Additional Questions - Chapter 7 - Chemical Kinetics - 12th Chemistry Guide Samacheer Kalvi Solutions

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Additional Questions
1 Mark Questions and Answers
I. Choose the correct answer.
Question 1.
Which one of the following is a slow reaction?
(a) Rusting of iron
(b) Combustion of carbon
(c) Reaction between $\mathrm{BaCl}_2$ and dil. $\mathrm{H}_2 \mathrm{SO}_4$
(d) Reaction between acidified $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ with $\mathrm{NaCl}$.
Answer:
(a) Rusting of iron
Question 2.
Which one of the following is the unit of rate of reaction?
(a) $\mathrm{s}^{-1}$
(b) $\mathrm{mol} \mathrm{s}^{-1}$
(c) $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}$
(d) $\mathrm{mol} \mathrm{L} \mathrm{s}$
Answer:
(c) $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}$
Question 3.
For a gas phase reaction, the unit of reaction rate is
(a) $\mathrm{s}^{-1}$
(b) $\mathrm{atm} \mathrm{s}^{-1}$
(c) $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}$
(d) $\mathrm{mol}^{-1} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$
Answer:
(b) atm s ${ }^{-1}$

Question 4.
For the reaction $\mathrm{A} \rightarrow 2 \mathrm{~B}$, the rate of the reaction is
(a) $+\frac{d[B]}{d t}=2-\frac{d[A]}{d t}$
(b) $+\frac{d[A]}{d t}=\frac{1}{2} \frac{d[B]}{d t}$
(c) Rate $=\frac{1}{2}=\frac{d[A]}{d t}$
(d) Rate $=2 \frac{d[B]}{d t}$
Answer:
(a) $+\frac{d[B]}{d t}=2-\frac{d[A]}{d t}$
Question 5.
Consider the following statement.
(i) In ionisation of cyclopropane, if the concentration of cyclopropane is reduced half, the rate increases twice.
(ii) The rate of the reaction depends upon the concentration of the reactant.
(iii) Order values must be determined experimentally.
Which of the above statement (s) is / are not correct?
(a) (i) only
(b) (ii) and (iii)
(c) (iii) only
(d) (ii) only
Answer:
(a) (i) only
Question 6.
In the reaction $2 \mathrm{NO}_{(\mathrm{g})}+\mathrm{O}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NO}_{2(\mathrm{~g})}$ the order of the reaction with respect to $\mathrm{NO}$ is
(a) first order
(b) second order
(c) third order
(d) zero order
Answer:
(b) second order
Question 7.
In the reaction $2 \mathrm{NO}_{(\mathrm{g})}+\mathrm{O}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NO}_{2(\mathrm{~g})}$. the order of the reaction with respect to $\mathrm{O}_2$ is $\ldots \ldots$
(a) zero order
(b) first order
(c) second order
(d) third order
Answer:
(b) first order

Question 8.
The overall order of the reaction $2 \mathrm{NO}_{(\mathrm{g})}+\mathrm{O}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NO}_{2(\mathrm{~g})}$ is
(a) 2
(b) 1
(c) 3
(d) 0
Answer:
(c) 3
Question 9.
Consider the following statements.
(i) Rate of the reaction does not depend on the initial concentration of the reactants.
(ii) Rate constant of the reaction depends on the initial concentration of reactants.
(iii) Rate constant of the reaction is equal to the rate of the reaction, when the concentration of each of the reactants is unity.
Which of the above statement(s) is / are not correct?
(a) (i) only
(b) (ii) only
(c) (i) and (ii)
(d) (iii) only
Answer:
(a) (iii) only
Question 10.
The overall molecularity of the reaction $2 \mathrm{H}_2 \mathrm{O}_{2(\mathrm{aq})} \underset{\rightarrow}{I^{-}} 2 \mathrm{H}_2 \mathrm{O}_1+\mathrm{O}_{2(\mathrm{~g})}$ is $\ldots \cdots \cdots \cdots$
(a) unimolecular
(b) bimolecular
(c) termolecular
(d) pentamolecular
Answer:
(b) bimolecular
Question 11.
Which of the following is the order of decomposition of hydrogen peroxide catalysed by $\mathrm{I}^{-}$
(a) First order
(b) Second order
(c) Zero order
(d) Third order

Question 12 .
Consider the following statements.
(i) order cannot be zero.
(ii) Molecularity can be zero (or) fractional (or) integer.
(iii) order can be determined only by experiment.
Which of the above statement(s) is / are not correct?
(a) (i) only
(b) (ii) only
(c) (iii) only
(d) (i) and (ii)
Answer:
(c) (iii) only
Question 13.
The overall order of the reaction $5 \mathrm{Br}^{-}+\mathrm{BrO}_3^{-}+6 \mathrm{H}^{+}$is .......
(a) 4
(b) $3 / 2$
(c) 12
(d) 1
Answer:
(a) 4
Question 14.
Which one of the following reaction is a fractional order reaction?
(a) $2 \mathrm{NO}+\mathrm{O}_2 \rightarrow 2 \mathrm{NO}_2$
(b) $\mathrm{CH}_3 \mathrm{CHO}_{(\mathrm{g})} \rightarrow \mathrm{CH}_{4(\mathrm{~g})}+\mathrm{CO}_{(\mathrm{g})}$
(c) $\left.2 \mathrm{H}_2 \mathrm{O}_2 \rightarrow 2 \mathrm{H}_2\right) \mathrm{O}_{(1)}+\mathrm{O}_2(\mathrm{~g})$
(d) $\mathrm{H}_2+\mathrm{Br}_2 \rightarrow 2 \mathrm{HBr}$
Answer:
(b) $\mathrm{CH}_3 \mathrm{CHO}_{(\mathrm{g})} \rightarrow \mathrm{CH}_{4(\mathrm{~g})}+\mathrm{CO}_{(\mathrm{g})}$
Question 15.
The order of decomposition of acetaldehyde is
(a) 1
(b) 1.5
(c) 2

(d) $5 / 2$
Answer:
(b) 1.5
Question 16.
Which one of the following is the unit of rate constant for a first order reaction?
(a) $\mathrm{mol}^{-1} \mathrm{~L} \mathrm{~s}^{-1}$
(b) $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}$
(c) $\mathrm{s}^{-1}$
(d) mol L S
Answer:
(c) $\mathrm{s}^{-1}$
Question 17.
Which one of the following is an example for first order reaction?
(a) $2 \mathrm{NO}_{(\mathrm{g})}+\mathrm{O}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NO}_{2(\mathrm{~g})}$
(b) $\mathrm{CH}_3 \mathrm{CHO}_{(\mathrm{g})} \rightarrow \mathrm{CH}_{4(\mathrm{~g})}+\mathrm{CO}_{(\mathrm{g})}$
(c) $\mathrm{SO}_2 \mathrm{Cl}_{2(1)} \rightarrow \mathrm{SO}_{2(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{~g})}$
(d) $2 \mathrm{HBr} \rightarrow \mathrm{H}_2+\mathrm{Br}_2$
Answer:
(c) $\mathrm{SO}_2 \mathrm{Cl}_{2(1)} \rightarrow \mathrm{SO}_{2(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{~g})}$
Question 18.
Which one of the following is not an example for first order reaction?
(a) $\mathrm{N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightarrow 2 \mathrm{NO}_{2(\mathrm{~g})} \frac{1}{2} \mathrm{O}_{2(\mathrm{~g})}$
(b) $\mathrm{SO}_2 \mathrm{Cl}_{2(1)} \rightarrow \mathrm{SO}_{2(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{~g})}$
(e) $\mathrm{H}_2 \mathrm{O}_{2(\mathrm{aq})} \rightarrow \mathrm{H}_2 \mathrm{O}_1 \frac{1}{2} \mathrm{O}_{2(\mathrm{~g})}$
(d) $\mathrm{CH}_3 \mathrm{CHO}_{(\mathrm{g})} \rightarrow \mathrm{CH}_{4(\mathrm{~g})}+\mathrm{CO}_{(\mathrm{g})}$
Answer:
(d) $\mathrm{CH}_3 \mathrm{CHO}_{(\mathrm{g})} \rightarrow \mathrm{CH}_{4(\mathrm{~g})}+\mathrm{CO}_{(\mathrm{g})}$
Question 19.
What is the order of isomerisation of cyclopropane to propene?
(a) 1.5
(b) $3 / 2$

