121

​Q121. A substance undergoes first order decomposition. This decomposition follows two parallel first order reactions as 
               
                The percentage distribution of B and C are :

         (a) 75 % B and 25% C                                       (b) 80% B and 20% C

         (c) 60% B and 40% C                                        (d) 90% B and 10% C     
               
         (e) 76.83% B and 23.17% C
                                         

Dear Student 

During the parallel reaction when there are too many reactions, then the reaction which is having the high rate constant will be the main reaction and all other will be the side reaction. 
As given in the question the k₁ > k₂ is more and hence the reaction A to B will be the main reaction, while the reaction from A to C will be the side reaction. 

So, The ratio of the percentage distribution is equal to  = 
                                              $$\begin{gathered} \frac{B}{C} = \frac{K_1}{K_2} \\ So, the percentage of the B will be \\ \frac{B}{B+C}\times 100=\frac{K_1}{K_1+K_2}\times 100 \\ = \frac{1.26 \times {10}^{-4}}{1.26\times {10}^{-4}+0.38 \times {10}^{-4}}\times 100 \\ = \frac{1.26}{1.64}\times 100 \\ = 75.4\% \\ So, the percentage of the C will be \\ \frac{{\displaystyle C}}{{\displaystyle B+C}}\times 100=\frac{{\displaystyle K_2}}{{\displaystyle K_1+K_2}}\times 100 \\ = \frac{{\displaystyle 0.38 \times {10}^{-4}}}{{\displaystyle 1.26\times {10}^{-4}+0.38 \times {10}^{-4}}}\times 100 \\ = \frac{{\displaystyle 0.38}}{{\displaystyle 1.64}}\times 100 \\ = 24.6\% \end{gathered}$$

So, the correct option is (1) 

Regards