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PARALLEL REACTION
Parallel reaction are those reaction in which the reactant can form one of two or more products 

Consider the following parallel reaction in which reactant A can form two products B & C.

 Parallel Reactions & Quantum Yield | Physical Chemistry

The rate law for the reactant and products are :

 Parallel Reactions & Quantum Yield | Physical Chemistry           = –kB[A] – kc[A] = –(kB + kC)[A]                         …(1)

Parallel Reactions & Quantum Yield | Physical Chemistry= kB[A]                                …(2)

 Parallel Reactions & Quantum Yield | Physical Chemistry = kC[A]                              ....(3)

Integration of equat ion (1) with the init ial condit ion [A]0 ≠ 0 and [B] = 0 = [C] yields

[A] = [A]0 e-(kB + kC )t                         .......(4)

Integration of equation (2), we get

Parallel Reactions & Quantum Yield | Physical ChemistryParallel Reactions & Quantum Yield | Physical Chemistry
Parallel Reactions & Quantum Yield | Physical Chemistry                   …(5)
Similarly

 Parallel Reactions & Quantum Yield | Physical Chemistry                    …(6)
i.e. the ratio of concentration of product is

 Parallel Reactions & Quantum Yield | Physical Chemistry

i.e. the product concentration ratio remains constant with time.
The yield, φ, is defined as the probability that a given product will be formed by decay of the reactant.

 Parallel Reactions & Quantum Yield | Physical Chemistry

The quantum yield of product [B] is φB = yield of [B] =

 Parallel Reactions & Quantum Yield | Physical Chemistry

The quantum yield of product [C] is

 Parallel Reactions & Quantum Yield | Physical Chemistry

Problem.  Find the quantum yield of [B] & [C] in the following reaction

Parallel Reactions & Quantum Yield | Physical Chemistry

Sol.

Parallel Reactions & Quantum Yield | Physical Chemistry                  …(1)
Parallel Reactions & Quantum Yield | Physical Chemistry                   …(2)

then

Parallel Reactions & Quantum Yield | Physical Chemistry
Parallel Reactions & Quantum Yield | Physical Chemistry

Problem.  Find the quantum yield of [B], [C] & [D] in the following reaction.

Parallel Reactions & Quantum Yield | Physical Chemistry

Sol.

Parallel Reactions & Quantum Yield | Physical Chemistry
Parallel Reactions & Quantum Yield | Physical Chemistry  …(1)

Parallel Reactions & Quantum Yield | Physical Chemistry…(2)

Parallel Reactions & Quantum Yield | Physical Chemistry…(3)

The ratio of formation of product [B], [C] & [D] are

 Parallel Reactions & Quantum Yield | Physical Chemistry
Parallel Reactions & Quantum Yield | Physical Chemistry
Parallel Reactions & Quantum Yield | Physical Chemistry
Parallel Reactions & Quantum Yield | Physical Chemistry

The document Parallel Reactions & Quantum Yield | Physical Chemistry is a part of the Chemistry Course Physical Chemistry.
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FAQs on Parallel Reactions & Quantum Yield - Physical Chemistry

1. What are parallel reactions in chemistry?
Ans. Parallel reactions in chemistry refer to two or more chemical reactions that occur simultaneously in the same system. These reactions may have different reaction rates, mechanisms, and products.
2. How do you calculate the quantum yield of a reaction?
Ans. The quantum yield of a reaction can be calculated by comparing the number of photons absorbed to the number of photons emitted. This is expressed as the ratio of the number of molecules undergoing a particular reaction to the number of photons absorbed by the system.
3. What is the significance of quantum yield in photochemistry?
Ans. The quantum yield is an important parameter in photochemistry as it provides information about the efficiency of a photochemical reaction. A high quantum yield indicates that a large fraction of the absorbed photons are utilized in the desired reaction, while a low quantum yield indicates a low efficiency of photon utilization.
4. Can parallel reactions have different quantum yields?
Ans. Yes, parallel reactions can have different quantum yields. This is because the efficiency of photon utilization depends on the specific reaction mechanism and the energy of the absorbed photons, which may differ between parallel reactions.
5. How can quantum yield be used to optimize a chemical reaction?
Ans. Quantum yield can be used to optimize a chemical reaction by providing insight into the efficiency of photon utilization. By understanding which reactions have the highest quantum yield, chemists can design reaction conditions that promote the desired reactions while minimizing unwanted side reactions. This can help to increase the yield and purity of the desired product.
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