Question

The time elapsed between $33\%$ and $67\%$ completion of a first order reaction is $30$ minutes. What is the time needed for $25\%$ completion?

• A. $15.5min$
• B. $12.5min$
• C. $18.5min$
• D. $16.5min$

Answer 1

The correct option is B $12.5min$

As per the question,

$30=-\frac{2.303}{k}log\frac{\left[100\right]}{[100-33]}$ + $\frac{2.303}{k}log\frac{\left[100\right]}{[100-67]}$

$\Rightarrow k=2.36\times {10}^{-2}{min}^{-1}$

$t=\frac{2.303}{2.36\times {10}^{-2}}log\frac{\left[100\right]}{\left[75\right]}$

$t=12.5min$