Embibe Experts Solutions for Chapter: Chemical Kinetics, Exercise 1: Exercise 1

A gaseous reactant '$\mathrm{X}$' at $60°\mathrm{C}$ undergo decomposition according to $1^{\mathrm{st} }$ order kinetics ${\mathrm{x}}_{\left(\mathrm{g}\right)}\to 2{\mathrm{y}}_{\left(\mathrm{g}\right)}+{\mathrm{z}}_{\left(\mathrm{g}\right)}$ in a closed vessel on starting with pure '$\mathrm{x}$' at the end of $18$ min the total pressure of the gaseous mixture was found to be $250 \mathrm{mm}$ of $\mathrm{Hg}$ and after long time the total pressure gaseous mixture was found to be $300 \mathrm{mmHg}$, than half life of the reaction in minutes is

A mixture of $2$ gases $-\mathrm{A}$ (reactive) and $\mathrm{X}$ (inert) is kept in a closed flask when A decomposes as per the following reaction at $500\mathrm{K}$:
$\mathrm{A}\left(\mathrm{g}\right)⟶2 \mathrm{B}\left(\mathrm{g}\right)+3\mathrm{C}\left(\mathrm{l}\right)+4\mathrm{D}\left(\mathrm{s}\right)$

$\mathrm{P}°=210 \mathrm{mmHg}$

${\mathrm{P}}_{\mathrm{t}}\left(10\mathrm{mins}\right)=330\mathrm{mmHg}$

${\mathrm{P}}_{\mathrm{x}}=430\mathrm{mmHg}$

Vapour pressure of $\mathrm{C}\left(\mathrm{l}\right)$ at $500\mathrm{K}$ is $20\mathrm{mmHg}$.
Calculate the half life for $\mathrm{A}$:

A radioactive material (${\mathrm{t}}_{\frac{1}{2}}=30$ days) gets spilled over the floor of a room. If initial activity is ten times the permissible value, after how many days will it be safe to enter the room

The mean lives of a radioactive substance are $1620$ years and $405$ years for $\alpha$ and $\beta$ emission respectively. The time required for the decay of ${\frac{3}{4}}^{\mathrm{th}}$ of the sample by emitting $\alpha$ and $\beta$ rays simultaneously is nearly

Consider the following reaction occurring in gas phase:

${\mathrm{Cl}}_2\left(\mathrm{g}\right)+{\mathrm{CHCl}}_3\left(\mathrm{g}\right)⟶\mathrm{HCl}\left(\mathrm{g}\right)+{\mathrm{CCl}}_4\left(\mathrm{g}\right)$

The reaction is experimentally found to obey the following rate law:

$\mathrm{R}=\mathrm{k}\left[{\mathrm{CHCl}}_3\right]{\left[{\mathrm{Cl}}_2\right]}^{\frac{1}{2}}$

Step 1: ${\mathrm{Cl}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{Cl}\left(\mathrm{g}\right)$

Step 2: $\mathrm{Cl}\left(\mathrm{g}\right)+{\mathrm{CHCl}}_3\left(\mathrm{g}\right)⟶\mathrm{HCl}\left(\mathrm{g}\right)+{\mathrm{CCl}}_3\left(\mathrm{g}\right)$

Step 3: $\mathrm{Cl}\left(\mathrm{g}\right)+{\mathrm{CCl}}_3\left(\mathrm{g}\right)⟶{\mathrm{CCl}}_4\left(\mathrm{g}\right)$

Based on this information, what conclusion can be drawn about this proposed mechanism:

The iron (III) nitrate catalyzes the decomposition of the hydrogen peroxide. A good experimental finding that supports this is

A certain reaction ${\mathrm{B}}^{\mathrm{n}+}$ is getting converted to ${\mathrm{B}}^{\left(\mathrm{n}+4\right)+}$ in solution. The rate constant of this reaction is measured by titrating a volume of the solution with a redox agent which reacts only with ${\mathrm{B}}^{\mathrm{n}+}$ and ${\mathrm{B}}^{\left(\mathrm{n}+4\right)+}$. In the process it converts ${\mathrm{B}}^{\mathrm{n}+}$ to ${\mathrm{B}}^{\left(\mathrm{n}+2\right)+}$ and ${\mathrm{B}}^{\left(\mathrm{n}+4\right)+}$ to ${\mathrm{B}}^{\left(\mathrm{n}-1\right)+}$. At $\mathrm{t}=0$, the volume of reagent consumed is $25\mathrm{mL}$ and at $\mathrm{t}=10$ minute, the volume used is $35.5\mathrm{mL}$. Calculate the rate constant in ${\mathrm{hr}}^{-1}$ for the conversion of ${\mathrm{B}}^{\mathrm{n}+}$ of ${\mathrm{B}}^{\left(\mathrm{n}+4\right)+}$ assuming it to be a first order reaction. [Assume that the redox reagent has the same $n-$factor with both the species]
[Given: ${\log }_{10}2=0·30,{\log }_{10}3=0·48,{\log }_{e}x=2·3{\log }_{10}x$]

The decomposition of ${\mathrm{N}}_2{\mathrm{O}}_5$ in ${\mathrm{CCl}}_4$ solution at $318 \mathrm{K}$ has been studied by monitoring the concentrration of ${\mathrm{N}}_2{\mathrm{O}}_5$ in the solution.. Intially the concentration of ${\mathrm{N}}_2{\mathrm{O}}_5$ is $2.32\mathrm{M}$ and after $184$ minutes, it is reduced to $2.08\mathrm{M}$. The reaction take place according to the given equation.
$2{ \mathrm{N}}_2{\mathrm{O}}_5⟶4{\mathrm{NO}}_2+{\mathrm{O}}_2$

What is the average rate of production of ${\mathrm{NO}}_2$ in milli moles ${\mathrm{\ell t}}^{-1}{\sec }^{-1}$ ?