(c) $5 / 2$
(d) 1
Answer:
(d) 1
Question 20.
Which one of the following is an example of pseudo first order reaction?
(a) $\mathrm{CH}_3 \mathrm{CHO}_{4(\mathrm{~g})} \rightarrow \mathrm{CH}_{4(\mathrm{~g})}+\mathrm{CO}_{(\mathrm{g})}$
(b) $2 \mathrm{H}_2 \mathrm{O}_{2(\mathrm{aq})} \rightarrow \mathrm{H}_2 \mathrm{O}_{(1)}+\mathrm{O}_{2(\mathrm{~g})}$
(c) $\mathrm{CH}_3 \mathrm{COOCH}_{3(\mathrm{aq})}+\mathrm{H}_2 \mathrm{O}_{(1)} \stackrel{H^{+}}{\longrightarrow} \mathrm{CH}_3 \mathrm{COOH}_{(\mathrm{aq})}+\mathrm{CH}_3 \mathrm{OH}_{(\mathrm{aq})}$
(d) Isomerisation of cyclo propane to propene
Answer:
(c) $\mathrm{CH}_3 \mathrm{COOCH}_{3(\mathrm{aq})}+\mathrm{H}_2 \mathrm{O}_{(1)} \stackrel{H^{+}}{\longrightarrow} \mathrm{CH}_3 \mathrm{COOH}_{(\mathrm{aq})}+\mathrm{CH}_3 \mathrm{OH}_{(\mathrm{aq})}$
Question 21.
Which one of the following is called pseudo first order reaction?
(a) Decomposition of acetaldehyde
(b) Acid hydrolysis of an ester
(c) Isomerisation of cyclopropane to propene
(d) Decomposition of hydrogen peroxide
Answer:
(b) Acid hydrolysis of an ester
Question 22 .
Which of the following is an example of zero order reaction?
(a) lodination of acetone in acid medium
(b) Hydrolysis of an ester in acid medium
(c) Decomposition of acetaldehyde
(d) Isomerisation of cyclopropane to propene
Answer:
(a) lodination of acetone in acid medium
Question 23 .
Which one of the follow is not zero order reaction?
(a) $\mathrm{H}_{2(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{~g})} \underline{h}\left\langle 2 \mathrm{HCI}_{(\mathrm{g})}\right.$
(b) $\mathrm{N}_2 \mathrm{O}_{(\mathrm{g})} \rightleftharpoons \mathrm{N}_{2(\mathrm{~g})}+\frac{1}{2} \mathrm{O}_{2(\mathrm{~g})}$
(c) $\mathrm{CH}_3 \mathrm{CHO}_{(\mathrm{g})} \rightarrow \mathrm{CH}_{4(\mathrm{~g})}+\mathrm{CO}_{(\mathrm{g})}$
(d) $\mathrm{CH}_3 \mathrm{COCH}_3+\mathrm{I}_2 \stackrel{\mathrm{H}^{+}}{\longrightarrow} \mathrm{CH}_2 \mathrm{COCH}_3+\mathrm{HI}$

Answer:
(c) $\mathrm{CH}_3 \mathrm{CHO}_{(\mathrm{g})} \rightarrow \mathrm{CH}_{4(\mathrm{~g})}+\mathrm{CO}_{(\mathrm{g})}$
Question 24.
Consider the following statements.
(i) For a first order reaction, half life period is independent of initial concentration.
(ii) Photo chemical reaction between $\mathrm{H}_2$ and $\mathrm{Cl}_2$ is a zero order reaction
(iii) Acid hydrolysis of an ester is a second order reaction
Which of the above statement is/are correct?
(a) (i) only
(b) (iii) only
(c) (i) \& (ii)
(d) (ii) \& (iii)
Answer:
(c) (i) \& (ii)
Question 25.
The formula of half life for an nth order reaction involving reactant $\mathrm{A}$ and $\mathrm{n} \neq 1$ is
(a) $t_{1 / 2}=\frac{2^{n-1}-1}{(n-1) k\left(\mathrm{~A}_0\right)^{n-1}}$
(b) $t_{1 / 2}=\frac{k_1}{0.693}$
(c) $t_{1 / 2}=\frac{2^n}{(n-1) k(\mathrm{~A})^{n+1}}$
(d) $t_{1 / 2}=\frac{2^{n-1}-1}{(n-1) k\left(\mathrm{~A}_g\right)^{n+1}}$
Answer:
(a) $t_{1 / 2}=\frac{2^{n-1}-1}{(n-1) k\left(A_0\right)^{n-1}}$
Question 26.
The half life period of first order reaction is 10 seconds. What is the time required for $99.9 \%$ completion of that reaction?
(a) 20 seconds
(b) 1000 seconds

(c) 100 seconds
(d) 999 seconds
Answer:
(c) loo seconds
Hint:
$
\begin{aligned}
& 10 \mathrm{xt}_{1 / 2}=\mathrm{t}_{99.9 \%} \\
& \therefore \mathrm{t}_{99.9 \%}=10 \times 10 \mathrm{sec}=100 \mathrm{sec}
\end{aligned}
$
Question 27.
Which one of the following is known as arrhenius equation?
(a) $\mathrm{k}=\mathrm{A} e^{-\left(\frac{E_a}{R T}\right)}$
(b) $\mathrm{k}=\mathrm{A} e^{\left(\frac{E_a}{R T}\right)}$
(c) $\mathrm{k}=\mathrm{A} e^{-\left(\frac{R T}{E_{\mathrm{a}}}\right)}$
(d) $\mathrm{k}=\mathrm{A} e^{-\left(\frac{R T}{E_a}\right)}$
Answer:
(a) $\mathrm{k}=\mathrm{A} e^{-\left(\frac{E_a}{R T}\right)}$
Question 28.
Which one of the following does not affect the rate of the reaction?
(a) Nature of the reactant
(b) Concentration of the reactants
(c) Surface area and temperature
(d) pressure
Answer:
(d) pressure
Question 29.
Consider the following statements.
(i) Higher the concentration, slower is the possibility for collision and rate also slower
(ii) Increase in surface area of reactant leads to more collisions per litre per second
(iii) Gas phas reactions are slower as compared to solid or liquid reactants

Which of the above statement is/are not correct?
(a) (ii)
(b) (i) \& (iii)
(c) (ii) \& (iii)
(d) (i) \& (ii)
Answer:
(b) (i) & (iii)
Question 30.
Which of the following reaction take place at a faster rate?
(a) $2 \mathrm{Na}_{(\mathrm{s})}+\mathrm{I}_{2(\mathrm{~s})} \rightarrow 2 \mathrm{NaI}_{(\mathrm{s})}$
(b) $2 \mathrm{Na}_{(\mathrm{s})}+\mathrm{I}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NaI}_{(\mathrm{s})}$
(c) $\mathrm{PbNO}_3(\mathrm{~s})+\mathrm{KI}_{(\mathrm{s})} \rightarrow \mathrm{PbI}(\mathrm{s})+\mathrm{KNO}_3$
(d) $\mathrm{CaCO}_3+\mathrm{HCI} \rightarrow \mathrm{CaCl}_2+\mathrm{H}_2 \mathrm{O}+\mathrm{CO}_2 \uparrow$
Marble
Answer:
(b) $2 \mathrm{Na}_{(\mathrm{s})}+\mathrm{I}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NaI}_{(\mathrm{s})}$
Question 31.
Which one of the following graph is not correct

(b) 

(c)

Answer:

Question 32.
The half life of paracetamol with in the body is
(a) 2 hours
(b) 2.5 hours
(c) 6 hours
(d) 10 hours
Answer:
(b) 2.5 hours
Question 33 .
What is the order of radioactive decay?
(a) first order
(b) zero order
(c) second order
(d) third order
Answer:
(a) first order
Question 34.
$\mathrm{t}_{1 / 2}$ of the reaction increases with increase in initial concentration of the reaction means the order of the reaction will be
(a) first order
(b) zero order
(c) second order
(d) third order
Answer:
(b) zero order
Question 35 .
The reaction rate that does not decrease with time is ...........
(a) pseudo first order reaction
(b) first order reaction
(c) zero order reaction
(d) second order reaction
Answer:
(c) zero order reaction

