Question

A first order reaction is $20$% complete in $10$ minutes. What is the specific rate constant for the reaction?

• A. $0.0970mi{n}^{-1}$
• B. $0.009mi{n}^{-1}$
• C. $0.0223mi{n}^{-1}$
• D. $2.223mi{n}^{-1}$

Answer 1

The correct option is C $0.0223mi{n}^{-1}$

$a-x=\frac{80}{100}\times a=0.8a,t=10min.$

$k=\frac{2.303}{t}\log \frac{a}{a-x}=\frac{2.303}{10}\log \frac{a}{0.8a}$

$k=0.2303\log \frac{10}{8}=0.2303(1-0.9030)$

$=0.2303\times 0.0970=0.0223min{.}^{-1}$

Hence, the correct answer is option $\text{C}$.