Ch.14 - Chemical Kinetics

Problem 5

Chapter 14, Problem 5

The following diagrams represent mixtures of NO(g) and O21g2. These two substances react as follows: 2 NO1g2 + O21g2¡2 NO21g2 It has been determined experimentally that the rate is second order in NO and first order in O2. Based on this fact, which of the following mixtures will have the fastest initial rate? [Section 14.3]

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Identify the reactants and their respective orders in the rate law. Here, NO is second order and O2 is first order.

Count the number of NO (blue spheres) and O2 (orange spheres) molecules in each diagram.

For Diagram I: Count the number of NO and O2 molecules.

For Diagram II: Count the number of NO and O2 molecules.

For Diagram III: Count the number of NO and O2 molecules.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is determined experimentally and indicates how the rate depends on the concentration of each reactant raised to a power, which corresponds to its order in the reaction. For the given reaction, the rate law is rate = k[NO]^2[O2]^1, showing that the reaction is second order in NO and first order in O2.

Reaction Order

Reaction order refers to the exponent of a reactant's concentration in the rate law, indicating how the rate of reaction changes with varying concentrations. A second-order reaction in a reactant means that doubling its concentration will quadruple the reaction rate, while a first-order reaction means that doubling the concentration will double the rate. Understanding the order helps predict how different mixtures will affect the initial reaction rate.

Initial Rate of Reaction

The initial rate of reaction is the speed at which reactants are converted to products at the very beginning of the reaction, typically measured right after the reactants are mixed. It is influenced by the concentrations of the reactants and their respective orders in the rate law. To determine which mixture has the fastest initial rate, one must calculate the rate using the concentrations of NO and O2 in each mixture according to the established rate law.

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Related Practice

Textbook Question

Consider the following graph of the concentration of a substance X over time. Is each of the following statements true or false? (d) As time progresses, the curve will eventually turn downward toward the x-axis. [Section 14.2]

You study the rate of a reaction, measuring both the concentration of the reactant and the concentration of the product as a function of time, and obtain the following results:

Which chemical equation is consistent with these data: (i) A → B, (ii) B → A, (iii) A → 2 B, (iv) B → 2 A?

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Textbook Question

Suppose that for the reaction K + L → M, you monitor the production of M over time, and then plot the following graph from your data:

(b) Is the reaction completed at t = 15 min? [Section 14.2]

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Textbook Question

Given the following diagrams at t = 0 min and t = 30 min

After four half-life periods for a first-order reaction, what fraction of reactant remains? [Section 14.4]

Which of the following linear plots do you expect for a reaction A¡products if the kinetics are (a) zero order, [Section 14.4]

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Open Question

Hydrogen sulfide (H2S) is a common and troublesome pollutant in industrial wastewaters. One way to remove H2S is to treat the water with chlorine, in which case the following reaction occurs: H2S(aq) + Cl2(aq) → S(s) + 2 H+(aq) + 2 Cl-(aq). The rate of this reaction is first order in each reactant. The rate constant for the disappearance of H2S at 28°C is 3.5 * 10^-2 M^-1 s^-1. If at a given time the concentration of H2S is 2.0 * 10^-4 M and that of Cl2 is 0.025 M, what is the rate of formation of Cl-?