Ch.14 - Chemical Kinetics

Problem 107d

Chapter 14, Problem 107d

The following mechanism has been proposed for the reaction of NO with H2 to form N2O and H2O: NO1g2 + NO1g2¡N2O21g2 N2O21g2 + H21g2¡N2O1g2 + H2O1g2 (d) The observed rate law is rate = k3NO423H24. If the proposed mechanism is correct, what can we conclude about the relative speeds of the first and second reactions?

Verified step by step guidance

Identify the overall reaction from the given mechanism: 2NO(g) + H2(g) -> N2O(g) + H2O(g).

Examine the proposed mechanism: Step 1: 2NO(g) -> N2O2(g), Step 2: N2O2(g) + H2(g) -> N2O(g) + H2O(g).

Analyze the rate law: rate = k[NO]^2[H2]. This suggests that the rate-determining step involves two NO molecules and one H2 molecule.

Compare the rate law with the mechanism: The rate law matches the stoichiometry of the first step, indicating that the first step is the slow, rate-determining step.

Conclude that the first reaction (formation of N2O2) is slower than the second reaction (formation of N2O and H2O), as the rate law is determined by the first step.

Verified Solution

Video duration:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

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

Reaction Mechanism

A reaction mechanism is a step-by-step description of the pathway through which reactants are converted into products. It outlines individual elementary steps, each with its own rate, and helps in understanding how the overall reaction occurs. In this case, the proposed mechanism involves two steps leading to the formation of N2O and H2O from NO and H2.

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 can provide insights into the mechanism of the reaction. The given rate law, rate = k[NO]^4[H2]^2, indicates that the rate depends on the concentrations of NO and H2, suggesting that the first step is likely the rate-determining step.

Rate-Determining Step

The rate-determining step is the slowest step in a reaction mechanism that controls the overall rate of the reaction. It is crucial for understanding the kinetics of the reaction. In this scenario, if the observed rate law corresponds to the concentrations of reactants in the first step, it implies that this step is slower than the second step, thus determining the overall reaction rate.

Recommended video:

Guided course

01:15

Rate Law Determination

Related Practice

Open Question

The first-order rate constant for the reaction of a particular organic compound with water varies with temperature as follows: Temperature (K) Rate Constant (s⁻¹) 300 3.2 × 10⁻¹¹, 320 1.0 × 10⁻⁹, 340 3.0 × 10⁻⁸, 355 2.4 × 10⁻⁷. From these data, calculate the activation energy in units of kJ/mol.

Textbook Question

At 28 C, raw milk sours in 4.0 h but takes 48 h to sour in a refrigerator at 5 C. Estimate the activation energy in kJ>mol for the reaction that leads to the souring of milk.

2177

views

Open Question

The following is a quote from an article in the August 18, 1998, issue of The New York Times about the breakdown of cellulose and starch: “A drop of 18 degrees Fahrenheit [from 77 _x001E_F to 59 _x001E_F] lowers the reaction rate six times; a 36-degree drop [from 77 _x001E_F to 41 _x001E_F] produces a fortyfold decrease in the rate.” (b) Assuming the value of Ea calculated from the 36 _x001E_ drop and that the rate of breakdown is first order with a half-life at 25 _x001E_C of 2.7 yr, calculate the half-life for breakdown at a temperature of -15 _x001E_C.

Textbook Question

Ozone in the upper atmosphere can be destroyed by the following two-step mechanism: Cl1g2 + O31g2¡ClO1g2 + O21g2 ClO1g2 + O1g2¡Cl1g2 + O21g2 (b) What is the catalyst in the reaction?

621

views

Textbook Question

The gas-phase decomposition of ozone is thought to occur by the following two-step mechanism.

Step 1: O₃(g) ⇌ O₂(g) + O(g) (fast)

Step 2: O(g) + O₃(g) → 2 O₂ (slow)

(b) Derive the rate law that is consistent with this mechanism. (Hint: The product appears in the rate law.)

866

views

Textbook Question

The gas-phase decomposition of ozone is thought to occur by the following two-step mechanism.

Step 1: O₃(g) ⇌ O₂(g) + O(g) (fast)

Step 2: O(g) + O₃(g) → 2 O₂ (slow)

(d) If instead the reaction occurred in a single step, would the rate law change? If so, what would it be?

1054

views