Doc: Pseudo First order reaction Class 12 Notes | EduRev

Chemistry Class 12

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Pseudo First Order Reaction

The order of a reaction is sometimes altered by conditions. Consider a chemical reaction between two substances when one reactant is present in large excess. During the hydrolysis of 0.01 mol of ethyl acetate with 10 mol of water, amounts of the various constituents at the beginning (= 0) and completion (t) of the reaction are given as under.

Doc: Pseudo First order reaction Class 12 Notes | EduRev

The concentration of water does not get altered much during the course of the reaction. So, in the rate equation Rate = k'[CH3COOC2H5] [H2O] the term [H2O] can be taken as constant. he equation, thus, becomes Rate = k[CH3COOC2H5] where k = k'[H2O] and the reaction behaves as first order reaction. The molecularity of acidic hydrolysis of sucrose and esters is 2, whereas their order is 1. In both the reactions water is in excess so that its concentration remains constant throughout the reaction. The rate of reaction therefore depends only on the concentration of sucrose and ester in two reactions respectively. So the reactions in which the molecularity is 2 or 3 but they conform to the first order kinetics are known as pseudo first order reactions OR pseudo uni-molecular reactions.

C12H22O11 + H2O + H+  → C6H12O6(glucose) + C6H12O6(fructose)

CH3COOC2H5(ester) + H2O + H+  → CH3COOH + C2H5OH

(In both the reactions, H  ion acts as a catalyst)

nth Order kinetics 

A Doc: Pseudo First order reaction Class 12 Notes | EduRev product

Doc: Pseudo First order reaction Class 12 Notes | EduRev

 -Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Half-life (t1/2) : at t = t1/2 , [A]t = Doc: Pseudo First order reaction Class 12 Notes | EduRev

⇒ k = Doc: Pseudo First order reaction Class 12 Notes | EduRev

t 1/2 =Doc: Pseudo First order reaction Class 12 Notes | EduRev ⇒ Doc: Pseudo First order reaction Class 12 Notes | EduRev

Problem : 5

For the non-equilibrium process, A + B → Products, the rate is first order w.r.t A and second order w.r.t. B. If 1.0 mole each of A and B are introduced into a 1 litre vessel and the initial rate were 1.0 x 10-2 mol/litre-sec, calculate the rate when half of the reactants have been used. 

Sol.  Rate = K[A] [B]2

Therefore, 10-2 = K[1] [1]2

or K = 10-2 litre2 mol-2 sec-1

Now ratell = 10-2 x 0.5 x (0.5)2

or New rate = 1.2 x 10-3 mol/L-sec

Analysis of some important first-order reactions  

Decomposition of Hydrogen peroxide (H2O2

H2O2(g) → H2O(g) + 1/2O2(g)

The rate of this first order reaction is measured by titrating a fixed volume of H2O2 (undecomposed) against a standard solution of KMnO4. Here KMnO4 acts as oxidising agent and H2O2 as reducing agent. The volumes of KMnO4 used for H2O2 after regular intervals of time are as follows.

Time instants

t = 0

t1

t2

t3

t4

t5

Vol. of KMnO4

Vo

V1

V2

V3

V4

V5

 

Volume of KMnO4 at t = 0 corresponds to volume of H2O2 initially present.

⇒ A0 ∝ V0

Volume of KMnO4 at time instants t1, t2, t3, .................... corresponds to volume of H2O2 remaining after t1, t2, t3, .................

⇒ A ∝ Vt

Now it being a first order reaction, follows first order kinetics, so

k t = 2.303 log10Doc: Pseudo First order reaction Class 12 Notes | EduRev

Now using the above expression, if we calculate the values of k for different time intervals t1, t2, ........... (for actual numerical data), the values of k should be same if the reaction follows first order kinetics.

