Question

A first order reaction complete \(60\)% in \(20\) minutes. How long will the reaction take to complete \(84\)%?

• A. \(54\) min
• B. \(68\) min
• C. \(40\) min
• D. \(76\) min

Hint:

Find $k$ from the 60% data, then use $t=\frac{2.303}{k}\log\frac{100}{100-x}$.

Answer 1

The Correct Option is C

Step 1: Use the fraction left
After $60\%$ the fraction left is $0.4$. After $84\%$ it is $0.16=(0.4)^2$.

Step 2: Apply first order
For first order, $\ln(a/(a-x))=kt$. Squaring the fraction doubles the log, so the time doubles: $2\times20=40$ min.

Final Answer:
$40$ min, option (C). \[ \boxed{\text{(C)}} \]