Question 36.
The rate of the reaction $\mathrm{X} \rightarrow \mathrm{Y}$ becomes 8 times when the concentration of the reactant ' $\mathrm{X}$ ' is doubled. The rate law of the reaction is ........
(a) $-\frac{d[x]}{d t}=\mathrm{k}[\mathrm{X}]^2$
(b) $-\frac{d[x]}{d t}=\mathrm{k}[\mathrm{X}]^3$
(c) $-\frac{d[x]}{d t}=\mathrm{k}[\mathrm{X}]^4$
(d) $-\frac{d[x]}{d t}=\mathrm{k}[\mathrm{X}]^8$
Answer:
(b) $-\frac{d[x]}{d t}=\mathrm{k}[\mathrm{X}]^3$
Question 37.
The decomposition of ammonia gas on platinum surface has a rate constant $\mathrm{k}=2.5 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ What is the order of the reaction?
(a) first order
(b) second order
(c) third order
(d) zero order
Answer:
(d) zero order
Question 38.
A reaction is $50 \%$ completed in 2 hours and $75 \%$ completed in 4 hours. Then the order of the reaction is
(a) first order
(b) zero order
(c) second order
(d) third order
Answer:
(a) first order

Question 39.
What is the rate equation for the reaction $\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$ has zero order?
(a) Rate $=\mathrm{k}$
(b) Rate $=\mathrm{k}[\mathrm{A}]$
(c) Rate $=\mathrm{k}[\mathrm{A}]$. $[\mathrm{B}]$
(a) Rate $=\mathrm{k} \cdot \frac{1}{[c]}$
Answer:
(c) Rate $=\mathrm{k}[\mathrm{A}]$. $[\mathrm{B}]$
Question 40.
How does the value of rate constant vary with reactant concentration?
(a) $k \propto \frac{c^{n-1}}{n+1}$
(b) $k \propto \frac{1}{c^{n-1}}$
(c) $k \propto \frac{1}{c^{n+1}}$
(d) $k \propto \frac{1}{\mathrm{C}}$
Answer:
(b) $k \propto \frac{1}{c^{n-1}}$
Question 41.
Identify the reaction order if the unit of rate constant is $\mathrm{s}^{-1} \ldots \ldots \ldots$.
(a) zero order reaction
(b) second order reaction
(c) first order reaction
(d) third order reaction
Answer:
(c) first order reaction

Question 42.
What is unit of zero order reaction?
(a) $\mathrm{s}^{-1}$
(b) $\mathrm{mol}^{-1} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$
(c) $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}$
(d) $\mathrm{mol} \mathrm{L}^{-1}$
Answer:
(c) $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}$
Question 43.
Which of the following factor affect the rate of the reaction'?
(a) volume
(b) pressure
(c) cone
(d) all the above
Answer:
(c) cone
Question 44.
Acid hydrolysis of an ester is an example of
(a) zero order reaction
(b) Pseudo first order reaction
(c) second order reaction
(d) first order reaction
Answer:
(b) Pseudo first order reaction
Question 45.
Polymerisation reactions follows order kinetics.
(a) fractional
(b) first
(c) zero
(d) Pseudo first
Answer:
(a) fractional
Question 46.
Activation energy of a chemical reaction can be determined by
(a) changing concentration of the reactants
(b) Evaluating rate constants at standard temperature
(c) Evaluating rate constants at two different temperature
(d) Evaluating reIocities of reaction at two different temperature
Answer:

(c) Evaluating rate constants at two different temperature
Question 47.
Which of the following is the fastest reaction?
(a) $\mathrm{u}=\mathrm{u} ~ \frac{1}{2} \quad \stackrel{250^{\circ} \mathrm{C}}{\longrightarrow}$
(b) $\mathrm{u}=\mathrm{u} \frac{1}{2} \quad 2 \stackrel{500^{\circ} \mathrm{C}}{\longrightarrow}$
(c) $\mathrm{u}=\ddot{\mathrm{u}} \frac{1}{2} \quad 2 \stackrel{750^{\circ} \mathrm{C}}{\longrightarrow}$
(d) $\mathrm{u}=\ddot{\mathrm{u}} \frac{1}{2} \quad 2 \stackrel{1000^{\circ} \mathrm{C}}{\longrightarrow}$
Answer:
(d) $\ddot{\mathrm{u}}=\ddot{\mathrm{u}} \frac{1}{2} \quad 2 \stackrel{1000^{\circ} \mathrm{C}}{\longrightarrow}$
Question 48.
Half life period of a reaction is found to be inversely proportional to the cube of its initial concentration. The order of the reaction is
(a) 2
(b) 5
(c) 3
(d) 4
Answer:
(d) 4
Question 49.
A large increase in the rate of a reaction for a rise in temperature is due to .........
(a) the decrease in the number of collisions
(b) increase in the number of activated molecules
(c) the shortening of mean free path
(d) the lowering of activation energy
Answer:

(b) increase in the number of activated molecules
Question 50.
The minimum energy of a molecule would possess in order to enter into a fruitful collision is known as
(a) Reaction energy
(b) collision energy
(c) Activation energy
(d) Threshold energy
Answer:
(a) Threshold energy
II. Fill in the blanks.
1. The unit of the rate of a reaction is ....................
2. For a ......... reaction, the unit of the reaction rate is $\mathrm{atm} \mathrm{s}$
3. An elementary step is characterised by its ..........
4. The total number of reactant species involved in an elementary step is called ....................
5. The sum of powers of concentration terms involved in the experimentally determined rate law is called ...........
6. The overall order of decomposition of acetaldehyde to methane and carbon monoxide is ...................
7. A second order reaction can be altered to a first order reaction by taking one of the reactant in large excess, it is called ..........
8. A reaction in which rate is independent of the concentration of the reactant over a wide range of concentration is called ..........
9. All radioactive disentegration reactions follow .......... kinetics.
10. For a first order reaction, half life does not depend on ..........
11. Half life period of zero order reaction is...................... proportional to initial concentration of the reactant.
12. Half life period .......... reaction is directly proportional to initial concentration of the reactant.
13. .......... was proposed by Max Trautz and William lewis.
14. Collision theory was proposed by .......... in 1916 and in ......... 1918.
15. For a gas at room temperature (298 K) and $\mathrm{I}$ atm, each molecule undergoes approximately ..................per second.

16. In order to react, the collidng molecules must possess a minimum energy called ....................
17. Generally the reaction rate tends to double when the temperature is increased by .........................
18. The number of collisions of reactant molecules per second is known as ...........
19. Heating is required for the reaction between $\mathrm{KMnO}_4$ and oxalate ion and is carried out at around ...............
20.......... reactions are faster as compared to reactions involving solid or liquid reactants.
21. The rate of the reaction ........... with the increase in the concentration of the reactants.
22. Higher the concentration of reactants greater is the possibility of and hence the .....................
23. In the presence of catalyst the energy of activation is .......... and hence greater number of molecules change over to products there by increasing the rate of the reaction.
24. Bio availability of drugs within the body and this branch of study is called ...................
$25 . \ldots \ldots \ldots .$. has a half life of 2.5 hours within the body.
26. The change in concentration of species per unit time gives the ......... of the reaction.
27. The rate constant is equal to the rate of the reaction when concentration of reactants is .........
28. Increase in surface area of reactant leads to more collisions per litre per second and hence the rate of the reaction is .................
29. Acid hydroJysis of an ester is an example of .................
30. Molecularity of a chemical reaction will never be equal to ................

Answer:
1. $\mathrm{moI} \mathrm{L}^{-1} \mathrm{~s}^{-1}$
2. gas phase
3. molecularity
4. Molecularity
5. order
6. $3 / 2$ or 1.5
7. Pseudo first order reaction
8. Zero order reaction
9. First order
10. initial concentration
11. directly
12. zero order
13. Collision theory
14. Max Trautz, William lewis
15. 10 collisions
16. Activation energy
17. $10^{\circ} \mathrm{C}$
18. Frequency factor (A)
19. $60^{\circ} \mathrm{C}$
20. Gas phase
21. increases
22. collisions, rate
23. lowered
24. Pharmaco kinetics
25. Paracetamol
26. rate
27. unity
28. increased
29. Pseudo first order reaction
30. zero

III. Match the following
Match the list I and II using the code given below the list.
Quetion 1.

Answer:
(a) $3,4,1,2$
Question 2.

Answer:
(a) $3,4,1,2$
Question 3.

Answer:
(a) $3,1,4,2$
Question 4.

