Chemical Kinetics — CBSE Class 12 board PYQs

The rate of a reaction increases sixteen times when the concentration of the reactant increases four times. The order of the reaction is

Assertion (A): The units of the rate constant of a zero order reaction and of the rate of reaction are the same.
Reason (R): In a zero order reaction, the rate of reaction is independent of the concentration of the reactants.

Will the rate constant of the reaction depend upon T if the E${}_{act}$ (activation energy) of the reaction is zero?

What is the effect of adding a catalyst on
(a) activation energy (E${}_a$), and
(b) Gibbs energy (ΔG) of a reaction?

Identify the reaction order from the following rate constant:

Define the term order of a reaction.

Why does the rate of a reaction not remain constant throughout the reaction process?

What is meant by the order of a reaction being zero?

Express the rate of the following reaction in terms of the disappearance of hydrogen:

For the reaction $\mathrm{C}{\mathrm{l}}_2(\mathrm{g})+2\mathrm{NO}(\mathrm{g})⟶2\mathrm{NOCl}(\mathrm{g})$, the rate law is expressed as Rate = k[Cl${}_2$][NO]${}^2$. What is the overall order of this reaction?

Define activation energy of a reaction.

Is there any reaction for which the reaction rate does not decrease with time?

What is meant by an elementary step in a reaction?

The rate of the reaction X → Y becomes 8 times when the concentration of the reactant X is doubled. Write the rate law of the reaction.

A reaction is 50% complete in 2 hours and 75% complete in 4 hours. What is the order of the reaction?

For the reaction A → B, the rate of reaction becomes twenty-seven times when the concentration of A is increased three times. What is the order of the reaction?

The reaction A + B → C has zero order. What is the rate equation?

When is the rate of reaction equal to the specific reaction rate?

A substance with initial concentration $a$ follows zero order kinetics with rate constant k mol L${}^{-1}$ s${}^{-1}$. In how much time will the reaction go to completion?

How does the value of the rate constant vary with reactant concentration?

State the rate law for chemical reactions.

Express the relation between the half-life period of a reactant and its initial concentration for a reaction of n${}^{th}$ order.

Give an example of a pseudo first order reaction.

In some cases it is found that a large number of colliding molecules have energy more than the threshold value, yet the reaction is slow. Why?

For the reaction ${\mathrm{N}}_2(\mathrm{g})+3{\mathrm{H}}_2(\mathrm{g})⟶2\mathrm{N}{\mathrm{H}}_3(\mathrm{g})$, express the rate of reaction in terms of the formation of ammonia.

State any one condition under which a bimolecular reaction may be kinetically first order.

For the reaction $2X⟶X_2$, the rate of reaction becomes three times when the concentration of X is increased 27 times. What is the order of the reaction?

The reaction $2{\mathrm{H}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})⟶2{\mathrm{H}}_2\mathrm{O}(\mathrm{l})$ is thermodynamically feasible. How is it that a mixture of hydrogen and oxygen kept at room temperature shows no tendency to form water?

Why is it that the instantaneous rate of a reaction does not change when a part of the reacting solution is taken out?

The rate of reaction is given by: Rate = k[N${}_2$O${}_5$]. In this equation, what does k stand for?

For the reaction $3{\mathrm{H}}_2(\mathrm{g})+{\mathrm{N}}_2(\mathrm{g})⟶2\mathrm{N}{\mathrm{H}}_3(\mathrm{g})$, how are the rate expressions $-\frac{d[{\mathrm{H}}_2]}{dt}$ and $+\frac{d[\mathrm{N}{\mathrm{H}}_3]}{dt}$ interrelated?

Show that in the case of a first order reaction, the time taken for completion of 99% of the reaction is twice the time required for 90% completion of the reaction. (log 10 = 1)

The rate constant of a reaction quadruples when the temperature changes from 300 K to 320 K. Calculate the activation energy for this reaction. (log 2 = 0.30, log 4 = 0.60, 2.303 R = 19.15 J K${}^{-1}$ mol${}^{-1}$)

What happens to the rate constant k and the activation energy E${}_a$ as the temperature of a chemical reaction is increased? Justify.

