Question

A first order reaction takes \(16\) minutes for it's \(50\%\) completion. What fraction that would react in \(32\) minutes from the beginning?

• A. \(1/2\)
• B. \(1/4\)
• C. \(1/8\)
• D. \(3/4\)

Hint:

32 minutes is two half-lives, so one quarter remains.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
For a first order reaction, the half life is constant. After each half life, half of what is left is used up.

Step 2: Calculate:
Given \(t_{1/2} = 16\) min. In \(32\) min, number of half lives \(= 32/16 = 2\).
Remaining fraction \(= \left(\frac{1}{2}\right)^2 = \frac{1}{4}\).
Fraction reacted \(= 1 - \frac{1}{4} = \frac{3}{4}\).

Step 3: Other options:
\(1/2\) is the fraction reacted after one half life. \(1/4\) is the fraction remaining, not reacted. \(1/8\) is what remains after three half lives.

Final Answer:
The fraction reacted is \(3/4\), option (D). \[ \boxed{\frac{3}{4}} \]