Decomposition of ammonium nitrite (NH4NO2) 

and benzene diazonium chloride (C6H5N = NCl) 

NH4NO2(g) → 2 H2O(g) + N2(g)

C6H5 - N = N - Cl(g) → C6H5 - Cl(g) + N2(g)

The rate of both the reaction is studied (measured) in similar manner. The volume of nitrogen (N2) is collected after a regular interval of time as follows 

Time instants

t = 0

ti

t2

t3

t4

t

Vol. of N2

0

V1

V2

V3

V4

V∝

At t = 0, clearly the volume of N2 = 0

Time instant t = ∞ means the end of a reaction i.e., when whole of NH4NO2 or C6H5 - N = N - Cl is decomposed.

⇒ At t = ∞, V∞  corresponds to the initial volume of NH4NO2 or C6H- N = N - Cl

(Note that the ratio of stoichiometric coefficient for both N2 : NH4NO2 or N2 : C6H5N = NCl is 1 : 1)

⇒ A0 ∝ V∞ 

At t = t1, t2, t3................ the volume of N2 corresponds to concentration of product formed i.e., equal to x.

⇒ x ∝ Vt

⇒ A0 - x ∝ V - Vt

kt = 2.303 log10Doc: Pseudo First order reaction Class 12 Notes | EduRev


Hydrolysis of Esters (CH3COOC2H5 )

CH3COOC2H5 (ester) + H2O + HCl(H+ ) → CH3COOH + C2H5OH

The reaction rate is measured by titrating the acid (CH3COOH) produced against a standard alkali solution. Note that when a test sample is prepared from the reacting mixture, there are two acids : one is mineral acid H  (HCl or any other) and second is CH3COOH produced. So volume of alkali used gives titration value for both acids. The data is collected in the following manner.

Time instants

t = 0

t1

t2

t3

t4

t

Vol. of NaOH

Vo

V1

V2

V3

V4

V

At t = 0, V0 is the volume NaOH used to neutralise the mineral acid present (H ) being used as catalyst.

(At t = 0, no CH3COOH is yet produced)

At t = ∞ (i.e., at the end of hydrolysis), V, is the volume of NaOH used to neutralise whole of CH3COOH plus vol. of HCl present At t = ∞, volume of CH3COOH corresponds to volume of ester taken initially

⇒ A0 ∝ V∞ - V0 (as V0 = vol. of HCl)

At t = t1, t2, t3............ V1, V2, V3, ................corresponds to vol. of HCl plus vol. of CH3COOH being produced.

⇒ x ∝ Vt - V0

⇒ A0 - x ∝ (V - V0) - (Vt - V0)

⇒ A0 - x ∝ V∞ - Vt

Doc: Pseudo First order reaction Class 12 Notes | EduRevkt = 2.303 log10Doc: Pseudo First order reaction Class 12 Notes | EduRev

Inversion of Cane Sugar (C12H22O11) 

C12H22O11 + H2O + H+ → C6H12O6(glucose) + C6H12O6 (fructose)

The rate is measured by measuring the change in the angle of rotation (optical activity) by a polarimeter. Sucrose is dextro-rotatory, glucose is dextro-rotatory and fructose is leavo-rotatory. The change produced in rotatory power in time t gives a measure of x, the quantity of sucrose decomposed in that time. The total change in the rotatory power produced at the end of the reaction gives the measure of A0, the initial concentration of sucrose.

If r0, r1 and r∞ represent rotations at the start of reaction, after time t and at the end of reaction respectively,

then

⇒ A0 ∝ r0 - r and x ∝ r0 - rt

Doc: Pseudo First order reaction Class 12 Notes | EduRev

DECOMPOSITION OF AsH3(g) 

In first-order reactions involving gases, sometime measuring the pressure of the reaction mixture is very good method for measuring reaction rates.

For example consider decomposition of arsine gas (AsH3)

AsH3(g) → As(s) + Doc: Pseudo First order reaction Class 12 Notes | EduRev

The rate of reaction is measured as the increase in pressure of the reaction mixture. Note that there is an increase in number of moles of the gaseous products to the right, so as the reaction proceeds, there will be an increase in pressure of contents (P ∝ n).

Let the initial pressure of AsH3(g) is P0, if x is the decrease in pressure of AsH3(g) after time t.

