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At 300 K, the half-life of a sample of a gaseous compound initially at 1 atm is 100 seconds. When the initial pressure at the same temperature is 0.5 atm, the half-life is 50 seconds.

What is the order of the reaction, \( x \)?

What is the value of \( x \)?

Answer :

Final answer:

Based on the information provided, the reaction is second-order because the half-life changes in direct proportion to the change in initial pressure.

Explanation:

To determine the order of the reaction based on the given information, we'll analyze the relationship between the initial pressure of the gaseous compound and its half-life. The half-life of a reaction is the time required for the concentration or pressure of the reactant to reduce to half its initial value.

For a first-order reaction, the half-life is independent of the initial concentration or pressure. This means that if the reaction was first-order, changing the initial pressure would not affect the half-life.

However, for second-order reactions, the half-life is inversely proportional to the initial concentration (or pressure in the case of gases).

In the student's scenario, when the initial pressure is halved from 1 atm to 0.5 atm, the half-life also halves from 100 sec to 50 sec.

This suggests that the half-life is directly proportional to the initial pressure, which is characteristic of a second-order reaction. Hence, the value of x, representing the order of the reaction, is 2.

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