NCERT Solutions

For the reaction: $2 \mathrm{~A}+\mathrm{B} \rightarrow \mathrm{A}_{2} \mathrm{~B}$ the rate $=k[\mathrm{~A}][\mathrm{B}]^{2}$ with $\mathrm{k}=2.0 \times 10^{-6} \mathrm{~mol}^{-2} \mathrm{~L}^{2} \mathrm{~s}^{-1}$. Calculate the initial rate of the reaction when $[\mathrm{A}]=0.1 \mathrm{~mol} \mathrm{~L}^{-1},[\mathrm{B}]=0.2 \mathrm{~mol} \mathrm{~L}^{-1}$. Calculate the rate of reaction after $[\mathrm{A}]$ is reduced to $0.06 \mathrm{~mol} \mathrm{~L}^{-1}$.

The decomposition of $\mathrm{NH}_{3}$ on platinum surface is zero order reaction. What are the rates of production of $\mathrm{N}_{2}$ and $\mathrm{H}_{2}$ if $k=2.5 \times 10^{-4} \mathrm{~mol}^{-1} \mathrm{~L} \mathrm{~s}^{-1}$ ?

The decomposition of dimethyl ether leads to the formation of $\mathrm{CH}_{4}, \mathrm{H}_{2}$ and $\mathrm{CO}$ and the reaction rate is given by $\text { Rate }=k\left[\mathrm{CH}_{3} \mathrm{OCH}_{3}\right]^{3 / 2}$

The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e., $\text { Rate }=k\left(p_{\mathrm{CH}_{3} \mathrm{OCH}_{3}}\right)^{3 / 2}$

If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?

Mention the factors that affect the rate of a chemical reaction.

What is the effect of temperature on the rate constant of a reaction? How can this effect of temperature on rate constant be represented quantitatively?

In a pseudo first order reaction in water, the following results were obtained:

Calculate the average rate of reaction between the time interval 30 to 60 seconds.

In a reaction between A and B, the initial rate of reaction ($r_0$) was measured for different initial concentrations of A and B as given below:

What is the order of the reaction with respect to A and B?

The following results have been obtained during the kinetic studies of the reaction: $2 \mathrm{~A}+\mathrm{B} \rightarrow \mathrm{C}+\mathrm{D}$

Determine the rate law and the rate constant for the reaction.

The reaction between A and B is first order with respect to A and zero order with respect to B. Fill in the blanks in the following table:

The half-life for radioactive decay of $^{14} \mathrm{C}$ is 5730 years. An archaeological artifact containing wood had only $80 \%$ of the $^{14} \mathrm{C}$ found in a living tree. Estimate the age of the sample.

The rate constant for a first order reaction is $60 \mathrm{~s}^{-1}$. How much time will it take to reduce the initial concentration of the reactant to its $1 / 16^{\text {th }}$ value?

During nuclear explosion, one of the products is $^{90} \mathrm{Sr}$ with half-life of 28.1 years. If $1 \mu \mathrm{g}$ of $^{90} \mathrm{Sr}$ was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically.

For a first order reaction, show that time required for $99 \%$ completion is twice the time required for the completion of $90 \%$ of reaction.

A first order reaction takes 40 min for $30 \%$ decomposition. Calculate $t_{1 / 2}$.

For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained.

Calculate the rate constant.

The following data were obtained during the first order thermal decomposition of $\mathrm{SO}_{2} \mathrm{Cl}_{2}$ at a constant volume. $\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow \mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})$

Calculate the rate of the reaction when total pressure is 0.65 atm. (Note: The unit for time in the table should be 's', not 's⁻¹').

The rate constant for the decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}$ at various temperatures is given below:

Draw a graph between $\ln k$ and $1 / T$ and calculate the values of $A$ and $E_{\text {a. Predict the rate constant at }} 30^{\circ}$ and $50^{\circ} \mathrm{C}$.

The rate constant for the decomposition of hydrocarbons is $2.418 \times 10^{-5} \mathrm{~s}^{-1}$ at 546 K. If the energy of activation is $179.9 \mathrm{~kJ} / \mathrm{mol}$, what will be the value of pre-exponential factor.

Consider a certain reaction $\mathrm{A} \rightarrow$ Products with $k=2.0 \times 10^{-2} \mathrm{~s}^{-1}$. Calculate the concentration of A remaining after 100 s if the initial concentration of A is $1.0 \mathrm{~mol} \mathrm{~L}^{-1}$.

Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with $t_{1/2}=3.00$ hours. What fraction of sample of sucrose remains after 8 hours ?

The decomposition of hydrocarbon follows the equation $k=\left(4.5 \times 10^{11} \mathrm{~s}^{-1}\right) \mathrm{e}^{-28000 K / T}$ Calculate $E_{\mathrm{a}}$.

The rate constant for the first order decomposition of $\mathrm{H}_{2} \mathrm{O}_{2}$ is given by the following equation: $\log k=14.34-1.25 \times 10^{4} K / T$ Calculate $E_{\mathrm{a}}$ for this reaction and at what temperature will its half-period be 256 minutes?

The decomposition of A into product has value of $k$ as $4.5 \times 10^{3} \mathrm{~s}^{-1}$ at $10^{\circ} \mathrm{C}$ and energy of activation $60 \mathrm{~kJ} \mathrm{~mol}^{-1}$. At what temperature would $k$ be $1.5 \times 10^{4} \mathrm{~s}^{-1}$ ?

The time required for $10 \%$ completion of a first order reaction at 298 K is equal to that required for its $25 \%$ completion at 308 K. If the value of $A$ is $4 \times 10^{10} \mathrm{~s}^{-1}$. Calculate $k$ at 318 K and $E_{\mathrm{a}}$.

The rate of a reaction quadruples when the temperature changes from 293 K to 313 K. Calculate the energy of activation of the reaction assuming that it does not change with temperature.