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

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.