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: Using the rate law:
$k = \frac{0.693}{16}$ min$^{-1}$. Then $\ln\frac{[A]_0}{[A]} = k t = 0.693\times\frac{32}{16} = 1.386$.
\[ \frac{[A]}{[A]_0} = e^{-1.386} = 0.25 \]
So $1 - 0.25 = 0.75 = \frac{3}{4}$ has reacted.

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