For a first order process A$\to$B, rate constant ${\mathrm{k}}_1=0.693{\min }^{-1}\mathrm{\&}$ another first order process $\mathrm{C}\to \mathrm{D},{\mathrm{K}}_2=\mathrm{x} {\min }^{-1} .\text{ If }99.99\mathrm{\%}\text{ of }\mathrm{C}\to \mathrm{D}$ requires time same as 50% of reaction A$\to$B, value of x ?(in min^-1)

Time required for 50% completion for reaction 1 is:
${\mathrm{t}}_{1/2}=\frac{0.693}{\mathrm{K}}$

Given k=0.639 min⁻¹

So ${\mathrm{t}}_{1/2}=\frac{0.693}{0.639 } =1 {\min }^{-1}$

2. For reaction 2, it takes 1 min to get 99.99% of reaction to be completed. Thus, it takes 0.5 min to get 50% reaction. Thus,

${\mathrm{t}}_{1/2}=\frac{0.693}{{\mathrm{K}}_2}$
${\mathrm{K}}_2=\frac{0.693}{{\mathrm{t}}_{1/2}}$
${\mathrm{K}}_2=\frac{0.693}{0.5}$

​K₂​=1.386 min⁻¹