# An organic compound undergoes first order decomposition. The time taken for its decomposition to $1}{8}$  and  $1}{10}$ of its intial concentration are  $\mathrm{t}1}{8}$ and $\mathrm{t}1}{10}$  respectively. What is the value of $\left[\frac{\mathrm{t}1}{8}}{\mathrm{t}1}{10}}\right]×10$

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### Solution:

$\mathrm{K}=\frac{2.303}{{\mathrm{t}}_{\frac{1}{8}}}\mathrm{log}\frac{\mathrm{a}}{\left(\frac{\mathrm{a}}{8}\right)}=\frac{2.303}{{\mathrm{t}}_{\frac{1}{8}}}\mathrm{log}8$ ---------(1)
$\mathrm{K}=\frac{2.303}{{\mathrm{t}}_{\frac{1}{8}}}\mathrm{log}\frac{\mathrm{a}}{\left(\mathrm{a}/10\right)}=\frac{2.303}{{\mathrm{t}}_{\frac{1}{8}}}\mathrm{log}10$  -----------(2)

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