PARALLEL REACTION: ILLUSTRATION: GENERAL TYPE (4):

Consider a parallel reaction follow first order chemical kinetics

Let t=0 concentration of (A) is [A]₀ and after time (t) concentration of (A) and (B)  are [A]_t and [B]_t respectively .

Concentration of [B] and [C] after time t:

Percentage Yield of Product:

ILLUSTRATIVE EXAMPLE (1): An organic compound A decomposes following two parallel first order mechanisms:

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

SOLUTION:

ILLUSTRATIVE EXAMPLE (2): An organic compound A decomposes by following two parallel first order mechanisms:

Select the correct statement(s)

(A) If three moles of A are completely decomposed then 2 moles of B and 1 mole of C will be

formed.

(B) If three moles of A are completely decomposed then 1 moles of B and 2 mole of C will be

formed.

(C) half life for the decomposition of A is 20 min

(D) half life for the decomposition of B is 0.33 min

SOLUTION: (BC)

Generalisation of parallel reaction:

PARALLEL REACTION: ILLUSTRATION TYPE (3):

Consider a parallel reaction follow first order chemical kinetics

Let t=0 concentration of (A) is [A]₀ and after time (t) concentration of (A) and (B)  are [A]_t and [B]_t respectively .

Percentage Yield of Product:

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PARALLEL REACTION: ILLUSTRATION TYPE (2):

Let t=0 concentration of (A) is [A]₀  and after time concentration of (A) and (B)  are [A]_t and [B]_t respectively .

[B]_t and [C]_t - Concentration of [B] and [C] after time t:

Concentration of (A) after time t is:

Similarly concentration of (C) after time t is:

Percentage Yield of Product:

Time of completion and half life of reactant:

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PARALLEL PATH OR CONCURRENT ELEMENTARY REACTIONS

The chemical reaction in which a substance reacts or decomposed in more than one way are called parallel or side reaction.

Some examples of parallel reactions:

PARALLEL REACTION: ILLUSTRATION TYPE (1):

Let a chemical reaction in which reactant (A) give two products (B) and (C) and both the reactions are first order reactions. Initially at t=0, pure (A) was present with concentration [A]0 and after time t concentration of (A) is [A]_t and concentration of (B) is [B]_t and concentration of (C) becomes [C]_t

[A]t -Concentration of [A] after time t:

[B]t -Concentration of [B] after time t:

[C]t -Concentration of [C] after time t:

Graphical representation of variation of conc of [A], [B], [C] with time: If K₁>>> K₂ then [B] is the main product and [C] is the side product

Ratio of concentration of (A) and (C) After time t is:

Percentage Yield of Product:

Time of completion and half life of reactant:

Question for Illustration (1):  Cu⁶⁴ (Half life=22.8 hours) decay by beta emission (38%), beta+ emission (19%) and electron capture (43%). write the decay product and calculate Half lives for each of the decay process. [IIT 2002]

Solution:

(1):

 (2)  Above are parallel reactions occurring from Cu⁶⁴   

T₁ T₂ and T₃ are the corresponding partial half lives and also K= K₁ + K₂ + K₃ (for parallel reaction) 

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CONSECUTIVE OR SEQUENTIAL REACTION:

A chemical reaction in which the product form is further decomposed into another product such kind reaction of reaction is known as sequential reaction.

If rate constant of reaction is K₁ and K₂ then the rate of reaction is for the reaction

For the determination of concentration of A after time t, integrating equation (1)

For the determination of concentration of B after time t,

Net rate of formation of [B]

Multiply e^K₂^t to both side and integrating

For the determination of concentration of [C] after time t,

Since by law of mass balance [A]₀=[A]_t +[B]_t+[C]_t

Graphical representation of concentration of A B and C after time t that is [A]_t , [B]_t and [C]_t respectively.

Case (1):  K₁ >>>K₂

Concentration of [B]_t: when K1>>>K2 in this case we can observed that reaction first (A to B) occurs first and gives nearly to completion before reaction (B to C) take place. Thus nearly all the (A) is converted to the intermediate (B) before any appreciable conversion of (B to C), thus

Concentration of [C]_t:

Graphical representation:

In general concentration of [A] decreases exponentially, and the concentration of [B] Initially increases up to a maximum and then decrease therefore and concentration of [C] increases steadily until it  reaches its final value [A]₀, when all A has changed into [C]

Case (2): K₂ >>>K₁

Concentration of [B]_t:

Since K₂>>>K₁ then second term in parenthesis rapidly approaches zero while the first term is still near unity consequently concentration of [B] approaches to K₁/K₂ [A] and decay more slowly according to 

Since k₁/K₂ is very small, the maximum concentration of [B] is much less than [A]₀

Concentration of [C]_t:

Graphical representation:

Calculation of Maximum concentration of [B] and Maximum time:

Examples of consecutive reactions:

Illustrative Examples: