Question

An organic compound undergoes first-order decomposition. The time taken for its decomposition to $1/8$ and $1/10$ of its initial concentration are $t_{1/8}$ and $t_{1/10}$ respectively. What is the value of $\frac{\left[t_{1/8}\right]}{\left[t_{1/10}\right]}\times 10$? $(take{\log }_{10}2=0.3)$

Answer 1

$\frac{t_{1/8}}{t_{1/10}}=\frac{\frac{2.303}{k}\log \frac{1}{1/8}}{\frac{2.303}{k}\log \frac{1}{1/10}}$
$\frac{t_{1/8}}{t_{1/10}}\times 10=\left[\frac{\log 8}{\log 10}\right]\times 10$
$=9$