}_2 \mathrm{if} {\mathrm{K}}_{\mathrm{eq}} = 4$ for this reaction.

A follows parallel path I order reactions giving B and C as :



If initial concentration of A is 0.25 M, calculate the concentration of C after 5 hours of reaction.
[Given : ${\lambda }_1=1\text{.}5\times 10^{-5}{\text{s}}^{-1}\text{, }{\lambda }_2=5\times 10^{-6}{\text{s}}^{-1}$]