The following mechanism has been proposed for the reaction of NO with H 2 to form N 2 O and H 2 O: NO(g) + NO(g) → N 2 O 2 (g) N 2 O 2 (g) + H 2 (g) → N 2 O(g) + H 2 O(g) (d) The observed rate law is rate = k[NO] 2 [H 2 ]. If the proposed mechanism is correct, what can we conclude about the relative speeds of the first and second reactions?

Hello everyone today. We are being told that there is a reaction between nitric oxide and carbon monoxide. That takes place in two steps. The first step involves two nitric oxide molecules coming together. And the second step involves one nitrous oxide and one carbon monoxide molecule coming together. And so the first thing I wanna do is you want to write the rate laws for each step. So for step one the rate law for this reaction would just simply be that the rate is equal to some constant K. That's times are multiplied by nitric oxide, N. 02. And since there's two of them coming together, we square it for our second step. So step to the first step one the rate would be equal to K. Or some constant times a three molecule times a carbon monoxide molecule. And so the rate law. The second step involves this N. 03 and this C. O molecule. And if it were the rate determining step, then C. O. Or carbon monoxide would be the term in the actual rate law which we saw from the question stem that the rate is equal to K. Times nitric oxide squared. And so since there actually is no C. O. Or carbon monoxide in the rate law, the first step step, one must be the rate law. So the first step must be the slow step. While the second step must be the fast step overall, I hope this helped. And until next time

Ch.14 - Chemical Kinetics

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Brown 14th Edition

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:
NO(g) + NO(g) → N₂O₂(g)
N₂O₂(g) + H₂(g) → N₂O(g) + H₂O(g)
(d) The observed rate law is rate = k[NO]²[H₂]. 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.

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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.

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Related Practice

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.

Textbook Question

The following mechanism has been proposed for the reaction of NO with H₂ to form N₂O and H₂O:

NO(g) + NO(g) → N₂O₂(g)

N₂O₂(g) + H₂(g) → N₂O(g) + H₂O(g)

(a) Show that the elementary reactions of the proposed mechanism add to provide a balanced equation for the reaction.

Textbook Question

Ozone in the upper atmosphere can be destroyed by the following two-step mechanism:

Cl(g) + O₃(g) → ClO(g) + O₂(g)

ClO(g) + O(g) → Cl(g) + O₂(g)

(a) What is the overall equation for this process?

Textbook Question

Ozone in the upper atmosphere can be destroyed by the following two-step mechanism:

Cl(g) + O₃(g) → ClO(g) + O₂(g)

ClO(g) + O(g) → Cl(g) + O₂(g)

(b) What is the catalyst in the reaction?

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)

(a) Write the balanced equation for the overall reaction.