(a) For the reaction $2{\mathrm{N}}_2{\mathrm{O}}_5(\mathrm{g})\to 4\mathrm{N}{\mathrm{O}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})$ at 318 K, calculate the rate of reaction if the rate of disappearance of N${}_2$O${}_5$(g) is $1.4\times 10^{-3}$ M s${}^{-1}$.
(b) For a first order reaction, derive the relationship t${}_{99\%}$ = 2 t …

Answer the following questions (any two):
a) Identify the order of a reaction from the following unit of its rate constant: L mol${}^{-1}$ s${}^{-1}$.
b) The conversion of molecules A to B follows second order kinetics. If the concentration of A is increased to three times, how will …

Observe the graph shown in the figure and answer the following questions:
a) What is the order of the reaction?
b) What is the slope of the curve?
c) Write the relationship between k and t${}_{1/2}$ (half-life period).

Analyse the given graph, drawn between concentration of reactant vs. time (see figure).
(a) Predict the order of the reaction.
(b) Theoretically, can the concentration of the reactant reduce to zero after infinite time? Explain.

How will the rate of a reaction be affected when:
(a) the surface area of the reactant is reduced,
(b) a catalyst is added in a reversible reaction,
(c) the temperature of the reaction is increased?

For the reaction 2H${}_2$O${}_2$ $\stackrel{{\text{I}}^{-},\text{alkaline medium}}{\to }$ 2H${}_2$O + O${}_2$, the proposed mechanism is:
(1) H${}_2$O${}_2$ + I${}^{-}$ → H${}_2$O + IO${}^{-}$ (slow)
(2) H${}_2$O${}_2$ + IO${}^{-}$ → H${}_2$O + I${}^{-}$ + O${}_2$ (fast)
(i) Write the rate law for the reaction.
(ii) Write …

The decomposition of NH${}_3$ on a platinum surface is a zero order reaction. If the rate constant (k) is 4 × 10${}^{-3}$ M s${}^{-1}$, how long will it take to reduce the initial concentration of NH${}_3$ from 0.1 M to 0.064 M?

A first order reaction is 50% completed in 40 minutes at 300 K and in 20 minutes at 320 K. Calculate the activation energy of the reaction. (Given: log 2 = 0.3010, log 4 = 0.6021, R = 8.314 J K${}^{-1}$ mol${}^{-1}$)

A first order reaction takes 20 minutes for 25% decomposition. Calculate the time when 75% of the reaction will be completed. (Given: log 2 = 0.3010, log 3 = 0.4771, log 4 = 0.6021)

For the reaction 2NH${}_3$(g) $\stackrel{\mathrm{Pt}}{\to }$ N${}_2$ + 3H${}_2$(g), Rate = k.
i) Write the order and molecularity of this reaction.
ii) Write the unit of k.

For the reaction $2{\mathrm{N}}_2{\mathrm{O}}_5(\mathrm{g})\to 4\mathrm{N}{\mathrm{O}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})$, the rate of formation of NO${}_2$(g) is $2.8\times 10^{-3}$ M s${}^{-1}$. Calculate the rate of disappearance of N${}_2$O${}_5$(g).

The rate constant for the first order decomposition of H${}_2$O${}_2$ is given by the equation:

Calculate E${}_a$ for this reaction, and the rate constant k if its half-life period is 200 minutes. (R = 8.314 J K${}^{-1}$ mol …

(a) For a reaction A + B → P, the rate law is given by r = k[A]${}^{1/2}$[B]${}^2$. What is the order of this reaction?
(b) A first order reaction is found to have a rate constant k = 5.5 × 10${}^{-14}$ s${}^{-1}$. Find the half-life of the reaction.

