Chemistry Reaction Kinetics MDCAT 2015
PMDC Verified Question 70 of 80
The half-life of N\(_{2}\)O\(_{5}\) at 45°C is 24 minutes. How long will it take for sample of N\(_{2}\)O\(_{5}\) to decay to 25% of its original concentration?
A
24 minutes
B
48 minutes
C
72 minutes
D
120 minutes
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: 48 minutes
Concept:

The half-life (\( t_{1/2} \)) is the time required for a reactant concentration to drop to half (50%) of its initial value. The decay of N\(_{2}\)O\(_{5}\) is a first-order process, meaning its half-life remains constant regardless of concentration.

Solution:

  • Initial concentration is 100%.
  • After one half-life (24 mins), the concentration decays to 50%: \( 100\% \rightarrow 50\% \).
  • After a second half-life (another 24 mins), the remaining 50% decays to 25%: \( 50\% \rightarrow 25\% \).
  • Total time = \( 24 \text{ mins} + 24 \text{ mins} = 48 \text{ minutes} \).


Why other options are incorrect:

24 minutes is only one half-life (decay to 50%). 72 minutes would be three half-lives (decay to 12.5%).

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