Question

Half life for a first order reaction is 6.93 hour. What is the time required for 80% completion of the reaction?

• A. 12 hours
• B. 18 hours
• C. 6 hours
• D. 16 hours

Hint:

For a quick mental check: 50% completion takes 1 half-life (6.93 hours). 75% completion takes 2 half-lives (13.86 hours). Since 80% completion requires slightly more than 2 half-lives, the answer must be just above 13.86 hours. This easily rules out 6, 12, and 18 hours, leaving 16 hours as the only logical option!

Answer 1

The Correct Option is D

Step 1: Get the rate constant.
For a first order reaction $k = \dfrac{0.693}{t_{1/2}} = \dfrac{0.693}{6.93} = 0.1$ per hour.

Step 2: Set up the time formula.
For 80 percent done, 20 percent is left. Use \[ t = \frac{2.303}{k}\log\frac{100}{20} \]

Step 3: Compute.
\[ t = \frac{2.303}{0.1}\log 5 = 23.03 \times 0.699 \approx 16\ \text{hours} \]
\[ \boxed{16\ \text{hours},\ \text{option 4}} \]