Question

If $50\%$ of the reactant that follows first order kinetics is converted into product(s) in $25min$ , how much of it would react in $100min$?

• A. 93.75%
• B. 87.5%
• C. 75%
• D. 100%

Answer 1

The correct option is A 93.75%

For any reaction, time taken for $50\%$ of a reactant to convert into product(s) is called the half life $\left(t_{\frac{1}{2}}\right)$
For a first order reaction:
$t_{\frac{1}{2}}=\frac{\ln 2}{k}=25mink=\frac{\ln 2}{25}mi{n}^{-1}$
$k=\text{Rate constant}$
Also,
For a first order reaction:
$A\to \text{Products}$

$\left[A\right]=\left[A_0\right]e^{-kt}...\left(i\right)$

Here,
$\left[A\right]=\text{Concentration of A at time t}$
$\left[A_0\right]=\text{Concentration of A initially}$

Putting $t=100min\&k=\frac{\ln 2}{25}in\left(i\right)$
$\left[A\right]=\left[A_0\right]e^{-\frac{\ln 2}{25}\times 100}$
$\left[A\right]=\left[A_0\right]e^{-\ln 2^4}$
$\left[A\right]=\frac{1}{16}\times \left[A_0\right]$
$\%\text{reacted}=\frac{\left[A_0\right]-\left[A\right]}{\left[A_0\right]}\times 100\%=\frac{\left[A_0\right]-\frac{\left[A_0\right]}{16}}{\left[A_0\right]}\times 100\%\%\text{reacted}=93.75\%$