Question:medium

What is the time required for 75 % completion of a first order reaction if rate constant is \(23.03 \text{minute}^{-1}\) ?

Show Hint

Use t = (2.303/k) log(100/25) and watch that k is per minute while options are in seconds.
Updated On: Oct 1, 2026
  • \(12.00\) s
  • \(3.6\) s
  • \(36\) s
  • \(6.0\) s
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Use the half-life:
For first order, $t_{1/2} = 0.693/k$. Convert $k$ first: $23.03 \text{ min}^{-1} = 23.03/60 = 0.3838 \text{ s}^{-1}$.
$t_{1/2} = 0.693/0.3838 = 1.806$ s.

Step 2: Count half-lives:
75 % completion means two half-lives, because 100 to 50 to 25 percent remains.
$t_{75\%} = 2 \times 1.806 = 3.61$ s.

Step 3: Match:
This agrees with option (B), 3.6 s. One half-life, 1.8 s, would only give 50 % completion and is not offered.

Final Answer:
$t \approx 3.6$ s, option (B). \[ \boxed{3.6 \text{ s (B)}} \]
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