Answer :
The order of the reaction can be deduced by analyzing the given data on how half-life changes with varying initial pressures; the reaction appears to be second-order because the half-life is dependent on the initial pressure, reducing as the pressure increases.
To determine the order of the reaction based on the given data showing how the half-life (time for half change) varies with different initial pressures, we can analyze the relationship between the pressure and the time it takes for the reaction to reach half completion. For a first-order reaction, the half-life is independent of concentration, while for a second-order reaction, the half-life is inversely proportional to the initial concentration (or pressure for gases if volume is constant).
Looking at the provided pressure and time data:
- p(kPa): 26.6, t(min): 150
- p(kPa): 40, t(min): 99.8
- p(kPa): 53.3, t(min): 75.3
We can see that an increase in pressure leads to a decrease in the half-life. This suggests that the reaction is most likely of second-order, since for a first-order reaction, a change in initial pressure would not affect the half-life. To confirm this, one would perform calculations to show that the half-life is inversely proportional to the initial pressure, which aligns with the characteristics of a second-order reaction.
