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Chemistry · Class 12 Science

Ch 6Chemical Kinetics — Class 12 Chemistry, concept-first.

Three important characteristics of a chemical reaction are its extent, its feasibility and its rate. In Standard XI we learnt how equilibrium constants predict the extent of a reaction, and in Unit 3 of this textbook we saw how thermodynamic properties such as the change in entropy or enthalpy tell us whether, under a…

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Rate of Reaction

The rate of a reaction is how rapidly its reactants are consumed or its products appear. It is expressed as either an AVERAGE rate over a finite time interval, , or the true INSTANTANEOUS rate at one exact moment, , foun…

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

6.1

Introduction

Three important characteristics of a chemical reaction are its extent, its feasibility and its rate. In Standard XI we learnt how equilibrium constants predict the extent of a reaction, and in Unit 3…

+Can you recall?i3 questions
  1. Q1What is the influence of particle size of reacting solid on rate of a chemical reaction ?Free
  2. Q2Why is finely divided nickel used in hydrogenation of oil ?Preview
  3. Q3What is effect of change of temperature on the rate of a chemical reaction ?Preview
6.2

Rate of reactions

The rate of a reaction describes how rapidly the reactants are consumed or the products are formed. The two subsections below make this idea precise, first as an average over a time interval and then…

6.2.1

Average rate of chemical reaction

The average rate of a reaction is obtained by dividing the change in concentration of a reactant or product by the time interval over which the change occurs:

6.2.2

Instantaneous rate of reaction

3 Q

To determine the instantaneous rate of a reaction, the progress of the reaction is followed by measuring the concentrations of a reactant or product at different time intervals.

+Intext Questions 6.2.2i1 question
  1. 6.1Write the rate expression for: $$\mathrm{2\ N_2O(g) \longrightarrow 4\ NO_2(g) + O_2(g)}$$ > [!NOTE] > The book prints the reactant as 2 N$_…Preview
+Problemsi1 question
  1. Problem 6.1For the reaction $\mathrm{2\ N_2O_5(g) \longrightarrow 4\ NO_2(g) + O_2(g)}$ in liquid bromine, N$_2$O$_5$ disappears at a rate of 0.02 mole…Preview
+Try this 6.2.21 question
  1. Q1For the reaction, $\mathrm{3I^-(aq) + S_2O_8^{2-}(aq) \longrightarrow I_3^-(aq) + 2\ SO_4^{2-}(aq)}$. Calculate the rate of formation of I$_…Preview
6.3

Rate of reaction and reactant concentration

The rate of a reaction at a given temperature, for a given time instant, depends on the concentration of the reactant. Such a rate-concentration relation is the rate law.

6.3.1

Rate law

Consider the general reaction

6.3.2

Writing the rate law

5 Q

Consider the reaction

+Try this 6.3.23 questions
  1. Q1For the reaction, $\mathrm{NO_2(g) + CO(g) \longrightarrow NO(g) + CO_2(g)}$, the rate of reaction is experimentally found to be proportiona…Free
  2. Q2For the reaction $\mathrm{2A + 2B \longrightarrow 2C + D}$, if concentration of A is doubled at constant [B] the rate increases by a factor…Preview
  3. Q3The rate law for the reaction $\mathrm{A + B \longrightarrow C}$ is found to be rate = $k$[A]$^2$[B]. The rate constant of the reaction at 2…Preview
+Problemsi2 questions
  1. Problem 6.2Write the rate law for the reaction, $\mathrm{A + B \longrightarrow P}$ from the following data : | [A] mol dm$^{-3}$ s$^{-1}$ (Initial) | […Free
  2. Problem 6.3For the reaction, $\mathrm{2\ NOBr(g) \longrightarrow 2\ NO(g) + Br_2(g)}$, the rate law is rate = $k$[NOBr]$^2$. If the rate of the reactio…Preview
6.3.3

