Question

For the first order reaction $A\to 2B,1$ mole of reactant $A$ gives $0.2$ moles of $B$ after $100$ minutes. The half life of the reaction is ...... min.
(Round off to the nearest integer).
[Use : $\ln 2=0.69,\ln 10=2.3$ Properties of logarithms : $\ln x^y=y\ln x;.\ln \left(\frac{x}{y}\right)=\ln x-\ln y$ ]
(Round off to the nearest integer)

Answer 1

Answer: 300

Now, $t=\frac{t_{1/2}}{\ln 2}\times \frac{\left[A_0\right]}{\left[A_t\right]}$
$100=\frac{t_{1/2}}{\ln 2}\times \ln \frac{1}{0.9}$
$\Rightarrow t_{1/2}=690\min .$
( taking $\ln 3=1.11$ )
Ans. 600 to $700$