Answer:
(a) $3,4,2,1$
IV. Assertion and Reason
Question 1.
Assertion (A): Decomposition of hydrogen peroxide catalysed by $\mathrm{I}^{-}$is a bimolecular first order reaction.
Reason (R): The above reaction take place in two steps, step 1 involves both $\mathrm{H}_2 \mathrm{O}_2$ and $\mathrm{I}$ and so it is bimolecular but order is determined experimentally as 1 .
(a) Both $\mathrm{A}$ and $\mathrm{R}$ are correct and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$.
(b) Both $\mathrm{A}$ and $\mathrm{R}$ are correct but $\mathrm{R}$ is not the correct explanation of $\mathrm{A}$
(c) $\mathrm{A}$ is correct but $\mathrm{R}$ is wrong
(d) $\mathrm{A}$ is wrong but $\mathrm{R}$ is correct
Answer:
(a) Both $\mathrm{A}$ and $\mathrm{R}$ arc correct and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$
Question 2.
$
5 \mathrm{Br}_{(\mathrm{aq})}^{-}+\mathrm{BrO}_{3(\mathrm{aq})}^{-}+6 \mathrm{H}^{+} \rightarrow 3 \mathrm{Br}_{2(1)}+3 \mathrm{H}_2 \mathrm{O}_{(1)}
$
Assertion (A): is equal to 4 .
Reason (R): The experimental rate law is.
Rate $=\mathrm{K}\left[\mathrm{Br}^{-}\right]\left[\mathrm{BrO}_3^{-}\right]\left[\mathrm{H}^{+}\right]^2$.
So $1+1+2=4$ order value is 4 .
(a) Both $\mathrm{A}$ and $\mathrm{R}$ are correct and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$.
(b) Both $A$ and $R$ are wrong
(c) $\mathrm{A}$ is correct but $\mathrm{R}$ is wrong
(d) $\mathrm{A}$ is wrong but $\mathrm{R}$ is correct
Answer:
(a) Both $\mathrm{A}$ and $\mathrm{R}$ are correct and $\mathrm{R}$ is the correct explanation olA.
Question 3.
Assertion (A): The rate of a reaction increases with the increase in the concentration of the reactants. Reason (R): The rate of the reaction depends upon the number of collisions between the reacting molecules. Higher the concentration, greater is the possibility for collision and hence the rate.
(a) Both $\mathrm{A}$ and $\mathrm{R}$ are correct and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$,
(b) Both $\mathrm{A}$ and $\mathrm{R}$ are correct but $\mathrm{R}$ is not the correct explanation of $\mathrm{A}$

(c) $\mathrm{A}$ is correct but $\mathrm{R}$ is wrong
(d) $\mathrm{A}$ is wrong but $\mathrm{R}$ is correct
Answer:
(a) Both $\mathrm{A}$ and $\mathrm{R}$ are correct and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$.
Question 4.
Assertion (A): Powdered calcium carbonate reacts much faster with dilute $\mathrm{HCL}$ than with the same mass of $\mathrm{CaCO}_3$ as marble.
Reason (R): For a given mass of a reactant, when the particle size decreases, surface area increases. Increase in surface area of the reactant leads to more collisions per litre per second and hence the rate of the reaction also increases.
(a) Both $\mathrm{A}$ and $\mathrm{R}$ are correct and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$.
(b) Both $\mathrm{A}$ and $\mathrm{R}$ arc correct but $\mathrm{R}$ is not correct explanation of $\mathrm{A}$
(c) $\mathrm{A}$ is correct but $\mathrm{R}$ is wrong
(d) $\mathrm{A}$ is wrong but $\mathrm{R}$ is correct
Answer:
(a) Both $\mathrm{A}$ and $\mathrm{R}$ are correct and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$.
Question 5.
Assertion (A): Catalyst presence increases the rate of the reaction
Reason (R): In the presence of a catalyst, energy of activation is lowered and hence greater number of molecules can across the energy harrier and change over to products thereby increasing the rate of the reaction.
(a) Both $\mathrm{A}$ and $\mathrm{R}$ are correct but $\mathrm{R}$ is not correct explanation of $\mathrm{A}$
(b) Both $\mathrm{A}$ and $\mathrm{R}$ are correct and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$
(c) $\mathrm{A}$ is correct but $\mathrm{R}$ is wrong
(d) $\mathrm{A}$ is wrong but $\mathrm{R}$ is correct
Answer:
(b) Both $\mathrm{A}$ and $\mathrm{R}$ are correct and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$
Question 6.
Assertion (A): Doctors adviced to take paracetamol once in 6 hours during fever and body pain Reason (R): Paracetarnol has a half life of 2.5 hours within the body. After 10 hours ( 4 half lives) only $6.25 \%$ of drug remains. Based on this, doctors adviced to take it once in 6 hours.
(a) Both $\mathrm{A}$ and $\mathrm{R}$ are wrong
(b) $\mathrm{A}$ is correct but $\mathrm{R}$ is wrong
(c) $\mathrm{A}$ and $\mathrm{R}$ are correct and $\mathrm{R}$ is the correct explanation of $\mathrm{A}$
(d) $\mathrm{A}$ and $\mathrm{R}$ are correct but $\mathrm{R}$ is not correct explanation of $\mathrm{A}$
Answer:

(a) Both A and R are correct and R is the correct explanation of A.
Question 7.
Assertion (A): Order of the reaction can be zero or fractional
Reason (R): We cannot determine order from balanced chemical equation
(a) Both $\mathrm{A}$ and $\mathrm{R}$ are correct but $\mathrm{R}$ is not correct explanation of $\mathrm{A}$.
(b) Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$
(c) $\mathrm{A}$ is correct but $\mathrm{R}$ is wrong
(d) $A$ is wrong but $R$ is correct
Answer:
(a) Both $\mathrm{A}$ and $\mathrm{R}$ are correct and $\mathrm{R}$ is not correct explanation of $\mathrm{A}$
Question 8.
Assertion (A): If the activation enery of a reaction is zero, temperature will have no effect on the rate constant
Reason (R): Lower the activation energy, faster is the reaction.
(a) Both A and R are correct and R is the correct explanation of A.
(b) Both $A$ and $R$ are correct but $R$ is not correct explanation of $A$
(c) $\mathrm{A}$ is correct but $R$ is wrong
(d) $A$ is wrong but $R$ is correct
Answer:
(b) Both $\mathrm{A}$ and $\mathrm{R}$ are correct but $\mathrm{R}$ is not correct explanation of $\mathrm{A}$
V. Find the odd one out
Question 1.
$(a) \mathrm{N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightarrow 2 \mathrm{NO}_{2(\mathrm{~g})}+1 / 2 \mathrm{O}_{2(\mathrm{~g})}$
(b) $\mathrm{SO}_2 \mathrm{Cl}_{2(\mathrm{~g})} \rightarrow \mathrm{SO}_{2(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{~g})}$
(c) $\mathrm{CH}_3 \mathrm{CHO}_{(g)} \stackrel{\Delta}{\longrightarrow} \mathrm{CH}_{4(\mathrm{~g})}+\mathrm{CO}_{(g)}$
(d) $\mathrm{H}_2 \mathrm{O}_{2(\mathrm{aq})} \rightarrow \mathrm{H}_2 \mathrm{O}_{(1)}+1 / 2 \mathrm{O}_{2(\mathrm{~g})}$
Answer:
(c) $\mathrm{CH}_3 \mathrm{CHO}_{(g)} \stackrel{\Delta}{\longrightarrow} \mathrm{CH}_{4(\mathrm{~g})}+\mathrm{CO}_{(g)}$
Hint: It is a fractional order reaction with order value $3 / 2$ where as others are first order reaction.

Question 2.
Define molecularity of a reaction.
Answer:
Molecularity of a reaction is the total number of reactant species that are involved in an elementary step.
Question 3.
Define order of a chemical reaction.
Answer:
Order of a chemical reaction is the sum of powers of concentration terms involved in the experimentally determined rate law.
Question 4.
Define Half life period.
Answer:
The half life ola reaction is defined as the time required for the reactant concentration to reach one half its initial value.
Question 5 .
Mention the factors affecting the reaction rate.
Answer:
The rate of the reaction is affected by the following factors.
1. Nature and state of the reactant
2. Concentration of the reactant
3. Surface area of the reactant
4. Temperature of the reaction
5. Presence of a catalyst
Question 6 .
How is surface area of the reactant affect the rate of the reaction?
Answer:
1. In heterogeneous reactions, the surface area of the solid reactants play an important role in deciding the rate.
2. For a given mass of a reactant, when the particle size decreases surface area increases. Increase in surface area of reactant leads to more collisions per litre per second and hence the rate of reaction is increased.

