For an elementary reaction, X ( g ) ⟶ Y ( g ) + Z ( g ) , the t 1 / 2 is 10 minutes. In what period…

${\mathrm{X}}_{\left(\mathrm{g}\right)}⟶{\mathrm{Y}}_{\left(\mathrm{g}\right)}+{\mathrm{Z}}_{\left(\mathrm{g}\right)}$

Let the concentration at$\mathrm{t}=0 = \mathrm{x}$

The concentration after time $\mathrm{t}=\mathrm{t} = \mathrm{a}-\mathrm{x}=10\%\mathrm{x} = 0.1\mathrm{x}$

$\mathrm{K}=\frac{0.693}{{\mathrm{t}}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}=\frac{0.693}{10}=0.0693$

According to the integrated rate law,

$\mathrm{t}=\frac{1}{\mathrm{K}}\ln \frac{\mathrm{a}}{\mathrm{a}-\mathrm{x}}=\frac{1}{0.0693}\ln \frac{1}{0.1}=\frac{1}{0.0693}\ln 10=\frac{2.303}{0.0693}=33.2$

Hence, the time is equal to the $33.2 \mathrm{minutes}$