Question

a two-step reaction mechanism is proposed for a gas-phase reaction, as represented above. which of the following correctly identifies both the chemical equation for step 1 and the rate law for the overall reaction? a the chemical equation for step 1 is 2 no₂(g) → no(g) + no₃(g), and the rate law is rate = no₂². b the chemical equation for step 1 is no₂(g) + co(g) → no(g) + co₂(g), and the rate law is rate = no₂co. c the chemical equation for step 1 is no₃(g) + 2 co(g) → no(g) + 2 co₂(g), and the rate law is rate = no₂co. d the chemical equation for step 1 is no₃(g) + no₂(g) + 2 co(g) → no(g) + no₂(g) + 2 co₂(g), and the rate law is rate = no₃no₂co².

Explanation:

Step1: Analyze Step 1 Reaction

In a two - step reaction mechanism, step 1 (usually the slow step, rate - determining) and step 2. For option A, the reaction \(2NO_2(g)
ightarrow NO(g)+NO_3(g)\) is a possible elementary step. The rate law for an elementary step is determined by the stoichiometry of the reactants. For a reaction \(aA + bB
ightarrow\) products, the rate law is \(rate = k[A]^a[B]^b\). Here, for \(2NO_2(g)
ightarrow NO(g)+NO_3(g)\), the rate law should be \(rate=k[NO_2]^2\) (assuming \(k = 1\) for the given options).

Step2: Evaluate Other Options

• Option B: The reaction \(NO_2(g)+CO(g)

ightarrow NO(g)+CO_2(g)\) is not a valid step 1 for a two - step mechanism (since the overall reaction and the mechanism logic don't support this as step 1, and also the rate law for a two - step mechanism with this as step 1 is incorrect as step 1 is usually the slow step and the given reaction is not the correct elementary step for the start of the mechanism).

• Option C: The reaction \(NO_3(g)+2CO(g)

ightarrow NO(g)+2CO_2(g)\) has \(NO_3\) as a reactant, but \(NO_3\) is an intermediate (should be produced in step 1, not a reactant in step 1), so this can't be step 1.

• Option D: The reaction has \(NO_2\) and \(NO_3\) as reactants, but \(NO_3\) is an intermediate, and the rate law is too complex and incorrect for a two - step mechanism's step 1.

Answer:

A. The chemical equation for step 1 is \(2NO_2(g)
ightarrow NO(g)+NO_3(g)\), and the rate law is \(rate = [NO_2]^2\).