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Arsenic is solid, so P(AS) = 0

After time t, let Pt be the total pressure, then

Pt = P(AsH3) + P(H2) = (P0 - x) + Doc: Pseudo First order reaction Class 12 Notes | EduRev

⇒ Pt = P0 + Doc: Pseudo First order reaction Class 12 Notes | EduRev ⇒ x = 2(Pt - P0)

Now A0 ∝ P0

and A ∝ P0 - x ≡ P0 - 2 (Pt - P0) ≡ 3P0 - 2Pt

kt = 2.303 log10Doc: Pseudo First order reaction Class 12 Notes | EduRev

On similar pattern, please try to write the expression for Ist order rate law for following first-order reactions. (in terms of P0 and Pt)

1. N2O(g) → N2(g) + Doc: Pseudo First order reaction Class 12 Notes | EduRevO2(g)

2. (CH3)3C - O - O - C(CH3)(g) → 2(CH3)2C = O(g) + C2H6(g)

Complex (First order) kinetics

(A) Parallel Kinetics

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Rate of change of A = [rate of change of A]I + [rate of change of A]II

- Doc: Pseudo First order reaction Class 12 Notes | EduRev = K1 [A] + K2 [A], Doc: Pseudo First order reaction Class 12 Notes | EduRev, Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

% of B in the mix of A & B = Doc: Pseudo First order reaction Class 12 Notes | EduRev

% of C in the = Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev


Generalization 

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev,Doc: Pseudo First order reaction Class 12 Notes | EduRev

Problem : 6 

An organic compound A decomposes following two parallel first order mechanisms : 

Doc: Pseudo First order reaction Class 12 Notes | EduRev ; Doc: Pseudo First order reaction Class 12 Notes | EduRev and k1 = 1.3 x 10-5 sec-1


Calculate the concentration ratio of C to A, if an experiment is allowed to start with only A for one hour.

Sol. 

Doc: Pseudo First order reaction Class 12 Notes | EduRev

But k1 = 1.3 x 10-5 sec-1 ; k2 = 9 x 1.3 x 10-5 sec-1 = 117 x 10-5 sec-1

(k1 + k2) = (1.3 x 10-5) + (11.7 x 10-5) sec-1 = 13 x 10-5 sec-1 ....(1)

Also Doc: Pseudo First order reaction Class 12 Notes | EduRev ⇒ [B]t = Doc: Pseudo First order reaction Class 12 Notes | EduRev ...(2)

Doc: Pseudo First order reaction Class 12 Notes | EduRev ; Doc: Pseudo First order reaction Class 12 Notes | EduRev = (k1 + k2)t

Doc: Pseudo First order reaction Class 12 Notes | EduRev [from eq. (2)] ⇒ Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev = 13 x 10-5 x 60x 60 = 0.468 [from eq. (1)]

⇒ 1 + Doc: Pseudo First order reaction Class 12 Notes | EduRevDoc: Pseudo First order reaction Class 12 Notes | EduRev = 1.5968 ; Doc: Pseudo First order reaction Class 12 Notes | EduRev


(2) Series Kinetics 

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRevDoc: Pseudo First order reaction Class 12 Notes | EduRev 

Doc: Pseudo First order reaction Class 12 Notes | EduRev, Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev, Doc: Pseudo First order reaction Class 12 Notes | EduRev

Graph of [A], [B], [C] Vs t: 

Doc: Pseudo First order reaction Class 12 Notes | EduRev 

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Time when [B] is maximum 

[B] = Doc: Pseudo First order reaction Class 12 Notes | EduRev
 

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

t =Doc: Pseudo First order reaction Class 12 Notes | EduRev

Reversible Kinetics 

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

O < t < teq Doc: Pseudo First order reaction Class 12 Notes | EduRev Chemical kinetics, teqDoc: Pseudo First order reaction Class 12 Notes | EduRev t < Doc: Pseudo First order reaction Class 12 Notes | EduRevDoc: Pseudo First order reaction Class 12 Notes | EduRev Chemical Equilibrium 

At equilibrium, rf = rb , k1 [A] equilibrium = k2 [B] equilibrium , Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev - 1, Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev ............ (I)