Order of the reaction

5 Q

For the reaction

+Problemsi3 questions
  1. Problem 6.4For the reaction $\mathrm{2NO(g) + 2H_2(g) \longrightarrow N_2(g) + 2\ H_2O(g)}$, the rate law is rate = $k$[NO]$^2$ [H$_2$]. What is the or…Free
  2. Problem 6.5The rate of the reaction, $\mathrm{A + B \longrightarrow P}$ is 3.6 $\times$ 10$^{-2}$ mol dm$^{-3}$ s$^{-1}$ when [A] = 0.2 mol dm$^{-3}$ a…Preview
  3. Problem 6.6Consider, $\mathrm{A + B \longrightarrow P}$. If the concentration of A is doubled with [B] being constant, the rate of the reaction doubles…Preview
+Try this 6.3.31 question
  1. Q1The reaction, $\mathrm{CHCl_3(g) + Cl_2(g) \longrightarrow CCl_4(g) + HCl(g)}$ is first order in CHCl$_3$ and 1/2 order in Cl$_2$. Write the…Preview
+Use your brain poweri1 question
  1. Q1The rate of the reaction $\mathrm{2A + B \longrightarrow 2C + D}$ is 6 $\times$ 10$^{-4}$ mol dm$^{-3}$ s$^{-1}$ when [A] = [B] = 0.3 mol dm…Preview
6.4

Molecularity of elementary reactions

Complex reactions are those which constitute a series of elementary reactions. The subsections below define an elementary reaction, its molecularity, the connection between order and molecularity for…

6.4.1

Elementary reaction

Consider,

6.4.2

Molecularity of reaction

The molecularity of a reaction refers to how many reactant molecules are involved in the reaction. In the two elementary reactions of the previous subsection there is only one reactant molecule: these…

6.4.3

Order and molecularity of elementary reactions

The rate law for the elementary reaction

6.4.4

Rate determining step

2 Q

A number of chemical reactions are complex: they take place as a series of elementary steps. One of these steps is slower than the others, and this slowest step is the rate determining step — it deter…

+Problemsi1 question
  1. Problem 6.7A reaction occurs in the following steps i. $\mathrm{NO_2(g) + F_2(g) \longrightarrow NO_2F(g) + F(g)}$ (slow) ii. $\mathrm{F(g) + NO_2(g) \…Preview
+Try this 6.4.41 question
  1. Q1A complex reaction takes place in two steps: i) $\mathrm{NO(g) + O_3(g) \longrightarrow NO_3(g) + O(g)}$ ii) $\mathrm{NO_3(g) + O(g) \longri…Preview
6.5

Integrated rate law

We introduced the differential rate law earlier: it describes how the rate of a reaction depends on the concentrations of the reactants in terms of derivatives.

6.5.1

Integrated rate law for the first order reactions in solution

Consider the first order reaction

6.5.2

Units of rate constant for the first order reaction

The integrated rate law is

6.5.3

Half life of the first order reactions (t₁/₂)

Radioactive processes follow first order kinetics. The half life of a reaction is the time required for the reactant concentration to fall to one half of its initial value.

6.5.4

Half life and rate constant of the first order reaction

The integrated rate law for the first order reaction is

6.5.5

Graphical representation of the first order reactions

i. The differential rate law for the first order reaction is

6.5.6

Examples of first order reactions

Some examples of reactions of first order are:

6.5.7

Integrated rate law for gas phase reactions

4 Q

For the gas phase reaction

+Problemsi3 questions
  1. Problem 6.8The half life of first order reaction is 990 s. If the initial concentration of the reactant is 0.08 mol dm$^{-3}$, what concentration would…Free
  2. Problem 6.9In a first order reaction 60% of the reactant decomposes in 45 minutes. Calculate the half life for the reactionPreview
  3. Problem 6.10Following data were obtained during the first order decomposition of SO$_2$Cl$_2$ at the constant volume. $$\mathrm{SO_2Cl_2(g) \longrightar…Preview
+Try this 6.5.71 question
  1. Q1The half life of a first order reaction is 0.5 min. Calculate time needed for the reactant to reduce to 20% and the amount decomposed in 55…Preview
6.5.8

Zero order reactions

The rate of a zero order reaction is independent of the reactant concentration.

6.5.9

Pseudo-first order reactions

Certain reactions which are expected to be of higher order follow first order kinetics. Consider the hydrolysis of methyl acetate:

+Intext Questions 6.5.9i1 question
  1. 6.1The reaction $\mathrm{C_{12}H_{22}O_{11}(aq) + H_2O(l)}$ (excess) $\mathrm{\longrightarrow C_6H_{12}O_6(aq) + C_6H_{12}O_6(aq)}$ (glucose, f…Preview
6.6

Collision theory of bimolecular reactions

Collision theory explains how bimolecular reactions actually happen at the molecular level — and why only a small fraction of molecular encounters produce products.

6.6.1

Collision between reactant molecules

Chemical reactions occur as a result of collisions between the reactant species. It may be expected that the rate of the reaction is equal to the rate of collisions.