3. For example, powdered calcium carbonate reacts much faster with dilute $\mathrm{HCl}$ than with the same mass of $\mathrm{CaCO}_3$ as marble.
Question 7.
Paracetamol is prescribed to take once in 6 hours. Justify this statement.
Answer:
1. Paracetamol is a well known antipyretic and analgesic that is prescribed in cases of fever and body pain.
2. Paracetamol has a half life of 2.5 hours within the body. (Le) the plasma concentration of the drug is halved after 2.5 hours. So after 10 hours (4 half lives), only $6.25 \%$ of drug remains. Based on this, the dosage and frequency will be decided.
3. In the case of paracetamol, it is usually prescribed to take once in 6 hours.
Question 8.
For a reaction, $\mathrm{A}+\mathrm{B} \rightarrow$ product; the rate law is given by $r=k[A]^{1 / 2}[B]^2$. What is the order of the reaction?
Answer:
Order of the reaction $=\frac{1}{2}+2=2 \frac{1}{2}$ or 0.5
Question 9.
The conversion of molecules $\mathrm{X}$ to $\mathrm{Y}$ follows second order kinetics. If concentration of $\mathrm{X}$ is increased to three times how will $; t$ affect the rate of formation of $Y$ ?
Answer:
For the reaction, $\mathrm{X} \rightarrow \mathrm{Y}$ as it follows second order kinetics, therefore the rate law equation will be Rate $=\mathrm{k}[\mathrm{X}]^2=\mathrm{ka}^2$
if $[\mathrm{X}]=\mathrm{a} \mathrm{mol}^{-1}$
if the concentration of $\mathrm{X}$ is increased three times, then
$[\mathrm{X}]=3 \mathrm{a} \mathrm{mol} \mathrm{L}^{-1}$
$\therefore$ Rate $=\mathrm{k}(3 \mathrm{a})^2=9 \mathrm{ka}^2$
Thus, the rate of the reaction will become 9 times. Hence the rate of formation of $Y$ will increase by 9 times.
Question 10.
Time required to decompose $\mathrm{SO}_2 \mathrm{Cl}_2$ to half of its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction.
Answer:

For a first order reaction,
$
\mathrm{k}=\frac{0.693}{\frac{t_1}{2}}=\frac{0.693}{60 \mathrm{~min}}=1.155 \times 10^{-2} \mathrm{~min}^{-1}=\frac{0.693}{600 \times 60}=1.925 \times 10^4 \mathrm{~s}^{-1}
$
Question 11.
What will be the effect of temperature on rate constant?
Answer:
Rate constant of a reaction is nearly doubled with rise in temperature by $10^{\circ} \mathrm{C}$. The exact dependence of the rate constant on temperature is given by Arrhenius equation:
Rate constant,
$
\mathrm{k}=\mathrm{A} e^{-\frac{E_a}{R T}}
$
Question 12.
A reaction is first order in $\mathrm{A}$ and second order in $\mathrm{B}$.
1. Write the differential rate equation.
2. How is the rate affected on increasing the concentration of $B$ three times?
3. How is the rate affected when the concentrations of both $A$ and $B$ arc doubled?
Answer:
1. $\frac{d x}{d t}=\mathrm{k}[\mathrm{A}]^1[\mathrm{~B}]^2$
2. If concentration of ' $\mathrm{B}$ ' is tripled, then the rate will become 9 times.
3. When concentration of both A and B are doubled, then the rate will become 8 times.
Question 13.
Define zero order reaction. Give the unit for its rate constant $(\mathrm{k})$.
Answer:
Zero Order Reaction. The reaction in which the rate of reaction is independent of the concentration of the reactants is called zero order reaction.
$
\text { Rate }=\mathrm{k}[\mathrm{A}]^0 \Rightarrow \mathrm{k}
$
Where $\mathrm{k}$ is the rate constant. Its unit is $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}$

Question 14.
Write units of rate constant $\mathrm{k}$ for zero order, first order, second order and $\mathrm{n}$ order reaction.
Answer:
Order of Reaction
1. Zero order reaction
2. First order reaction
3. Second order reaction
4. nth order reaction
Unit of k:
1. $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}$
2. $\mathrm{s}^{-1}$
3. $\mathrm{mol} \mathrm{L} \mathrm{s}^{-1}$
4. $(\mathrm{mol} / \mathrm{L})^{1-\mathrm{n}} \mathrm{s}^{-1}$
Question 15.
What is the effect of catalyst on the activation energy? Why?
Answer:
A Catalyst lower down the activation energy. It provides an alternate path to the reaction. It forms an unstable intermediate which readily changes into products.
Question 16.
Give two differences between zero order and first order reaction.
Answer:
Zero Order:
1. Its ' $\mathrm{k}$ ' has unit $=\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}$
2. Its $t 1 / 2$ is directly proportional to initial conc. of reactant
First order:
1. Its ' $\mathrm{k}$ ' has unit $=$ time $^{-1}=\sec ^{-1}$
2. Its half life is independent of the initial conc. of the reactant.
3 Mark Questions and Answers

Question 1.
Write the differences between the rate and rate constant of the reaction.
Answer:
Rate of a reaction:
1. It represents the speed at which the reactants are converted into products at any instant
2. It is measured as decrease in the concentration of the reactants (or) increase in the concentration of products
3. It depends on the initial concentration of reactants
Rate constant of a reaction:
1. It is a proportionality constant
2. It is equal to the rate of the reaction, when the concentration of each of the reactants is unity
3. It does not depend on the initial concentration of the reactants
Question 2.
What are the examples of first order reaction?
Answer:
1. Decompostion of dinitrogen pentoxide
$
\mathrm{N}_2 \mathrm{O}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NO}_{2(\mathrm{~g})}+\frac{1}{2} \mathrm{O}_{2(\mathrm{~g})}
$
2. Decomposition of thionylchloride
$
\mathrm{SO}_2 \mathrm{Cl}_{2(\mathrm{~g})} \rightarrow \mathrm{SO}_{2(\mathrm{~g})}+\mathrm{CI}_{2(\mathrm{~g})}
$
3. Decomposition of $\mathrm{H}_2 \mathrm{O}_2$ in aqueous solution
$
\mathrm{H}_2 \mathrm{O}_{2(\mathrm{aq})} \rightarrow \mathrm{H}_2 \mathrm{O}_{(1)}+\frac{1}{2} \mathrm{O}_{2(\mathrm{~g})}
$
4. Isomerisation of cyclopropane to propene
Question 3.
For the reaction $\mathrm{R} \rightarrow \mathrm{P}$, the concentration of a reactant changes from $0.03 \mathrm{M}$ to $0.02 \mathrm{M}$ in 25 minutes. Calculate the average rate of reaction using units of time both in minutes and seconds.
Answer:
$
\begin{aligned}
& =\frac{\Delta[R]}{\Delta t}=\frac{[R]_2-[R]_1}{t_2-t_{\mathrm{I}}} \\
& =\frac{0.02 \mathrm{M}-0.03 \mathrm{M}}{25 \mathrm{~min}}=\frac{-0.01 \mathrm{M}}{25 \mathrm{~min}}=4 \times 10^{-4} \mathrm{~min}^{-1} \\
& =\frac{-0.01 \mathrm{M}}{25 \times 60}=\text { üüü } \times-6-1
\end{aligned}
$

Question 4.
In a reaction, $2 \mathrm{~A} \rightarrow$ products. the concentration of $\mathrm{A}$ decreases from $0.5 \mathrm{moI} \mathrm{L}^{-1}$ to $0.4 \mathrm{~mol} \mathrm{~L}^{-1}$ in 10 minutes. Calculate the rate during this interval.
Answer:
Average rate
$
\begin{aligned}
& =\frac{1}{2} \frac{\Delta[\mathrm{A}]}{\Delta t}=\frac{1}{2} \frac{[\mathrm{A}]_2-[\mathrm{A}]_1}{t_2-t_1} \\
& =-\frac{1}{2}\left(\frac{0.4 \mathrm{M}-0.5 \mathrm{M}}{10 \mathrm{~min}}\right)=-\frac{1}{2}\left(\frac{-0.1 \mathrm{M}}{10 \mathrm{~min}}\right)=5 \times 10^{-3} \mathrm{M} \mathrm{min}^{-1}
\end{aligned}
$
Question 5.
A first order reaction has a rate constant, $1.15 \times 10^{-3} \mathrm{~s}^{-1}$. How long will $5 \mathrm{~g}$ of this reactant take to reduce to $3 \mathrm{~g}$ ?
Answer:
Here,
$[\mathrm{R}]_0=5 \mathrm{~g}$
$[\mathrm{R}]=3 \mathrm{~g}$
$\mathrm{k}=1.15 \times 10^{-3} \mathrm{~s}^{-1}$ As the reaction is of first order,
$
\begin{aligned}
\mathrm{k} & =\frac{2.303}{t} \log \frac{[R]_0}{[R]} \\
\mathrm{t} & =\frac{2.303}{\text { üüü } \times-3-1} \log \frac{5 g}{3 g}=2.00 \times 10^3(\log 1.667) \mathrm{s} \\
& =2.0 \times 10^3 \times 0.2219 \mathrm{~s}=443.85=444 \mathrm{~s}
\end{aligned}
$