The rate of a reaction becomes four times when the temperature changes from 293 K to 313 K. Calculate the energy of activation (E${}_a$) of the reaction, assuming that it does not change with temperature.

In a first order reaction, the concentration of the reactant is reduced from 0.6 mol L${}^{-1}$ to 0.2 mol L${}^{-1}$ in 5 minutes. Calculate the rate constant of the reaction.

What are pseudo first order reactions? Give one example of such reactions.

Identify, giving reasons, the reaction order from each of the following rate constants:
i) k = 2.3 × 10${}^{-5}$ L mol${}^{-1}$ s${}^{-1}$
ii) k = 3 × 10${}^{-4}$ s${}^{-1}$

List two main differences between the order and the molecularity of a reaction.

The thermal decomposition of HCO${}_2$H is a first order reaction with a rate constant of $2.4\times 10^{-3}$ s${}^{-1}$ at a certain temperature. Calculate how long it will take for three-fourths of the initial quantity of HCO${}_2$H to decompose. (log 0.25 = −0.6021)

What do you understand by the rate law and rate constant of a reaction? Identify the order of a reaction if the units of its rate constant are:
i) L${}^{-1}$ mol s${}^{-1}$
ii) L mol${}^{-1}$ s${}^{-1}$

Distinguish between the 'rate expression' and the 'rate constant' of a reaction.

A first order reaction has a rate constant of 0.0051 min${}^{-1}$. If we begin with 0.10 M concentration of the reactant, what concentration of the reactant will be left after 3 hours?

Nitrogen pentoxide decomposes according to the equation $2{\mathrm{N}}_2{\mathrm{O}}_5(\mathrm{g})\to 4\mathrm{N}{\mathrm{O}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})$. This first order reaction was allowed to proceed at 40°C and the data below were collected:

[N${}_2$O${}_5$] (M) | Time (min)
0.400 | 0.00
0.289 | 20.0
0.209 | …

The rate constant for a reaction of zero order in A is 0.0030 mol L${}^{-1}$ s${}^{-1}$. How long will it take for the initial concentration of A to fall from 0.10 M to 0.075 M?

A reaction is of first order in reactant A and of second order in reactant B. How is the rate of this reaction affected when (i) the concentration of B alone is increased to three times, (ii) the concentrations of A as well as B are doubled?

Define the following:
i) Elementary step in a reaction
ii) Rate of a reaction

A reaction is of second order with respect to a reactant. How will the rate of the reaction be affected if the concentration of this reactant is (i) doubled, (ii) reduced to half?

For a decomposition reaction the values of the rate constant k at two different temperatures are given below:
k${}_1$ = 2.15 × 10${}^{-8}$ L mol${}^{-1}$ s${}^{-1}$ at 650 K
k${}_2$ = 2.39 × 10${}^{-7}$ L mol${}^{-1}$ s${}^{-1}$ at 700 K
Calculate the value of the activation energy for this reac …

The half-life of a first order reaction is 5 × 10${}^4$ s. What percentage of the initial reactant will react in 2 hours? Calculate.

List the factors which influence the rate of a chemical reaction.

What is meant by the 'rate constant, k' of a reaction? If concentration is expressed in mol L${}^{-1}$ and time in seconds, what would be the units of k (i) for a zero order reaction and (ii) for a first order reaction?

A first order decomposition reaction takes 40 minutes for 30% decomposition. Calculate its t${}_{1/2}$ value.

The rate of a reaction increases to four times when the prevailing temperature is raised from 300 K to 320 K. Calculate the energy of activation of this reaction, assuming that it does not change with temperature. (R = 8.314 J mol${}^{-1}$ K${}^{-1}$)

The half-life for the decay of radioactive ${}^{14}$C is 5730 years. An archaeological artefact containing wood has only 80% of the ${}^{14}$C activity found in living trees. Calculate the age of the artefact.

