High School

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The time for half-change for a gaseous reaction was measured for various initial pressures, and the following data were obtained:

| Pressure (p, kPa) | Time (t, min) |
|-------------------|---------------|
| 26.6 | 150 |
| 40.0 | 99.8 |
| 53.3 | 75.3 |

Find out the order of the reaction.

Answer :

Based on the data provided, which shows the half-life decreasing as initial pressure increases, the order of the gaseous reaction appears to be first-order. This is further supported by an example provided by the student.

To determine the order of a gaseous reaction based on the given data, we evaluate how the half-life (time for half change) is affected by initial pressure. For first-order reactions, the half-life is independent of the initial concentration (or pressure for gases), whereas for second-order reactions, the half-life is inversely proportional to the initial concentration. In this case, the student has gathered data showing that as the initial pressure increases, the time for half change decreases. This suggests that the reaction is not zero-order because time decreases instead of staying constant, and it's not likely to be second-order because the time for half change would increase with increasing pressure (which is not happening here). The student also provides an example stating, "The reaction is first order. k = 1.0 imes 10^7 L mol^-1 min^-1", supporting the idea that the reaction could be first-order where the rate constant k is directly proportional to the reaction progress over time.

A detailed analysis, ideally using rate laws, should be conducted to confirm the reaction order quantitatively. However, the data pattern hints at a first-order reaction.

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