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Chapter 14: Problem 112

If the plot of the reactant concentration versus time is nonlinear, but the concentration drops by \(50 \%\) every 10 seconds, then the order of the reaction is (a) zero order; (b) first order; (c) second order; (d) third order.

Short Answer

Expert verified
The order of reaction is first (option b).

Step by step solution

01

Understand What the Problem is Asking

The problem specifies that the plot of reactant concentration versus time is nonlinear, and the concentration drops by \(50 \%\) every 10 seconds. So, it can be deduced that this problem involves half-lives.
02

Identify What a Half-Life is in Regards to Kinetics

A half-life refers to the amount of time required for the concentration of a reactant to decrease by 50%. The key point here is that for a first-order reaction, the half-life is independent of the initial concentration. This means that it takes the same amount of time for the concentration to decrease by \(50 \%\) regardless of its initial concentration.
03

Compare with Given Information

Given that the concentration of the reactant drops by \(50 \%\) every 10 seconds, this behavior is a unique characteristic of a first-order reaction. Therefore, the reaction order is first.
04

Verify with Kinetics Theory

In kinetics, zero order means that the rate of reaction is independent of the concentration of reactants, which is not applicable in this case. Second order would mean that the rate doubles for every halving of concentration, and that does not apply either. Third order is when the rate changes based on changes to the concentration to the third power, which also does not apply here. Hence, the first order reaction is confirmed as it aligns with the given condition.

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Most popular questions from this chapter

If even a tiny spark is introduced into a mixture of \(\mathrm{H}_{2}(\mathrm{g})\) and \(\mathrm{O}_{2}(\mathrm{g}),\) a highly exothermic explosive reaction occurs. Without the spark, the mixture remains unreacted indefinitely. (a) Explain this difference in behavior. (b) Why is the nature of the reaction independent of the size of the spark?

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