Question

The reaction \(2\mathrm{X} \rightarrow \mathrm{B}\) is a zeroth order reaction. If the initial concentration of X is 0.2 M, the half-life is 6 h. When the initial concentration of X is 0.5 M, the time required to reach its final concentration of 0.2 M will be:

• A. 18.0 h
• B. 9.0 h
• C. 7.2 h
• D. 12.0 h

Hint:

For a zero-order reaction \(t_{1/2} = [A]_0/2k\); get k from the first data set, then use \(t = ([A]_0-[A])/k\).

Answer 1

The Correct Option is A

For a zero-order reaction, \([A]_0 - [A] = kt\) and \(t_{1/2} = \frac{[A]_0}{2k}\).
From the first data set: \(6 = \frac{0.2}{2k}\), so \(k = \frac{0.2}{12} = \frac{1}{60}\ \mathrm{M\ h^{-1}}\).
For the second case: \(t = \frac{0.5-0.2}{k} = 0.3 \times 60 = 18\ \mathrm{h}\).
Answer: (1) 18.0 h