Question

In a first order reaction, the initial concentrated of the reactant was $M/10.$ After $8$ minutes $20$ seconds the concentrated becomes $M/100.$. What is the rate constant?

• A. $5\times {10}^{-3}se{c}^{-1}$
• B. $2.303\times {10}^{-5}se{c}^{-1}$
• C. $2.303\times {10}^{-4}se{c}^{-1}$
• D. $4.606\times {10}^{-3}se{c}^{-1}$

Answer 1

The correct option is D $4.606\times {10}^{-3}se{c}^{-1}$

$K=\frac{2.303}{t}log\left[\frac{a_0}{a}\right]$

$K=\frac{2.303}{500}log\frac{\frac{1}{10}}{\frac{1}{100}}$

$=\frac{2.303}{500}log10=4.606\times {10}^{-3}se{c}^{-1}$