6.6.2

Activation

For the reaction to occur, the colliding reactant molecules must possess a certain minimum kinetic energy. This minimum kinetic energy is the activation energy.

6.6.3

Orientation of reactant molecules

The requirement for a successful collision described above is sufficient for reactions involving simple molecules (or ions), however not for those involving complex molecules.

6.6.4

Potential energy barrier

Consider again the reaction

6.7

Temperature dependence of reaction rates

The concentrations change only a little with temperature. The rate constant, however, shows a strong dependence on the temperature — this section develops that dependence quantitatively through the Ar…

6.7.1

Arrhenius equation

Arrhenius suggested that the rate of a reaction varies with temperature as

6.7.2

Graphical determination of activation energy

Taking the logarithm of both sides of Eq. (6.18) we obtain

6.7.3

Determination of activation energy

For two different temperatures and ,

6.7.4

Graphical description of effect of temperature

It has been realized that the average kinetic energy of molecules is proportional to temperature. The collision theory suggests a bimolecular reaction occurs only if the reacting molecules have suffic…

+Problemsi3 questions
  1. Problem 6.12The rate constants for a first order reaction are 0.6 s$^{-1}$ at 313 K and 0.045 s$^{-1}$ at 293 K. What is the activation energy?Free
  2. Problem 6.13A first order gas phase reaction has activation energy of 240 kJ mol$^{-1}$. If the pre-exponential factor is 1.6 $\times$ 10$^{13}$ s$^{-1}…Preview
  3. Problem 6.14The half life of a first order reaction is 900 min at 820 K. Estimate its half life at 720 K if the activation energy is 250 kJ mol$^{-1}$.Preview
6.8

Effect of a catalyst on the rate of reaction

A catalyst is a substance added to the reactants that increases the rate of the reaction without itself being consumed in the reaction. Consider

1. Choose the most correct option.

+Choose the most correct option10 questions
  1. Q1**i.** The rate law for the reaction $\mathrm{aA + bB \longrightarrow P}$ is rate = $k$[A] [B]. The rate of reaction doubles if a. concentra…Free
  2. Q2**ii.** The order of the reaction for which the units of rate constant are mol dm$^{-3}$ s$^{-1}$ is a. 1 b. 3 c. 0 d. 2Free
  3. Q3**iii.** The rate constant for the reaction $\mathrm{2\ N_2O_5(g) \longrightarrow 2\ N_2O_4(g) + O_2(g)}$ is 4.98 $\times$ 10$^{-4}$ s$^{-1}…Free
  4. Q4**iv.** Time required for 90 % completion of a certain first order reaction is t. The time required for 99.9 % completion will be a. t b. 2t…Preview
  5. Q5**v.** Slope of the graph ln[A]$_t$ versus t for first order reaction is a. -$k$ b. $k$ c. $k$/2.303 d. -$k$/2.303Preview
  6. Q6**vi.** What is the half life of a first order reaction if time required to decrease concentration of reactant from 0.8 M to 0.2 M is 12 h?…Preview
  7. Q7**vii.** The reaction, $\mathrm{3\ ClO^- \longrightarrow ClO_3^- + 2\ Cl^-}$ occurs in two steps, (i) $\mathrm{2\ ClO^- \longrightarrow ClO_…Preview
  8. Q8**viii.** The elementary reaction $\mathrm{O_3(g) + O(g) \longrightarrow 2\ O_2(g)}$ is a. unimolecular and second order b. bimolecular and…Preview
  9. Q9**ix.** Rate law for the reaction, $\mathrm{2\ NO + Cl_2 \longrightarrow 2\ NOCl}$ is rate = $k$[NO$_2$]$^2$[Cl$_2$]. Thus $k$ would increas…Preview
  10. Q10**x.** For an endothermic reaction, X $\rightleftharpoons$ Y. If $E_f$ is activation energy of the forward reaction and $E_r$ that for rever…Preview