 Doc: Pseudo First order reaction Class 12 Notes | EduRev = - k1 [A] + k2 [B], Doc: Pseudo First order reaction Class 12 Notes | EduRev = - k1 [A] + k2 [ [A]o - [A] ] = - (k1 + k2) [A] + k2 [A]o

= (k1 + k2) Doc: Pseudo First order reaction Class 12 Notes | EduRev

By substituting the value from equation (I)

Doc: Pseudo First order reaction Class 12 Notes | EduRev ⇒ Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev
 

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Problem : 7  For a reversible first order reaction, 

A Doc: Pseudo First order reaction Class 12 Notes | EduRev B ; Kf = 10-2 sec-1 

and Doc: Pseudo First order reaction Class 12 Notes | EduRev = 4 ; If A0 = 0.01 ML-1 and B0 = 0, what will be concentration of B after 30 sec ?

Sol. 

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev = Doc: Pseudo First order reaction Class 12 Notes | EduRev = Doc: Pseudo First order reaction Class 12 Notes | EduRev

Therefore, Kb = 0.25 x 10-2 and xeq = Doc: Pseudo First order reaction Class 12 Notes | EduRev = 0.008

t = Doc: Pseudo First order reaction Class 12 Notes | EduRev

30 = Doc: Pseudo First order reaction Class 12 Notes | EduRev log Doc: Pseudo First order reaction Class 12 Notes | EduRev

Therefore, Doc: Pseudo First order reaction Class 12 Notes | EduRev

Therefore,  x = 2.50 x 10-3

Doc: Pseudo First order reaction Class 12 Notes | EduRev


(1) Initial Rate Method 

A + B Doc: Pseudo First order reaction Class 12 Notes | EduRev product

rate = k [A] [B]; Order = m + n

 

[A]

[B]

rate

Experiment 1

0.1

0.1

2 x 10-3

Experiment 2

0.1

0.2

4 x 10-3

Experiment 3

0.2

0.1

32 x 10-3

Experiment (1) and Experiment (2) 

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

n = 1 

Experiment (1) and Experiment (3) 

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

m = 4 

Order (m + n) = 4 + 1 = 5 

(2) Half - life method

Doc: Pseudo First order reaction Class 12 Notes | EduRev

t1/2Doc: Pseudo First order reaction Class 12 Notes | EduRev

2 hr 0.2

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

n = 0 

Doc: Pseudo First order reaction Class 12 Notes | EduRev

(3) Integrated Rate law Method 

                     A Doc: Pseudo First order reaction Class 12 Notes | EduRev product

t = 0            1000 M

t = 60 sec    100 M

t = 120 sec  10 M

n = 0 k = Doc: Pseudo First order reaction Class 12 Notes | EduRev = Doc: Pseudo First order reaction Class 12 Notes | EduRev = 15

k = Doc: Pseudo First order reaction Class 12 Notes | EduRev

n = 1

k = Doc: Pseudo First order reaction Class 12 Notes | EduRev

k = Doc: Pseudo First order reaction Class 12 Notes | EduRev

(4) Ostwald Isolation method

rate = k[A]m [B]n [C]o [D]p - - - - - - - -

Experiment 1 : [A] = In small quantity ; [B], [C], [D] - - - - - - - in excess 

The rate equation reduces to

rate = k' [A]mDoc: Pseudo First order reaction Class 12 Notes | EduRev  r1 = k' [A]1m

r2 = k' [A]2m

Doc: Pseudo First order reaction Class 12 Notes | EduRev, log Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Experiment 2: [B] = In small quantity . & [A], [C], [D] - - - - - - Doc: Pseudo First order reaction Class 12 Notes | EduRev in excess.

rate = k' [B]nDoc: Pseudo First order reaction Class 12 Notes | EduRev repeated

Order of reaction = m + n + o + p + - - - - - - - - 


Activation Energy (Ea

A mixture of magnesium and oxygen does not react at room temperature. But if a burning splinter is introduced to the mixture, it burns vigorously. Similarly a mixture of methane and oxygen does not react at room temperature, but if a burning match-stick is put in the mixture, it burns rapidly. Why it happen like this, that some external agents has to be introduced in order to initiate the reaction ?

