Question

The time for 50% completion of a zero-order reaction is 30 min. Time for 80% completion of this reaction is ......... min.

Hint:

For zero-order reactions, the time for a certain percentage completion can be calculated using the integrated rate equation.

Answer 1

Correct Answer: 48

Zero-order reaction

For a zero-order reaction:
\[[A] = [A]_0 - kt\]

Fraction completed = \(\dfrac{[A]_0 - [A]}{[A]_0}\).

Given:

50% completion time \(t_{50} = 30\ \text{min}\).

So at 50% completion:
\[[A] = \frac{1}{2}[A]_0\]
\[\frac{1}{2}[A]0 = [A]0 - k t{50}\]
\[k t{50} = \frac{1}{2}[A]_0\]

Thus,
\[k = \frac{[A]0}{2 t{50}} = \frac{[A]_0}{60}\]

For 80% completion

80% completion means:
\[[A] = 0.2[A]_0\]

Use zero-order equation:
\[0.2[A]0 = [A]0 - k t{80}\]
\[k t{80} = 0.8[A]_0\]

Substitute \(k = \dfrac{[A]_0}{60}\):
\[\frac{[A]0}{60} t{80} = 0.8[A]_0\]

Cancel \([A]0\):
\[\frac{t{80}}{60} = 0.8\]
\[t_{80} = 48\ \text{min}\]

\[\boxed{t_{80} = 48\ \text{min}}\]