Long free-response question

Rate law and mechanism for NO and H₂

Unit 5
10 points
About 23 minutes

You can use a calculator on this question, just like on exam day.

A multipart question, often built around a lab setup or a data table, that mixes several topics. You calculate, explain and justify your answers across many lettered parts. On the exam: 3 questions (Questions 1–3), part of the 1-hour-45-minute free-response section; calculator allowed.

The question and its sources

At high temperature, nitrogen monoxide reacts with hydrogen according to the equation 2 NO(g) + 2 H₂(g) → N₂(g) + 2 H₂O(g). The overall reaction is exothermic. A student measures initial rates at a constant temperature.

Table 1. Initial-rate data

Experiment	Initial [NO] (M)	Initial [H₂] (M)	Initial rate of formation of N₂ (M/s)
1	0.0100	0.0100	2.5 × 10⁻⁴
2	0.0200	0.0100	1.0 × 10⁻³
3	0.0100	0.0300	7.5 × 10⁻⁴

Source: Hypothetical data

Proposed mechanism

Step 1: 2 NO(g) ⇌ N₂O₂(g) (fast, reversible)

Step 2: N₂O₂(g) + H₂(g) → N₂O(g) + H₂O(g) (slow)

Step 3: N₂O(g) + H₂(g) → N₂(g) + H₂O(g) (fast)

Source: Hypothetical mechanism for this question

Suggested time: 23 minutes

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Part (a)

1 point

Determine the order of the reaction with respect to NO. Justify your answer using the data in Table 1.

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Part (b)

1 point

Determine the order of the reaction with respect to H₂. Justify your answer using the data in Table 1.

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Part (c)

2 points

Write the rate law for the reaction, and calculate the value of the rate constant, k. Include units with your answer.

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Part (d)

1 point

In experiment 1, what is the initial rate of disappearance of NO? Explain.

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Part (e)

1 point

A classmate claims that the overall reaction occurs in a single elementary step. Explain why the experimental data do not support this claim.

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Part (f)

1 point

Identify all reaction intermediates in the proposed mechanism.

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Part (g)

1 point

Show that the proposed mechanism is consistent with the rate law you wrote in part (c).

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Part (h)

1 point

Describe the reaction energy profile you would draw for the proposed three-step mechanism. Include what is plotted on each axis, the number of peaks, which step has the largest activation energy, and the relative energies of the reactants and the products.

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Part (i)

1 point

The rate of the reaction increases when the temperature is increased. Explain this observation using the collision model.

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