Textbook Question
The reaction 2 NO2 → 2 NO + O2 has the rate constant k = 0.63 M-1s-1. (a) Based on the units for k, is the reaction first or second order in NO2?
Ch.14 - Chemical Kinetics
Chapter 14, Problem 96
Consider two reactions. Reaction (1) has a constant halflife, whereas reaction (2) has a half-life that gets longer as the reaction proceeds. What can you conclude about the rate laws of these reactions from these observations?
Verified step by step guidance1
Step 1: Understand the concept of half-life. The half-life of a reaction is the time it takes for the concentration of a reactant to decrease by half. It is a measure of how quickly a reaction proceeds.
Step 2: For reaction (1), the half-life is constant. This means that the time it takes for the reactant to decrease by half is the same no matter how much reactant is left. This is characteristic of a first-order reaction, where the rate of the reaction is directly proportional to the concentration of one reactant.
Step 3: For reaction (2), the half-life gets longer as the reaction proceeds. This means that the time it takes for the reactant to decrease by half increases as the reaction continues. This is characteristic of a zero-order reaction, where the rate of the reaction is independent of the concentration of the reactants.
Step 4: Therefore, from these observations, we can conclude that reaction (1) follows a first-order rate law, while reaction (2) follows a zero-order rate law.
Step 5: Remember that the order of a reaction is determined experimentally and it tells us how the rate of a reaction changes as the concentrations of the reactants change. It is an important concept in chemical kinetics.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Half-life
Half-life is the time required for the concentration of a reactant to decrease to half of its initial value. In first-order reactions, the half-life is constant and independent of the concentration, while in second-order reactions, the half-life increases as the reaction progresses, indicating a dependence on reactant concentration.
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Zero-Order Half-life
Rate Law
The rate law of a reaction expresses the relationship between the rate of the reaction and the concentration of its reactants. It is determined experimentally and can indicate the order of the reaction, which affects how the rate changes as reactants are consumed. A constant half-life suggests a first-order reaction, while a changing half-life indicates a second-order or higher reaction.
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Reaction Order
Reaction order refers to the power to which the concentration of a reactant is raised in the rate law. It provides insight into the mechanism of the reaction. A first-order reaction has a linear relationship between concentration and rate, while a second-order reaction shows a quadratic relationship, leading to a longer half-life as reactants are consumed.
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Related Practice
Textbook Question
The reaction 2 NO2 → 2 NO + O2 has the rate constant k = 0.63 M-1s-1.
(b) If the initial concentration of NO2 is 0.100 M, how would you determine how long it would take for the concentration to decrease to 0.025 M?
Textbook Question
Americium-241 is used in smoke detectors. It has a first-order rate constant for radioactive decay of k = 1.6 * 10-3 yr-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1. (a) What are the half-lives of these two isotopes? (b) Which one decays at a faster rate?