2. Answer the following in one or two sentences.

+Answer in one or two sentences10 questions
  1. Q1**i.** For the reaction, $\mathrm{N_2(g) + 3\ H_2(g) \longrightarrow 2\ NH_3(g)}$, what is the relationship among $\dfrac{\mathrm{d[N_2]}}{\…Free
  2. Q2**ii.** For the reaction, $\mathrm{CH_3Br(aq) + OH^-(aq) \longrightarrow CH_3OH(aq) + Br^-(aq)}$, rate law is rate = $k$[CH$_3$Br][OH$^-$] a…Free
  3. Q3**iii.** What is the relationship between coefficients of reactants in a balanced equation for an overall reaction and exponents in rate law…Free
  4. Q4**iv.** Why all collisions between reactant molecules do not lead to a chemical reaction?Preview
  5. Q5**v.** What is the activation energy of a reaction?Preview
  6. Q6**vi.** What are the units for rate constants for zero order and second order reactions if time is expressed in seconds and concentration of…Preview
  7. Q7**vii.** Write Arrhenius equation and explain the terms involved in it.Preview
  8. Q8**viii.** What is the rate determining step?Preview
  9. Q9**ix.** Write the relationships between rate constant and half life of first order and zeroth order reactions.Preview
  10. Q10**x.** How do half lives of the first order and zero order reactions change with initial concentration of reactants?Preview

3. Answer the following in brief.

+Answer the following in brief17 questions
  1. Q1**i.** How instantaneous rate of reaction is determined?Free
  2. Q2**ii.** Distinguish between order and molecularity of a reaction.Free
  3. Q3**iii.** A reaction takes place in two steps, 1. $\mathrm{NO(g) + Cl_2(g) \longrightarrow NOCl_2(g)}$ 2. $\mathrm{NOCl_2(g) + NO(g) \longrig…Free
  4. Q4**iv.** Obtain the relationship between the rate constant and half life of a first order reaction.Preview
  5. Q5**v.** How will you represent zeroth order reaction graphically?Preview
  6. Q6**vi.** What are pseudo-first order reactions? Give one example and explain why it is pseudo-first order.Preview
  7. Q7**vii.** What are requirements for the colliding reactant molecules to lead to products?Preview
  8. Q8**viii.** How catalyst increases the rate of reaction? Explain with the help of potential energy diagram for catalyzed and uncatalyzed react…Preview
  9. Q9**ix.** Explain with the help of Arrhenius equation, how does the rate of reaction changes with (a) temperature and (b) activation energy.Preview
  10. Q10**x.** Derive the integrated rate law for first order reaction.Preview
  11. Q11**xi.** How will you represent first order reactions graphically.Preview
  12. Q12**xii.** Derive the integrated rate law for the first order reaction, $\mathrm{A(g) \longrightarrow B(g) + C(g)}$ in terms of pressure.Preview
  13. Q13**xiii.** What is zeroth order reaction? Derive its integrated rate law. What are the units of rate constant?Preview
  14. Q14**xiv.** How will you determine activation energy: (a) graphically using Arrhenius equation (b) from rate constants at two different tempera…Preview
  15. Q15**xv.** Explain graphically the effect of temperature on the rate of reaction.Preview
  16. Q16**xvi.** Explain graphically the effect of catalyst on the rate of reaction.Preview
  17. Q17**xvii.** For the reaction $\mathrm{2A + B \longrightarrow}$ products, find the rate law from the following data. | [A]/M | [B]/M | rate/M s…Preview

4. Solve

[!NOTE] Most items of this group print the expected answer in parentheses at the end of the question - the book's own printed answers, kept exactly as printed.

+Solve9 questions
  1. Q1**i.** In a first order reaction, the concentration of reactant decreases from 20 mmol dm$^{-3}$ to 8 mmol dm$^{-3}$ in 38 minutes. What is…Free
  2. Q2**ii.** The half life of a first order reaction is 1.7 hours. How long will it take for 20% of the reactant to react? (32.9 min)Free
  3. Q3**iii.** The energy of activation for a first order reaction is 104 kJ/mol. The rate constant at 25 $^0$C is 3.7 $\times$ 10$^{-5}$ s$^{-1}$…Free
  4. Q4**iv.** What is the energy of activation of a reaction whose rate constant doubles when the temperature changes from 303 K to 313 K? (54.66…Preview
  5. Q5**v.** The rate constant of a reaction at 500$^0$C is 1.6 $\times$ 10$^3$ M$^{-1}$s$^{-1}$. What is the frequency factor of the reaction if…Preview
  6. Q6**vi.** Show that time required for 99.9% completion of a first order reaction is three times the time required for 90% completion.Preview
  7. Q7**vii.** A first order reaction takes 40 minutes for 30% decomposition. Calculate its half life. (77.66 min)Preview
  8. Q8**viii.** The rate constant for the first order reaction is given by log$_{10}$ $k$ = 14.34 - 1.25 $\times$ 10$^4$ T. Calculate activation e…Preview
  9. Q9**ix.** What fraction of molecules in a gas at 300 K collide with an energy equal to activation energy of 50 kJ/mol ? (2 $\times$ 10$^{-9}$)Preview

