## NCERT Solutions For Class 12 Chemistry Chapter 4 Chemical Kinetics

Topics and Subtopics in **NCERT Solutions for Class 12 Chemistry Chapter 4 Chemical Kinetics****:**

Section Name | Topic Name |

4 | Chemical Kinetics |

4.1 | Rate of a Chemical Reaction |

4.2 | Factors Influencing Rate of a Reaction |

4.3 | Integrated Rate Equations |

4.4 | Pseudo First Order Reaction |

4.5 | Temperature Dependence of the Rate of a Reaction |

4.6 | Collision Theory of Chemical Reactions |

NCERT TEXTBOOK QUESTIONS SOLVED

**4.1.For the reaction R—>P, the concentration of a reactant changes from 0.03 M to 0.02 M in 25 minutes. Calculate the average rate of reaction using units of time both in minutes and seconds.**

** Ans.**

**4.2.In a reaction, 2A —-> Products, the concentration of A decreases from 0.5 mol L ^{-1} to 0.4 molL^{-1} in 10 minutes. Calculate the rate during this interval?**

**Ans.**

**4.3.Fora reaction,A+B —> Product; the rate law is given by, r =****k [ A] ^{1/2} [B]^{2}**

**. What is the order of the reaction?**

**Ans.**Order of reaction. = 1/2+ 2 = 2

^{1/2}or 2.5

**4.4.The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y ?**

**Ans**.The reaction is : X—>Y

According to rate law,

rate = k[X]^{2}

If [X] is increased to 3 times, then the new rate is

rate’ = k[3X]^{2}

rate’ = 9 k [X]^{2} = 9 rate

Thus, rate of reaction becomes 9 times and hence rate of formation of Y increases 9-times.

**4.5. A first order reaction has a rate constant 1.15 x 10 ^{-3} s^{-1}. How long will 5 g of this reactant take to reduce to 3 g?**

**Ans.**

**4.6.Time required to decompose SO _{2}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.**

**Ans.**For 1st order reaction,

**4.7. What will be the effect of temperature on rate constant?**

**Ans.**With the rise in temperature by 10°, the rate constant of a reaction is nearly doubled. The dependence of rate constant on temperature is given the Arrhenius equation, k = A e^{-Ea/RT} where A is the Arrhenius constant and Ea is activation energy of the reaction.

**4.8.The rate of the chemical reaction doubles for and increase of 10 K in absolute temperature from 298 K. Calculate E _{a}.**

**Ans.**

**4.9.The activation energy for the reaction, 2 HI(g) —-> H _{2}+I_{2} (g) is 209.5 k J mol^{-1} at 581 K.Calculate the fraction of molecules of reactants having energy equal to or greater than activation energy?**

**Ans**.Fraction of molecules having energy equal to or greater than activation energy is given by:

NCERT EXERCISES

**4.1 From the rate expression for the following reactions determine their order of reaction and the dimensions of the rate constants:**

** **

**Sol:**

**4.2 For the reaction, 2A + B ————> A _{2 }B, the rate = k [AJ[B]2 with k = 2.0 x 10^{-6} mol^{-2} L^{2} s^{-1}. Calculate the initial rate of the reaction when [A] = 0.1 mol L^{-1}, [B] = 0.2 mol L^{-1}. Calculate the rate of reaction after [A] is reduced to 0.06 mol L^{-1}.**

**Sol.**Initial rate of reaction = k [A] [B]

^{2}

= (20 x 10

^{-6}mol

^{-2}s

^{-1}) (0.1 mol L

^{-1}) (0.2 mol L

^{-1})

^{2}= 8 x 10-9molL

^{-1}s

^{-1}.

When [A] is reduced from 010 mol L

^{-1}to 0.06 molL

^{-1}, i.e., 0.04 mol L

^{-1}of A has reacted, the concentration of B reacted, is = 1/2 x 0.04 mol L

^{-1}= 0.02 mol L

^{-1}

Concentration of B, remained after reaction with A = 0.2 – 0-02=0.18 mol L

^{-1}

Now, rate=(20 x 10

^{-6}mol

^{-2}L

^{2}s

^{-1}) (0.06 mol L

^{-1}) (0.18 molL

^{-1})

^{2}

= 3-89 x 10

^{-9}mol L

^{-1}s

^{-1}

**4.3 The decomposition of NH _{3} on platinum surface is zero order reaction. What are the rates of production of N_{2} and H_{2} if Ar=2.5 x 10^{-4} mol-1 Ls^{-1}.**

