Question

A first order reaction is 50% completed in 16 minutes. Find the percentage of reactant reacting in 32 minutes.

• A. 25%
• B. 40%
• C. 50%
• D. 75%

Hint:

After $n$ half-lives, the amount remaining is $A_0 / 2^n$. The amount reacted is $1 - (1/2^n)$.

Answer 1

The Correct Option is D

Step 1: Identify Half-life
50% completion time is the half-life ($t_{1/2} = 16$ min).
Step 2: Amount remaining after n half-lives
32 minutes = 2 half-lives ($n = 32/16 = 2$).
Amount remaining = $(\frac{1}{2})^n = (\frac{1}{2})^2 = \frac{1}{4} = 25%$.
Step 3: Calculate Amount Reacted
$% \text{ Reacted} = 100% - % \text{ Remaining} = 100% - 25% = 75%$.
Step 4: Conclusion
The percentage reacted in 32 minutes is 75%.
Final Answer:(D)