Question

At 300 K, the half-life period of a gaseous reaction at an initial pressure of 40 kPa is 350 s. When pressure is 20 kPa, the half-life period is 175 s. What is the order of the reaction?

• A. Three
• B. Two
• C. One
• D. Zero

Hint:

For zero-order reactions, the half-life depends only on the initial concentration (or pressure) and the rate constant. It is independent of the concentration (or pressure) during the reaction.

Answer 1

The Correct Option is D

To determine the order of the reaction, we can use the relationship between the half-life of a reaction and its order. The half-life (t_1/2) of a reaction varies with the initial concentration or pressure of the reactant in a manner that depends on the order of the reaction:

• Zero-order reaction: t_1/2 = [A]₀/2k. The half-life is directly proportional to the initial concentration.
• First-order reaction: t_1/2 = 0.693/k. The half-life is independent of the initial concentration.
• Second-order reaction: t_1/2 = 1/k[A]₀. The half-life is inversely proportional to the initial concentration.

Given that at 300 K, the half-life is 350 s when the pressure is 40 kPa, and the half-life is 175 s when the pressure is 20 kPa, observe the relationship:

For zero-order: t_1/2 = [A]₀/2k. If the initial pressure is halved (from 40 kPa to 20 kPa), the half-life should also halve if the reaction is zero-order, which matches the given data: 350 s to 175 s.

Thus, the reaction is zero-order.

Answer 2

For a zero-order reaction, the half-life is independent of the concentration (or pressure in this case) and is given by the formula: \[ t_{1/2} = \frac{[A]_0}{2k} \] Where: 
- \( t_{1/2} \) is the half-life, 
- \( [A]_0 \) is the initial concentration (or pressure), 
- \( k \) is the rate constant. From the given data: - At \( [A]_0 = 40 \, \text{kPa} \), \( t_{1/2} = 350 \, \text{s} \), - At \( [A]_0 = 20 \, \text{kPa} \), \( t_{1/2} = 175 \, \text{s} \). Since the half-life for a zero-order reaction is independent of the concentration (or pressure), we observe that halving the pressure also halves the half-life. 
This matches the observed behavior, confirming that the reaction is zero-order. 
Thus, the order of the reaction is Zero.