Question

A first order reaction is 75% completed in 1000 s at 300 K. What is its half-life period at 300 K?

• A. 500 s
• B. 250 s
• C. 750 s
• D. 230 s
• E. 800 s

Hint:

Memorize these relationships for first-order reactions:
\(t_{75\%} = 2 \times t_{1/2}\)
\(t_{87.5\%} = 3 \times t_{1/2}\)
\(t_{99.9\%} \approx 10 \times t_{1/2}\)

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In first-order kinetics, the time taken for a certain percentage of completion is related to the half-life (\(t_{1/2}\)).

Step 3: Detailed Explanation:
For a first-order reaction:
After 1st half-life: 50% remains.
After 2nd half-life: 25% remains (meaning 75% is completed).
So, the time required for 75% completion (\(t_{75\%}\)) is exactly twice the half-life (\(t_{1/2}\)).
\[ t_{75\%} = 2 \times t_{1/2} \]
Given \(t_{75\%} = 1000 \text{ s}\):
\[ 1000 = 2 \times t_{1/2} \]
\[ t_{1/2} = \frac{1000}{2} = 500 \text{ s} \]

Step 4: Final Answer:
The half-life period is 500 s.