Parallel Reactions & Quantum Yield | Physical Chemistry PDF Download

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.

The rate law for the reactant and products are :

            = –k_B[A] – k_c[A] = –(k_B + k_C)[A]                         …(1)

= k_B[A]                                …(2)

  = k_C[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^{-(k_B + k_C )t}                         .......(4)

Integration of equation (2), we get

                   …(5)
Similarly

                     …(6)
i.e. the ratio of concentration of product is

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.

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

The quantum yield of product [C] is

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

Sol.

                  …(1)
                   …(2)

then

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

Sol.

  …(1)

…(2)

…(3)

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