Question

For the first order reaction \[ A \rightarrow P \] Based on the given data, find the time \(x\) (in min):

Given:
\(t = 0 \, \text{min} \Rightarrow [A] = 0.625 \, M\)
\(t = x \, \text{min} \Rightarrow [A] = 0.0625 \, M\)
\(t = 20 \, \text{min} \Rightarrow [A] = 0.00625 \, M\)

• A. \(5\)
• B. \(10\)
• C. \(15\)
• D. \(20\)

Answer 1

The Correct Option is B

Concept: For a first-order reaction, concentration decreases exponentially with time. In equal time intervals, the concentration follows a geometric progression. \[ [A]_t = [A]_0 e^{-kt} \] Thus, the ratio of concentrations in equal time intervals remains constant.
Step 1: Compare concentration ratios. \[ \frac{0.0625}{0.625} = 0.1 \] \[ \frac{0.00625}{0.0625} = 0.1 \] Both ratios are the same, so the time intervals are equal.
Step 2: Determine the time intervals. Total time from \(0\) to \(20\) minutes corresponds to two equal intervals. \[ \text{Interval} = \frac{20}{2} = 10 \text{ minutes} \] Therefore, \[ x = 10 \text{ minutes} \]