Question

99% of a first order reaction was completed in 32 minutes. When will 99.9% of the reaction complete?

• A. 48 minute
• B. 49 minute
• C. 46 minute
• D. 50 minute

Hint:

For first-order reactions: \[ t_{90%} : t_{99%} : t_{99.9%} = 1 : 2 : 3 \] Use this direct ratio method to solve questions quickly.

Answer 1

The Correct Option is A

Concept: For first-order reactions: \[ t = \frac{2.303}{k}\log\frac{a}{a-x} \] Special results: \[ t_{90%} = \frac{2.303}{k} \] \[ t_{99%} = \frac{4.606}{k} \] \[ t_{99.9%} = \frac{6.909}{k} \] Hence: \[ t_{99.9%} = \frac{3}{2}t_{99%} \]

Step 1: Write given information Given: \[ t_{99%} = 32 \text{ minutes} \] We use relation: \[ \frac{t_{99.9%}}{t_{99%}} = \frac{3}{2} \]

Step 2: Calculate \(t_{99.9%}\) \[ t_{99.9%} = \frac{3}{2}\times 32 \] \[ = 48 \text{ minutes} \] Final Answer: \[ \boxed{48 \text{ minutes}} \]