Question 6.
Time required to decompose $\mathrm{SO}_2 \mathrm{CI}_2$ to half of its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction. For a first order reaction,

Answer:
$
\mathrm{k}=\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{60 \mathrm{~min}}=1.155 \times 10^{-2} \mathrm{~min}^{-1}=\frac{0.693}{60 \times 60}=1.925 \times 10^{-4} \mathrm{~s}^{-1}
$
Question 7.
A reaction is second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is-
1. doubled
2. reduced to half.
Answer:
1. Reaction is second order with respect to the reactant
$
\begin{aligned}
& \therefore \text { Rate }=\mathrm{k}[\mathrm{A}]^2=\mathrm{ka}^2 . \\
& \text { when }[\mathrm{A}]=2 \mathrm{a} \\
& \text { Rate } \mathrm{k}(2 \mathrm{a})^2 \\
& =4 \mathrm{ka}^2
\end{aligned}
$
$=4$ times
Therefore, when concentration of the reactant is doubled the rate will become 4 times
2. when $[A]=\frac{1}{2}$
Rate $=\mathrm{k}\left(\frac{1}{2} a\right)^2=\frac{1}{4} \mathrm{ka}^2=\frac{1}{4} \mathrm{k}$
Therefore, rate will be reduced to one-fourth of the initial rate.
Question 8 .
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 $1 / 6^{\text {th }}$ value?

Answer:
$
\mathrm{t}=\frac{2303}{k} \log \frac{x}{x / 16}=\frac{2.303}{60 s^{-1}} \log 16=4.62 \times 10^{-2} \mathrm{~s}
$
Question 9.
For a first order reaction, show that time required for $99 \%$ completion is twice the time required for the completion of $90 \%$ of reaction.
Answer:
For a first order reaction, $\mathrm{t}=\mathrm{k}=\frac{2.303}{t} \log \frac{a}{a-x}$
$99 \%$ completion means that
$\mathrm{x}=99 \%$ of $\mathrm{a}=0.99 \mathrm{a}$
$\mathrm{t}_{99 \%}=\frac{2303}{k} \log \frac{a}{a-0.99 a}=\frac{2.303}{k} \log 10^2=2 \times \frac{2303}{k}$
$90 \%$ completion means that
$\mathrm{x}=90 \%$ of $\mathrm{a}=0.90 \mathrm{a}$
$\mathrm{t}_{99 \%}=\frac{2303}{k} \log \frac{a}{a-0.99 a}=\frac{2.303}{k} \log 10=\frac{2.303}{k}$
$\frac{t_{99 \%}}{t_{90 \%}}=\left(\frac{2 \times 2303}{k}\right) / \frac{2.303}{k}=2$
or
$\mathrm{t}_{99 \%}=2 \times \mathrm{t}_{90 \%}$
Question 10.
Calculate the half life of a first order reaction whose rate constant is $200 \mathrm{~s}^{-1}$
Answer:
Here rate constant
$\mathrm{k}=200 \mathrm{~s}^{-1}$
$\therefore$ Half - life of a first order reaction is
$
\mathrm{t}_{1 / 2}=\frac{0.693}{k}=\frac{0.693}{200}=3.46 \times 10^{-3} \mathrm{sec}
$

Question 11.
The decomposition of dinitrogen pentoxide $\left(\mathrm{N}_2 \mathrm{O}\right)$ follows the first order rate law. Calculate the rate constant from the given data.
$
\begin{aligned}
& \mathrm{t}=800 \mathrm{sec},\left[\mathrm{N}_2 \mathrm{O}_5\right]=1.45 \mathrm{moI} \mathrm{L}^{-1}=\left[\mathrm{A}_2\right] \\
& \mathrm{t}=1600 \mathrm{sec} \\
& {\left[\mathrm{N}_2 \mathrm{O}_3\right]=0.88 \mathrm{moI} \mathrm{L}^{-1}=\left[\mathrm{A}_2\right]}
\end{aligned}
$
Answer:
Applying the formula,
$
\begin{aligned}
& \mathrm{k}=\frac{2.303}{\left(t_2-t_1\right)} \log 10 \frac{\left[A_1\right]}{\left[A_2\right]} \\
& =\frac{2.303}{(1600-800)} \log 10 \frac{1.45}{0.88}=\frac{2.303}{800} \times 0.2169 \\
& =6.24 \times 10^{-4} \mathrm{sec}^{-1}
\end{aligned}
$

Question 13.
A first order reaction is $20 \%$ completed in 10 minutes. Calculate the time taken for the reaction to go to $80 \%$ completion.
Answer:
Applying the first order equation,
$
\mathrm{k}=\frac{2303}{t} 10 \mathrm{~g} \frac{[R]_0}{[R]}
$
At $\mathrm{t}=10 \mathrm{~min}$
$\mathrm{R}=100-20$
$\mathrm{k}=\frac{2303}{t} \log 10 \frac{100}{(100-20)}$
$\mathrm{t}=\frac{2303}{10} \log 10 \frac{100}{80}$
$=0.0223 \mathrm{~min}^{-1}$
Question 14.
For a reaction: $2 \mathrm{NH}_{3(\mathrm{~g})} \stackrel{P t}{\longrightarrow} \mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})}$ Rate $=\mathrm{K}$
1. Write the order and molecularity of this reaction.
2. Write the unit of $\mathrm{K}$.
Answer:

1. Order of reaction Zero order. Molecularity $=2$
2. Unit of $\mathrm{K}=\operatorname{mol~} \mathrm{L}^{-1} \sec ^{-1}$
5 Marks Questions and Answers
Question 1.
How would you calculate the order of the reaction $2 \mathrm{NO}+\mathrm{O}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NO}_2(\mathrm{~g})$ by an experiment?
(or)
prove that $2 \mathrm{NO}+\mathrm{O}_2 \rightarrow 2 \mathrm{NO}_2$ is a third order reaction.
Answer:
$
2 \mathrm{NO}_{(\mathrm{g})}+\mathrm{O}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NO}_2(\mathrm{~g})
$
Series of experiments are conducted by keeping the concentration of one of the reactants as constant and changing the concentration of the others.

Rate $=\mathrm{k}[\mathrm{NO}]^{\mathrm{m}}\left[\mathrm{O}_2\right]^{\mathrm{n}}$
For experiment 1 , the rate law is
Rate $_1=\mathrm{k}[\mathrm{NO}]^{\mathrm{m}}\left[\mathrm{O}_2\right]^{\mathrm{n}}$
$19.26 \times 10^{-2}=\mathrm{k}[1.3]^{\mathrm{m}}[1.1]^{\mathrm{n}}$
For experiment 2
Rate $_2=\mathrm{k}[\mathrm{NO}]^{\mathrm{m}}\left[\mathrm{O}_2\right]^{\mathrm{n}}$
$38.40 \times 10^{-2}=\mathrm{k}[1.3]^{\mathrm{m}}[2.2]^{\mathrm{n}}$
For experiment 3
Rate $_3=\mathrm{k}[\mathrm{NO}]^{\mathrm{m}}\left[\mathrm{O}_2\right]^{\mathrm{n}}$
$76.8 \times 10^{-2}=\mathrm{k}[2.6]^{\mathrm{m}}[1.1]^{\mathrm{n}}$
$\frac{(2)}{(1)} \Rightarrow \frac{38.40 \times 10^{-2}}{19.26 \times 10^{-2}}=\frac{k[1.3]^m[2.2]^n}{k[1.3]^m[1.1]^n}$
$2=\left(\frac{2.2}{1.1}\right)^n$
$4=2^{\mathrm{m}}$
$\Rightarrow \mathrm{n}=1$
Therefore the reaction is first order with respect to $\mathrm{O}_2$
$
\begin{aligned}
& \frac{(3)}{(2)} \Rightarrow \frac{76.8 \times 10^{-2}}{19.26 \times 10^{-2}}=\frac{k[2.6]^m[1.1]^n}{k[1.3]^m[1.1]^n} \\
& 2=\left(\frac{2.6}{1.3}\right)^m \\
& 4=2^{\mathrm{m}}
\end{aligned}
$
$
\Rightarrow \mathrm{m}=1
$
Therefore the reaction is second order with respect to $\mathrm{NO}$
The rate law is Rate $=\mathrm{k}[\mathrm{NO}]^2\left[\mathrm{O}_2\right]^1$
The overall order of the reaction $=2+1=3$

