Question

A substance undergoes first order decomposition. The decomposition follows two parallel first order reactions as $K_1=1.26\times {10}^{-4}se{c}^{-1}$ and $K_2=3.8\times {10}^{-5}se{c}^{-1}$.

The percentage distribution of B and C are:

• A. $80$% $B$ and $20$% $C$
• B. $76.83$% $B$ and $23.17$% $C$
• C. $90$% $B$ and $10$% $C$
• D. $60$% $B$ and $40$% $C$

Answer 1

The correct option is B $76.83$% $B$ and $23.17$% $C$

For parallel path reaction,

$K_{average}=K_1+K_2=1.26\times {10}^{-4}+3.8\times {10}^{-5}$

$=1.64\times {10}^{-4}se{c}^{-1}$

Also, Fractional yield of $B=\frac{K_B}{K_{av}}$

$=\frac{1.26\times {10}^{-4}}{1.64\times {10}^{-4}}$

$=0.7683$

Hence, the percentage distribution of B is $76.83$%.

Fraction yield of $C=\frac{K_C}{K_{av}}$

$=\frac{3.8\times {10}^{-5}}{1.64\times {10}^{-4}}$

$=0.2317$

Hence, the percentage distribution of C is $23.17$%.