Question

Half life period of a first order reaction is $10$ min. Starting with initial concentration $12M$, the rate after $20$ min is :

• A. $0.0693M$ ${min}^{-1}$
• B. $0.693\times 2M$ ${min}^{-1}$
• C. $0.0693\times 3M$ ${min}^{-1}$
• D. $0.0693\times 4M$ ${min}^{-1}$

Answer 1

The correct option is C $0.0693\times 3M$ ${min}^{-1}$

For first-order reaction :

$k=\frac{ln2}{10}=0.0693mi{n}^{-1}$

$[A{]}_t=[A{]}_o{e}^{-kt}=12\times e^{-\frac{ln2}{10}\times 20}=3M$

$Rate=k[A{]}_t=0.0693\times 3Mmi{n}^{-1}$

$Rate=K\left[Reactant\right]=0.0693\times 3Mmi{n}^{-1}$