Question 2.
Derive the integrated rate law for a first order reaction?
Answer:
A reaction whose rate depends on the reactant concentration raised to the first power is called a first order reaction. First order reaction is $\mathrm{A} \rightarrow$ product. Rate law can be expressed as, Rate $=\mathrm{k}[\mathrm{A}]^1$. Where, $\mathrm{k}$ is the first order rate constant
$
\begin{aligned}
& \frac{-d[A]}{d t}=\mathrm{k}[\mathrm{A}]^1 \\
& \frac{-d[A]}{[A]}=\mathrm{k} . \mathrm{dt} .
\end{aligned}
$
Integrate the above equation (I) between the limits of time $t=0$ and time equal to $t$, while the concentration varies from initial concentration $\left[\mathrm{A}_0\right]$ to $[\mathrm{A}]$ at the later time.
$
\begin{aligned}
& \int_{\mathrm{A}_0}^{\mathrm{A}} \frac{-d[\mathrm{~A}]}{[\mathrm{A}]}=k \int_0^t d t \\
& -\ln [\mathrm{A}]_{\mathrm{A}_0}^{\mathrm{A}}=k(t)_0^t \\
& -\ln [\mathrm{A}]-\left(-\mathrm{In}\left[\mathrm{A}_0\right]\right)=\mathrm{k}(\mathrm{t}-0) \\
& -\ln [\mathrm{A}]+\mathrm{In}\left[\mathrm{A}_0\right]=\mathrm{kt} \\
& \ln \left(\frac{\left[\mathrm{A}_0\right]}{[\mathrm{A}]}\right)=k t
\end{aligned}
$
This equation (2) is in natural logarithm. To convert it into usual logarithm with base 10 , we have to multiply the term by 2.303
$
\begin{aligned}
& 2.303 \log \left(\frac{\left[\mathrm{A}_0\right]}{[\mathrm{A}]}\right)=\mathrm{kt} \\
& \mathrm{k}=\frac{2.303}{\mathrm{t}} \log \left(\frac{\left[\mathrm{A}_0\right]}{[\mathrm{A}]}\right)
\end{aligned}
$
Question 3.
Explain the effect of temperature on reaction rate based on Arrhenius theory.
Answer:
1. Generally, the rate of a reaction increases with increasing temperature. However, there are very few exceptions.
2. As a rough rule, for many reactions near room temperature, reaction rate tends to double when the temperature is increased by $10^{\circ} \mathrm{C}$.

3. A large number of reactions are known which do not take place at room temperature but occur readily at higher temperature. Example - Reaction between $\mathrm{H}_2$ and $\mathrm{O}_2$ to form $\mathrm{H}_2 \mathrm{O}$ takes place only when an electric spark is passed.
4. Arrhenius suggested that the rates of most reactions vary with temperature in such a way that the rate constant is directly proportional to
$e^{-\frac{E_0}{R T}}$ and he proposed a relation between the rate constant and temperature.
$
\mathrm{k}=\mathrm{A} e^{-\frac{E_a}{R T}}
$
where
$\mathrm{k}=$ frequency factor
$\mathrm{R}=$ gas constant
$\mathrm{E}_{\mathrm{a}}=$ Activation energy
$\mathrm{T}=$ Absolute temperature (in kelvin)
The factor A does not vary significantly with temperature and hence it may be taken as a constant.
5. Taking logarithm on both side of the equation (1)
$
\begin{aligned}
& \ln \mathrm{k}=\ln \mathrm{A}+\ln e^{-\mathrm{E}_{\mathrm{a}} / \mathrm{RT}} \\
& \ln \mathrm{k}=\ln \mathrm{A}-\frac{\mathrm{E}_{\mathrm{a}}}{\mathrm{RT}} \quad[\because \ln e=1] \\
& \ln \mathrm{k}=\ln \mathrm{A}-\frac{\mathrm{E}_{\mathrm{a}}}{\mathrm{R}}\left(\frac{1}{\mathrm{~T}}\right)
\end{aligned}
$
6. The plot of Ink vs $\left(\frac{1}{T}\right)$ is a straight line with negative slope $\frac{E_a}{R T}$. If the rate constant for a reaction at two different temperatures is known, we can calculate the activation energy.
$
\ln \mathrm{k}_2-\ln \mathrm{k}_1-\left[\frac{E_a}{\mathrm{RT} \mathrm{T}_2}\right]+\left[\frac{E_a}{\mathrm{RT}}\right]
$
This equation can be used to calculate $\mathrm{E}$ from rate $\mathrm{E}_{\mathrm{a}}$ constants $\mathrm{k}_1 \& \mathrm{k}_2$ at temperature $\mathrm{T}_1$ and $\mathrm{T}_2$
Question 4.
Explain about the factors that affecting the reaction rate.
Answer:
The rate of a reaction is affected by the following factors.
1. Nature and state of the reactant
(a) A chemical reaction involves breaking of certain existing bonds of the reactant and forming new bonds which lead to the product. The net energy involved in this process is dependent on the nature of 

the reactant and hence the rates are different for different reactants.
(b) Gas phase reactions are faster as compared to the reactions involving solid or liquid reactants. For example, reaction of sodium metal with iodine vapours is faster than the reaction between solid sodium and solid iodine.
2. Concentration of the reactant
The rate of the reaction increases with the increase in the concentration of the reactants. According to collision theory, the rate of the reaction depends upon the number of collisions between the reacting molecules. Higher the concentration, greater is the possibility for collision and hence the rate.
3. Effect of surface area of the reactant:
In heterogeneous reactions, the surface areas of the solid reactants plays an important role in deciding the rate. For a given mass of a reactant, when the particle size decreases surface area increases.

Increase in surface area of reactant leads to more collisions per litre per second and hence the rate of reaction is increased. For example, powdered calcium carbonate reacts much faster with dilute $\mathrm{HCI}$ than with the same mass of $\mathrm{CaCOl}$ as marble
4. Temperature:
For many reactions near room temperature, the reaction rate tends to double when the temperature is increased by $10^{\circ} \mathrm{C}$. For eg, Reaction between $\mathrm{H}_2$ and $\mathrm{O}_2$ to form $\mathrm{H}_2 \mathrm{O}$ take place only when an electric spark is passed. So when the temperature increases, the rate of the reaction also increases.
5. Effect of presence of catalyst
(a) A catalyst is substance which alters the rate of a reaction without itself undergoing any permanent chemical change. They may participate in the reaction, but again regenerated and the end of the reaction.
(b) In the presence of a catalyst, the energy of activation is lowered and hence greater number of molecules can cross the energy barrier and change over to products, thereby increasing the rate of the reaction.
Question 5.
The decomposition of $\mathrm{A}$ into product has value of $\mathrm{k}$ 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 $\mathrm{k}$ be $1.5 \times 10^4 \mathrm{~s}^{-1}$ ?
Answer:
$
\mathrm{k}_1=4.5 \times 10^3 \mathrm{~s}^{-1}
$

