MCQ
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 $\frac{\left[1_{t / 8}\right]}{\left[ t _{1 / 10}\right]} \times 10 ?\left(\log _{10} 2=0.3\right)$
  • A
    $8$
  • $9$
  • C
    $7$
  • D
    $6$

Answer

Correct option: B.
$9$
b
$Kt _{1 / 8}=\ln \left\{\frac{ C _{ O }}{ C _0 / 8}\right\}=\ln 8 $

$Kt _{1110}=\ln \left\{\frac{ C _0}{ C _{ O } / 10}\right\}=\ln 10$

then $\frac{t_{1 / 8}}{t_{1 / 10}} \times 10=\frac{\ln 8}{\ln 10} \times 10=\frac{\log 2}{\log 10} \times 10=9$

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