**Sol.**

**4.4 The decomposition of dimethyl ether leads to the formation of CH _{4}, H_{2} and CO and die reaction, rate is given by **

**Rate=k [CH**

_{3}OCH_{3}]^{3/2}The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also, be expressed in terms of the partial pressure of dimethyl ether, i.e., Rate= k (PCH_{3}OCH_{3})^{3/2}**If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?**

**Sol.**As the concentration in the rate law equation is given in terms of pressure,

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

**Sol.** Factors affecting the rate 6f chemical reaction are following:

(i) Natpre of reactants

(ii) Concentration of reactants

(iii) Surface area of reactants

(iv) Effect of temperature

(v) Presence of catalyst

(vi) Presence of light

**4.6 A reaction is second order with respect to a reactant How is the rate of reaction affected if the concentration of the reactant is (i) doubled (ii) reduced to** **half?**

**Sol.**

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

**Sol.** The rate constant of a reaction increases with increase of temperature and becomes nearly double for every 10 °C rise of temperature. Quantitatively, this temperature effect on the rate constant is represented as, k = Ae^{-Ea/RT}

where E_{a } is the activation energy of the reaction, and A represents the frequency factor.

**4.8 In a pseudo first order hydrolysis of ester in water, the following results were obtained:**

**t/s 0 30 60 90**

**[Ester] mol L ^{-1} 0-55 0-31 0 17 0 085**

**(i) Calculate the average rate of reaction between the time interval 30 to 60 seconds.**

**(ii) Calculate the pseudo first order rate constant for the hydrolysis of ester.**

**Sol.**

**4.9 A reaction is first order in A and second order in B.**

**(i) Write the differential rate equation.**

**(ii) How is the rate affected on increasing the concentration of B three times?**

**(iii) How is the rate affected when the concentrations of both A and B is doubled?**

**Sol.**

**4.10 In a reaction between A and B, the initial rate of reaction (r _{0 }) was measured for different initial concentrations of A and B as given below:**

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

**Sol.**

**4.11 The following results have been obtained during the kinetic studies of the reaction.**

**2A+B ——–> C + D**

** **

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

**Sol.**

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

** **

**Sol.**

**4.13 Calculate the half-life of a first order reaction from their rate constants given below:**

**(i) 200 s ^{-1} (ii) 2 min^{-1}**

**(iii) 4 years**

^{-1}**Sol.**

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

**Sol.** Radioactive decay follows first order kinetics.

**4.15 The experimental data for decomposition of N _{2}O_{5}**

**Sol.**

**Question 16.**

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

**Solution: **

**Question 17.**

During nuclear explosion, one of the products is ^{90}Sr with 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 ?

**Solution: **

**Question 18.**

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

**Solution: **

**Question 19.**

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

**Solution: **

**Question 20.**

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

Calculate the rate constant

**Solution: **

**Question 21.**

The following data were obtained during the first order thermal decomposition of SO_{2}Cl_{2} at a constant volume.

Calculate the rate of the reaction when total pressure is 0.65 atm.

**Solution: **

**Question 22.**

The rate constant for the decomposition of N_{2}O_{5} at various temperatures is given below :

Draw a graph between In k and 1/7 and calculate the value of A and Ea. Predict the rate constant at 30°C and 50°C.

**Solution:**

The values of rate constants for the decomposition of N_{2}O_{5} at various temperatures are given below :

**Question 23.**

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

**Solution: **

**Question 24.**

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

**Solution: **

**Question 25.**

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

**Solution:**

Sucrose decomposes according to first order rate law, hence

**Question 26.**

The decomposition of a hydrocarbon follows the equation

**Solution: **

**Question 27.**

The rate constant for the first order decomposition of H_{2}O_{2} is given by the following equation:

log k = 14.34 – 1.25 × 104 K/T

Calculate Ea for this reaction and at what temperature will its half-period be 256 minutes?

**Solution: **

**Question 28.**

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

**Solution: **

**Question 29.**

The time required for 10% completion of the first order reaction at 298 K is equal to that required for its 25% completion at 308 K. If the value of A is 4 × 10^{10} s^{-1}, calculated at 318 K and E_{a}.

**Solution: **

**Question 30.**

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

**Solution: **

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