Question

An organic compound undergoes decomposition via first order kinetics. The time taken for its decomposition to $\frac{1}{8}$th and $\frac{1}{10}$th of its initial concentration are $\frac{t_1}{8}$ and $\frac{t_1}{10}$ respectively. What is the value of $\frac{\left[\frac{t_1}{8}\right]}{\left[\frac{t_1}{10}\right]}\times 10?({\log }_{10}2=0.3)$

Answer 1

For first oeder reaction:
$kt=ln\frac{\left[A_0\right]}{\left[A_t\right]}$
let assume a reaction which follow first order kinetics
$A⟶P$

$k{t}_{1/8}=ln8$
$k{t}_{1/10}=ln10$
$\frac{t_{1/8}}{t_{1/10}}=\frac{ln8}{ln10}=\frac{log8}{log10}=3log2=0.910\times 0.9=9$