Explore topic-wise InterviewSolutions in .

(a) 2N₂O_5(g) → 4NO_2(g) + O_2(g)

The rate law expression given for the reaction is,

Rate = k x [N₂O₅]

Hence,

The reaction is of first order.

(b) CHCl_3(g) + Cl_2(g) → CCl_4(g) + HCl_(g)

The given rate law expression is, 

R = k [CHCl₃] x [Cl₂]^1/2

Here,

The order of a reaction is one with respect to CHCl_3(g) and half with respect to Cl_2(g).

Therefore,

The overall order of the reaction is 1 + 1/2 = 1.5.

(c) C₂H₅Cl_(g) → C₂H_4(g) + HCl_(g)

The given rate law expression is, 

Rate = k[C₂H₅Cl]

Hence,

The reaction has order equal to one.

(d) 2NO_2(g) + F_2(g) → 2NO₂F_(g)

The given rate law expression for the reaction is,

Rate = k[NO₂] [F₂]

Hence,

The reaction is first order with respect to NO₂ and first order with respect to F₂.

The overall order of the reaction is,

n = \(n_{NO_2}\) + nF₁ = 1 + 1 = 2.

Since the reaction is first order in CHCl₃ and 1/2 order in Cl₂, the rate law for the reaction will be, Rate = k[CHCl₃] × [Cl₂]^1/2

The overall order (n) of the reaction will be, n \(= l + = \frac{1}{2} = \frac{3}{2}.\)

Option : (a) 0

(d) all the above.

Option : (b) integral

For the reaction,

2NO_(g) + O_2(g) → 2NO_2(g)

Molecularity = 3.

(1) The order and molecularity of elementary reaction are same.

(2) Consider second order bimolecular reaction,

2NO_2(g) → 2NO_(g) + O₂.

(3) The rate of the reaction is given by,

Rate = k [NO₂]²

(4) Similarly consider unimolecular first order reaction,

C₂H₅I_(g) → C₂H_4(g) + HI_(g)

Rate = k [C₂H₅I]

Features of rate-determining step : 

• The overall reaction can never occur faster than its rate-determining step. 
• The rate-determining step can occur anywhere in the reaction mechanism and depends on nature of reactants, conditions of the reaction, etc. 
• The rate law of a rate-determining step can directly be obtained from its stoichiometric equation. 
• The rate law of a rate-determining step can directly be obtained from its stoichiometric equation. 

In complex reactions, the slowest step determines the overall rate of the reaction. This step is known as rate determining step.

Molecularity of a reaction is the total number of reactant species that are involved in an elementary step.

(c) (iii) only

Option : (b) is always integral

Zero Order Reaction. 

The reaction in which the rate of reaction is independent of the concentration of the reactants is called zero order reaction.

Rate = k [A]⁰ ⇒ k

Where k is the rate constant. Its unit is mol L^-1s^-1

1. Order of reaction Zero order. Molecularity = 2 

2. Unit of K = mol L^-1sec^-1

(b) bimolecular

Elementary reaction – Each and every single step in a reaction mechanism is called an elementary reaction.

Differences between order and molecularity: Order of a reaction: 

1. It is the sum of the powers of concentration terms involved in the experimentally determined rate law.

2. It can be zero (or) fractional (or) integer.

3. It is assigned for a overall reaction.

Molecularity of a reaction: 

1. It is the total number of reactant species that are involved in an elementary step. 

2. It is always a whole number, cannot be zero or a fractional number. 

3. It is assigned for each elementary step of mechanism.

Zero Order:

1. Its ‘k’ has unit = mol L^-1s^-1 

2. Its t 1/2 is directly proportional to initial conc. of reactant

First order: 

1. Its ‘k’ has unit = time^-1 = sec^-1 

2. Its half life is independent of the initial conc. of the reactant.

(a) 3, 4, 1, 2

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

Consider following examples :

(i) H_2(g) + I_2(g) → 2HI_(g)

R = k[H₂] [I₂]

(ii) 2H₂O_2(g) → 2H₂O_(I) + O_2(g)

Experimentally it is observed that the rate of the reaction is proportional to the concentration of H₂O₂.

∴ R = k [H₂O₂]

(iii) NO_2(g) + CO_(g) → NO_(g) + CO_2(g)

Experimentally it is observed that rate of the reaction does not depend on the concentration of CO but it is proportional to [NO₂]².

