Consider the following two parallel irreversible first order reactions at temperature T

Q. Consider the following two parallel irreversible first order reactions at temperature T,

where 𝑘₁and 𝑘₂ are the rate constants and their values are 5 × 10^–2 and 15 × 10^–2 min^–1, respectively, at temperature T. If the initial concentration of the reactant ‘P’ is 4 mol L^–1, then the concentration of product ‘R’ after 10 min of reaction is __________mol L^–1. (Round off to two decimal places)

(Assume only P is present at the beginning of the reaction.)

Ans: 2.50 – 2.65

Solution:

First Order Reaction is a chemical reaction in which the rate of the reaction is directly proportional to the concentration of one reactant.

R → P, ln [A] = -k t + ln [A0]

Calculation:- 

[R]t = k2 / k1 + k2  [P]o (1 – e-^1(k1+k2)t) ⇒

[R]t =  15 x 10-2 min-1 / (5+15) x 10-2 min-1  [4 mol L-1] (1 – e^{-1(5+15)x 10-2 x10}) ⇒

[R]t = 3 (1 – e^{-20 x 1/100 x 10)} ⇒ 

[R]t = 2.59 mol L-1