Activity :

+Activity2 questions
  1. Q1**1.** If you wish to determine the reaction order and rate constant for the reaction, $\mathrm{2AB_2 \longrightarrow A_2 + 2B_2}$. a) What…Free
  2. Q2**2.** The activation energy for two reactions are $E_a$ and $E'_a$ with $E_a$ > $E'_a$. If the temperature of reacting system increases fro…Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 26 questions26 questions
  1. Q1Explain graphical method to determine activation energy of a reaction.Preview
  2. Q2$A \rightarrow B$ is a first order reaction with rate $6.6 \times 10^{-5}\ M\ s^{-1}$. When [A] is 0.6 M, rate constant of the reaction is _…Preview
  3. Q3For a chemical reaction, $A \rightarrow$ products, the rate of reaction doubles when the concentration of 'A' is increased by a factor of 4,…Preview
  4. Q4Derive the relationship between half life and rate constant for first order reaction.Preview
  5. Q5In the Arrhenius equation for a first order reaction, the values of 'A' or 'Ea' are $4 \times 10^{13}\ sec^{-1}$ and $98.6\ kJ\ mol^{-1}$ re…Preview
  6. Q6The half-life period of zero order reaction $A \rightarrow$ product is given by — (a) $\dfrac{[A]_0}{k}$ (b) $\dfrac{0.693}{k}$ (c) $\dfrac{…Preview
  7. Q7A certain reaction occurs in the following steps — (i) $Cl_{(g)} + O_{3(g)} \rightarrow ClO_{(g)} + O_{2(g)}$ (ii) $ClO_{(g)} + O_{(g)} \rig…Preview
  8. Q8Write Arrhenius equation. Derive an expression for temperature variations.Preview
  9. Q9Write the mathematical relation between half life of zero order reaction and its rate constant.Preview
  10. Q10Distinguish between order and molecularity of a reaction.Preview
  11. Q11Define instantaneous rate of reaction. Explain pseudo first order reaction with suitable example.Preview
  12. Q12Identify the molecularity of following elementary reaction: $NO_{(g)} + O_{3(g)} \longrightarrow NO_{3(g)} + O_{(g)}$Preview
  13. Q13Explain pseudo-first order reaction with suitable example.Preview
  14. Q14Define half life of first order reaction. Obtain the expression for half life and rate constant of the first order reaction.Preview
  15. Q15Which of the following correctly represents integrated rate law equation for a first order reaction in gas phase: (a) $k = \frac{2.303}{t}\t…Preview
  16. Q16What is Pseudo first order reaction? Derive integrated rate law equation for zero order reaction.Preview
  17. Q17Show that, time required for 99.9% completion of a first order reaction is three times the time required for 90% completion. Give electronic…Preview
  18. Q18If unit of rate constant is mol dm$^{-3}$s$^{-1}$, the order of reaction would be _____. (a) zero (b) 1 (c) 2 (d) 3Preview
  19. Q19For the reaction A + B → P. If [B] is doubled at constant [A], the rate of reaction doubled. If [A] is triple and [B] is doubled, the rate o…Preview
  20. Q20Derive the relation between half life period and rate constant for first order reaction. Write the net cell reaction during discharging of l…Preview
  21. Q21The rate law equation for A → Product, is rate = k[A]$^x$. What is the effect of increase in concentration of 'A' on rate of reaction, if x…Preview
  22. Q22Derive the relation between half life and rate constant for a first order reaction.Preview
  23. Q23Define zero order reaction. A reaction takes place in two steps: (i) NO(g) + Cl$_2$(g) → NOCl$_2$(g) (ii) NOCl$_2$(g) + NO(g) → 2NOCl(g). Wr…Preview
  24. Q24The unit of rate constant is per second, the order of reaction is – (a) Zero (b) First (c) Second (d) ThirdPreview
  25. Q25A chemical reaction occurs in two steps: (i) $NO_2Cl_{(g)} \xrightarrow{slow} NO_{2(g)} + Cl_{(g)}$ (ii) $NO_2Cl_{(g)} + Cl_{(g)} \xrightarr…Preview
  26. Q26(i) Draw the structure of 2, 4-dinitrophenylhydrazone of acetaldehyde. (ii) The rate of A + B → P is 3.6 × 10$^{-2}$ mol/dm$^3$/s. When [A]…Preview