The decomposition of NH${}_3$ on a platinum surface, $2\mathrm{N}{\mathrm{H}}_3(\mathrm{g})\stackrel{\mathrm{Pt}}{\to }{\mathrm{N}}_2(\mathrm{g})+3{\mathrm{H}}_2(\mathrm{g})$, is a zero order reaction with k = $2.5\times 10^{-4}$ mol L${}^{-1}$ s${}^{-1}$. What are the rates of production of N${}_2$ and H${}_2$?

The rates of most reactions double when their temperature is raised from 298 K to 308 K. Calculate the activation energy of such a reaction. (R = 8.314 J mol${}^{-1}$ K${}^{-1}$, log 2 = 0.3010)

The rate constant for a first order reaction is 60 s${}^{-1}$. How much time will it take to reduce the concentration of the reactant to 1/10th of its initial value?

Show that in the case of a first order reaction, the time required for 99.9% of the reaction to be complete is 10 times that required for half of the reaction to take place. (log 2 = 0.3010)

A certain reaction is 50% complete in 20 minutes at 300 K and the same reaction is again 50% complete in 5 minutes at 350 K. Calculate the activation energy if it is a first order reaction. (R = 8.314 J K${}^{-1}$ mol${}^{-1}$; log 4 = 0.602)

The rate of a particular reaction triples when the temperature changes from 50°C to 100°C. Calculate the activation energy of the reaction. (log 3 = 0.4771; R = 8.314 J K${}^{-1}$ mol${}^{-1}$)

a) Calculate the number of α-particles and β-particles emitted when ${}_{92}^{238}$U changes to ${}_{82}^{206}$Pb.
b) What is meant by K-capture in nuclear chemistry?

The rate of a particular reaction doubles when the temperature changes from 27°C to 37°C. Calculate the activation energy of such a reaction. (R = 8.314 J K${}^{-1}$ mol${}^{-1}$)

During a nuclear explosion, one of the products is ${}^{90}$Sr with a half-life of 28.1 years. If 1 μg of ${}^{90}$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?

The activation energy of a reaction is 75.2 kJ mol${}^{-1}$ in the absence of a catalyst and 50.14 kJ mol${}^{-1}$ with a catalyst. How many times will the rate of the reaction grow in the presence of the catalyst if the reaction proceeds at 25°C? (R = 8.314 J K${}^{-1}$ mol${}^{-1}$)

A first order reaction takes 69.3 minutes for 50% completion. Set up an equation for determining the time needed for 80% completion of this reaction.

Prove that the time required for the completion of three-fourths of a first order reaction is twice the time required for the completion of half of the reaction.

The following reaction takes place in one step:

How will the rate of the above reaction change if the volume of the reaction vessel is diminished to one-third of its original volume? Will there be any change i …

The rate constant for a first order reaction becomes six times when the temperature is raised from 350 K to 400 K. Calculate the activation energy for the reaction. (R = 8.314 J K${}^{-1}$ mol${}^{-1}$)

i) Write the rate law for a first order reaction.
ii) Justify the statement that the half-life of a first order reaction is independent of the initial concentration of the reactant.

A possible mechanism for the reaction 2NO(g) + O${}_2$(g) → 2NO${}_2$(g) is:
i) NO + O${}_2$ ⇌ NO${}_3$ (fast)
ii) NO${}_3$ + NO → NO${}_2$ + NO${}_2$ (slow)
Write the rate law and the order of the reaction.

What is known as 'activation energy'? How is the activation energy affected by (i) the use of a catalyst and (ii) a rise in temperature?

What are photochemical reactions? Explain the mechanism of the photochemical reaction occurring between hydrogen and chlorine gas.