∴ R = k[NO₂]²

1. Decompostion of dinitrogen pentoxide

N₂O_2(g) → 2NO_2(g) + \(\frac{1}{2}\)O_2(g)

2. Decomposition of thionylchloride

SO₂Cl_2(g) → SO_2(g) +  Cl_2(g)

3. Decomposition of H₂O₂ in aqueous solution

H₂O_2(aq) → H₂O₍₁₎ + \(\frac{1}{2}\)O_2(g)

4. Isomerisation of cyclopropane to propene

(i) Due to high activation energy

(ii) Rate = k[A₂]⁰[B₂]⁰

(i) First order.

(ii) S^-1/time^-1

Rate constant is the rate of reaction when the concentration of reactant is unity.

(i) The reaction is a zero order reaction. 

(ii) The slope of curve is (-k) i.e., negative of rate constant.

Unit is mol L ^-1 s^-1 .

Factors influencing the rate of reactions are : 

(i) Concentration of reactants 

(ii) Temperature of the reaction

(iii) Pressure 

(iv) Catalyst 

(v) Nature of the reactants 

(vi) Surface area of the reactants.

First order of reaction.

Option : (c) 2^(n-m)

(b) Activation energy

A catalyst provides a new path to the reaction with low activation energy. i.e., it lowers the activation energy.

(b) Both A and R are correct and R is the correct explanation of A

1. t_{1/2 =} 0.693/k

(d) Without knowing the rate constant, t cannot be determined from the given data.

For a first order reaction 

t_1/2 =  \(\frac{0.693}{k}\) t_1/2 does not depend on the initial concentration and it remains constant (whatever may be the initial concentration) 

t_1/2 = 2.5 hrs

t_1/2 = 60 min
For first order reaction,
k = \(\frac { 0.693 }{ t_{ 1/2 } } \)
= \(\frac { 0.693 }{ 60 }\)
k = 0.01155 min^-1 = 1.155 x 10^-2
\(\frac { 1.155 }{ 60 } \times 10^{ -2 }\) s^-1
k = 1.925 x 10^-4 s^-1

According to Arrhenius equation,
k= Ae^-Ea/RT                 …. (1)
According to equation
k= (4.5 x 10¹¹ s^-1)e^{-28000 k/T}           …..(2)
Compare equation (1) and (2)
\(-\frac { Ea }{ RT } =\frac { -28000K }{ T }\)
or      E_a = 28000 K x R
or      E_a = 28000 K x 8.314J K^-1mol^-1
E_a = 232792 J/mol
E_a = 232.79 kJ/mol
The activation energy is 232.79 kJ/mol

According to question, r₁ = k[X]²        …(i)
If concentration is increased to three times, then
r₂ = k [3X]²
r₂ = k 9 X²
r₂ = 9k [X]²         …(ii)
Divide eq (ii) by eq. (i)
\({ r_{ 2 } }{ r_{ 1 } } =\frac { 9k[X]^{ 2 } }{ k[X]^{ 2 } } \)
\(\frac { r_{ 2 } }{ r_{ 1 } } =9 \)
r₂ = 9 x r_ı
i.e., if concentration is increased there times, the rate increases 9 times.

(a) fractional

(c) Assertion is true but reason is false.

For a first reaction, when the concentration of reactant is doubled, then the rate of reaction also doubled. Rate constant is independent of concentration and is a constant at a constant temperature, i.e., it depends on the temperature and hence, it will not be doubled and when the concentration of the reactant is doubled.

(iv) Rate constant increases exponentially with decreasing activation energy and increasing temperature.

Correct answer is

c. E_f > E_r

The enthalpy change is 110 kJ/mol. 

Zero order as the rate of reaction is independent of concentration of reactant.

The activation energy for combustion reactions of fuels in very high at room temperature, therefore, they do not burn by themselves.

e^-Ea/RT corresponds to the fraction of molecules that have kinetic energy greater than E_a .

Option : (d) A = ke^E_a/RT

Option : (b) A/k = e^-E_a/RT

Arrhenius equation is represented as \(k = A \times e^{-E_a/RT}\)

where

k = Rate constant at absolute temperature T

E_a = Energy of activation 

R = Gas constant 

A = Frequency factor or pre-exponential factor.

Arrhenius equation:

k = \(Ae^\frac{-E_a}{Rt}\)

A = Arrhenius factor (frequency factor)

R = Gas constant

k = Rate constant

E_a = Activation energy

T = Absolute temperature (in K)

The rate of a chemical reaction depends on the following factors :

• Nature of the reactants.
• The concentration of the reactants. In case of a gaseous reaction the rate depends on the pressures of the reactants.
• Temperature of the reaction. 
• The presence of a catalyst and its nature.