$
\begin{aligned}
& \mathrm{T}_1=10+273 \mathrm{~K}=283 \mathrm{~K} \\
& \mathrm{k}_2=1.5 \times 10^4 \mathrm{~s}^{-1} \\
& \mathrm{~T}_2=? \\
& \mathrm{E}_{\mathrm{a}}=6 \mathrm{o} \mathrm{kJ} \mathrm{mol}^{-1}
\end{aligned}
$
According to Arrhenius equation
$
\log \frac{k_2}{k_1}=\frac{E_a}{2.303 R}\left[\frac{T_2-T_1}{T_1 T_2}\right]
$
or $\quad \log \frac{1.5 \times 10^4}{4.5 \times 10^3}=\frac{60000 \mathrm{Jmol}^{-1}}{2.303 \times 8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}} \times\left[\frac{\mathrm{T}_2-283}{283 \mathrm{~T}_2}\right]$
$
\begin{aligned}
\log 3.333 & =3133.63\left[\frac{\mathrm{T}_2-283}{283 \mathrm{~T}_2}\right] \\
\frac{0.5228}{3133.63} & =\left[\frac{\mathrm{T}_2-283}{283 \mathrm{~T}_2}\right] \\
0.0472 \mathrm{~T}_2 & =\mathrm{T}_2-283 \\
0.9528 \mathrm{~T}_2 & =283 \\
\mathrm{~T}_2 & =\frac{283}{0.9528}=297 \mathrm{~K}=\left(297-273^{\circ} \mathrm{C}\right)=24^{\circ} \mathrm{C}
\end{aligned}
$

Question 6.
For a decomposition reaction the values of rate constant $\mathrm{k}$ at two different temperatures are given below:
$
\begin{aligned}
& \mathrm{k}_1=2.15 \times 10 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1} \text { at } 650 \mathrm{~K} \\
& \mathrm{k}_2=2.39 \times 10 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1} \text { at } 700 \mathrm{~K}
\end{aligned}
$
Calculate the value of activation energy for this reaction. $\left(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$
Answer:
Here
$
\begin{aligned}
& \mathrm{k}_1=2.15 \times 10 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1} \text { at } 650 \mathrm{~K} \\
& \mathrm{~T}_1=650 \mathrm{~K} \\
& \mathrm{~T}_2=700 \mathrm{~K} \text { and } \\
& \mathrm{k}_2=2.39 \times 10 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1} \text { at } 700 \mathrm{~K} \\
& \mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}
\end{aligned}
$

Using the formula
$
\begin{aligned}
\log \frac{k_2}{k_1} & =\frac{\mathrm{E}_{\mathrm{a}}}{2.303 \mathrm{R}}\left[\frac{\mathrm{T}_2-\mathrm{T}_1}{\mathrm{~T}_1 \mathrm{~T}_2}\right] \\
\log \frac{2.39 \times 10^{-7}}{2.15 \times 10^{-8}} & =\frac{E_a}{2.303 \times 8.314}\left[\frac{700-650}{650 \times 700}\right] \\
\log 1.111 \times 10 & =\frac{E_a}{19.147} \times \frac{50}{455000} \\
1.0457 & =\frac{E_a}{19.147} \times \frac{1}{9100} \\
\mathrm{E}_{\mathrm{a}} & =182202.812 \mathrm{~J} \text { or } 182.203 \mathrm{~kJ}
\end{aligned}
$
Question 7.
For a certain chemical reaction variation In concentration, In IRI Vs time (s) plot is given below. For this reaction write/draw:
1 . What is the order of the reaction?
2. What is the units of rate constant $(\mathrm{k})$ ?
3. Give the relationship between $\mathrm{k}$ and $\mathrm{t}_{1 / 2}$ (half-life period).
4. What does the slope of above line indicate?
5. Draw the plot of $\log \left[R_0\right] /[R]$ vs time (s)

Answer:
1. First order
2. time $^{-1}\left(\mathrm{~s}^{-1}\right)$
3.
$\mathrm{k}=\frac{0.693}{\frac{t_1}{2}}$
4. Rate constat $(\mathrm{k})$ of reaction

Question 8 .
A substance reacts according to the first order rate law and the specific reaction rate for the reaction $j$ s $1 \times 10^{-2} \mathrm{~s}^{-1}$. If the initial concentration is $1.0 \mathrm{M}$.
1. What is the initial rate?
2. What $;$ s the reaction rate after 1 minute?
Answer:
1. Initial rate of a first order reaction
$
\begin{aligned}
& =\mathrm{k} \mathrm{C} \\
& =1 \times 10^{-2} \times 1.0 \\
& =1 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}
\end{aligned}
$
2. Concentration after 60 seconds is calculated by applying the first order kinetic equation,
or
$
\begin{aligned}
\mathrm{k} & =\frac{2.303}{60} \log _{10} \frac{1}{1-x} \\
1 \times 10^{-2} & =\frac{2.303}{60}[-\log (1-x)] \\
\frac{60 \times 10^{-2}}{2.303} & =-\log (1-x)=0.2605 \\
\log (1-x) & =-0.2605=1.73395 \\
(1-x) & =\operatorname{antilog} \text { of }(1.7395) \\
& =0.5489 \mathrm{~mol} \mathrm{~L}^{-1}
\end{aligned}
$
Rate of reaction after 1 minute
$
\begin{aligned}
& =\mathrm{k} \times \mathrm{C} \\
& =1 \times 10^{-2} \times 0.5489 \\
& 5.489 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}
\end{aligned}
$
Question 9.
A first order reaction is $50 \%$ completed in 30 minutes at $27^{\circ} \mathrm{C}$ and in 10 minutes at $47^{\circ} \mathrm{C}$. Calculate the reaction rate constant at $27^{\circ} \mathrm{C}$ and the energy of activation of the reaction in $\mathrm{kJ} \mathrm{mol}^{-1}$
Answer:
For a first order reaction

At $27^{\circ} \mathrm{C}$,
$
\mathrm{k}_{27^{\circ} \mathrm{C}}=\frac{0.693}{30}=0.0231 \mathrm{~min}^{-1}
$
At $47^{\circ} \mathrm{C}$
$
\mathrm{k}_{47^{\circ} \mathrm{C}}=\frac{0.693}{10}=0.0693 \mathrm{~min}^{-1}
$
Now applying the following equation:
$\log _{10} \frac{0.0231}{0.0693}=\frac{-E_a}{2303 \times 8.314} \cdot\left(\frac{320-300}{320 \times 300}\right)$
or
or $\quad-\log _{10} 0.3333=\frac{E_a}{19.1471} \times \frac{20}{96000}$ or
$
\begin{aligned}
\mathrm{E}_{\mathrm{a}} & =\frac{19.1471 \times 96000}{20} \times \log 0.3333 \\
& =-91906 \times(-0.4772) \\
& =43857 \mathrm{~J} \mathrm{~mol}^{-1} \\
& =43.857 \mathrm{~kJ} \mathrm{~mol}^{-1}
\end{aligned}
$
Question 10.
In Arrhenius equation for a certain reaction, the values of $\mathrm{A}$ and $\mathrm{E}$ (activation energy) are $4 \times 10^{13}$ $\mathrm{sec}^{-1}$ and $98.6 \mathrm{KJ} \mathrm{mol}^{-1}$ respectively. If the reaction is of first order, at what temperature will its half life period be 10 minutes?
Answer:
According to the Arrhenius equation.
$
\mathrm{k}=\mathrm{A} e^{-\frac{E_a}{R T}}
$
or
$
\log _e k=\log _e \mathrm{~A}-\frac{\mathrm{E}_{\mathrm{a}}}{\mathrm{RT}}
$
or $2.303 \log _{10} \mathrm{k}=2.303 \log _{10} \mathrm{~A}-\frac{E_a}{R T}$
For a first order reaction
$
\mathrm{t}_{1 / 2}=\frac{0.693}{k} \frac{0.693}{600}
$

So,
$
\begin{aligned}
& \mathrm{k}=\frac{0.693}{600} \mathrm{sec}^{-1}\left(\mathrm{t}_{1 / 2}=10 \mathrm{~min}=600 \mathrm{sec}\right) \\
& =1.1 \times 10^{-3} \mathrm{sec}^{-1}
\end{aligned}
$
$
\begin{aligned}
& \text { Hence, } \log \left(1.1 \times 10^{-3}\right) \\
& =\log \left(4 \times 10^{13}\right)-\frac{98.6 \times 10^3}{2.303 \times 8.314 \times \mathrm{T}} \\
& \mathrm{T}=310.95 \mathrm{~K} \\
&
\end{aligned}
$
Common Errors:
1. Order and molecularity may get confused
2. Unit of first order Rate constant and zero order may get con fused.
3. $\mathrm{t}_{1 / 2}$ - Half liefe period may be difficult to remember
Rectifications:
1. Order and molecularity are same for the single step process. But for reactions of more than one step, they may be different.
2. First order $\mathrm{sec}^{-1}$, Zero order $-\mathrm{mol}$ litre $^{-1} \mathrm{sec}^{-1}$
3. $\mathrm{t}_{1 / 2}=0.693 / \mathrm{k}_1$ for first order reaction.