The rate constant of a reaction is $1.5\times 10^7$ s${}^{-1}$ at 50°C and $4.5\times 10^7$ s${}^{-1}$ at 100°C. Calculate the value of the activation energy, E${}_a$, for the reaction. (R = 8.314 J K${}^{-1}$ mol${}^{-1}$)

A first order reaction is 20% complete in 20 minutes. Calculate the time it will take for the reaction to be 80% complete.

Why does the rate of most reactions increase when the temperature of the reaction mixture is increased? In what units is the rate of a reaction expressed?

The decomposition of a compound is found to follow a first order rate law. If it takes 15 minutes for 20% of the original material to react, calculate:
i) the specific rate constant,
ii) the time at which 10% of the original material remains unreacted,
iii) the time it takes for …

Which aspect of a reaction is influenced by the presence of a catalyst — the rate, or the possibility of the reaction?

State the role of the activated complex in a reaction and state its relation with activation energy.

The following experimental data were collected for the reaction Cl${}_2$(g) + 2NO(g) → 2NOCl(g):

Trial | [Cl${}_2$] (mol L⁻¹) | [NO] (mol L⁻¹) | Initial rate (mol L⁻¹ s⁻¹)
1 | 0.010 | 0.010 | 1.20 × 10⁻⁴
2 | 0.010 | 0.030 | 10.8 × 10⁻⁴
3 | 0.020 | 0.030 | 21.6 × 10⁻⁴

Construct the …

The rate constant k of a reaction varies with temperature according to the equation $\log k=\text{constant}-\frac{E_a}{2.303R}\cdot \frac{1}{T}$, where E${}_a$ is the activation energy. When a graph is plotted for log k vs 1/T, a straight line with a slope of −6670 K is obtain …

a) Draw a schematic graph showing how the rate of a reaction changes with change in concentration of the reactant.
b) The rate of a reaction is given by: Rate = k[A]${}^2$[B]${}^1$. What are the units of the rate and of the rate constant for this reaction?

For the decomposition of N${}_2$O${}_5$ at 298 K, the rate law is $-\frac{d[{\mathrm{N}}_2{\mathrm{O}}_5]}{dt}=k[{\mathrm{N}}_2{\mathrm{O}}_5]$. Starting with 2.5 moles of N${}_2$O${}_5$(g) in a five-litre container, how many moles per litre of N${}_2$O${}_5$ would remain after 75 seconds if the rate constant for th …

The rate of the reaction 2NO + Cl${}_2$ → 2NOCl is doubled when the concentration of Cl${}_2$ is doubled, and it becomes eight times when the concentrations of both NO and Cl${}_2$ are doubled. Deduce the order of the reaction.

For the hydrolysis of methyl acetate in aqueous solution, the following results were obtained:

t (s) | 0 | 30 | 60
[CH${}_3$COOCH${}_3$] (mol L${}^{-1}$) | 0.60 | 0.30 | 0.15

i) Show that it follows a pseudo first order reaction, as the concentration of water remains constant.
ii) Ca …

a) For a reaction A + B → P, the rate is given by: Rate = k[A][B]${}^2$.
i) How is the rate of reaction affected if the concentration of B is doubled?
ii) What is the overall order of reaction if A is present in large excess?
b) A first order reaction takes 30 minutes for 50% compl …

a) Explain the following terms:
i) Rate of reaction
ii) Activation energy of a reaction
b) The decomposition of phosphine, PH${}_3$, proceeds according to the equation $4\mathrm{P}{\mathrm{H}}_3(\mathrm{g})\to {\mathrm{P}}_4(\mathrm{g})+6{\mathrm{H}}_2(\mathrm{g})$. It is found that the reaction follows the rate equ …

a) Derive the general form of the expression for the half-life of a first order reaction.
b) The decomposition of NH${}_3$ on a platinum surface is a zero order reaction. What are the rates of production of N${}_2$ and H${}_2$ if k = 2.5 × 10${}^{-4}$ mol L${}^{-1}$ s${}^{-1}$?

List the factors on which the rate of a chemical reaction depends.