According to the theory of reaction rates "for a chemical reaction to take place, reactant molecules must make collisions among themselves". Now in actual, only a fraction of collisions are responsible for the formation of products, i.e., not all collisions are effective enough to give products. So the collisions among reactant molecules are divided into two categories :-

Effective collisions and In-effective collisions

Effective collisions are collisions between the molecules which have energies equal to or above a certain minimum value. This minimum energy which must be possessed by the molecules in order to make an effective collision (i.e., to give a molecule of products) is called as threshold energy. So it is the effective collisions which bring about the occurrence of a chemical reaction.

Ineffective collisions are the collisions between the molecules which does not posses the threshold energy. These can not result in a chemical reaction.

Now most of the times, the molecules of reactants do not possess the threshold energy. So in order to make effective collisions (i.e., to bring about the chemical reaction), an additional energy is needed to be absorbed by the reactant molecules. This additional energy which is absorbed by the molecules so that they achieve the threshold energy is called as energy of activation or simply activation energy. It is represented as Ea.

A reaction which needs higher activation energy is slow at a given temperature.
 

Doc: Pseudo First order reaction Class 12 Notes | EduRev

Doc: Pseudo First order reaction Class 12 Notes | EduRev

For example : Doc: Pseudo First order reaction Class 12 Notes | EduRev is faster at ordinary temperature whereas the following reaction :

CO(g) + Doc: Pseudo First order reaction Class 12 Notes | EduRev → CO2(g) is slower at the same temperature as the value of Ea for the second reaction is much higher.


Factors Affecting Rate of Reaction 

(a) Catalyst : The rate of reaction increased by addition of catalyst, because catalyst lowers, the activation energy and increased the rate of reaction. A catalyst is a substance which increases the rate of a reaction without itself undergoing any permanent chemical change. For example, MnO2 catalyses the following reaction so as to increase its rate considerably.

2KClO3 Doc: Pseudo First order reaction Class 12 Notes | EduRev 2 KCl + 3O2

The word catalyst should not be used when the added substance reduces the rate of reaction. The substance is then called inhibitor. The action of the catalyst can be explained by intermediate complex theory. According to this theory, a catalyst participates in a chemical reaction by forming temporary bonds with the reactants resulting in an intermediate complex. This has a transitory existence and decomposes to yield products and the catalyst.

It is believed that the catalyst provides an alternate pathway or reaction mechanism by reducing the activation energy between reactants and products and hence lowering the potential energy barrier as shown in Fig. It is clear from Arrhenius equation that lower the value of activation energy faster will be the rate of a reaction. A small amount of the catalyst can catalyse a large amount of reactants. A catalyst does not alter Gibbs energy, DG of a reaction. It catalyses the spontaneous reactions but does not catalyse non-spontaneous reactions. It is also found that a catalyst does not change the equilibrium constant of a reaction rather, it helps in attaining the equilibrium faster, that is, it catalyses the forward as well as the backward reactions to the same extent so that the equilibrium state remains same but is reached earlier.


(b) Temperature : With increase in temperature the rate of reaction increases. It is generally found for every 10o increase in temperature. The rate constant double.

The ratio of rate constants with 10o difference in their temperature is called temperature coefficient.

Doc: Pseudo First order reaction Class 12 Notes | EduRev= Q = Temperature coefficient of reaction Doc: Pseudo First order reaction Class 12 Notes | EduRev


(c) Concentration :

Rate = A e-Ea/RT [A]m [B]n - - - - - - - - - 

With increase in concentration of reactants the rate of the reaction increases because number of, collision (effective collisions) increases.

(d)  Nature of Reactants :

Ionic Reactants : 

Generally ionic reactions in aq. media are fast than the reaction involving covalent reactants.

As covalent reactants involving breaking of bond then formation of bond where as ionic reaction involve in single step.

(e)  Surface Area : Increase in surface area increases the number of collisions and hence rate increases

(f) Radiation : Some reactions exposes to sunlight also increases the rate of reaction.

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