Nitric oxide NO reacts with dioxygen to form nitrogen dioxide.

The mechanistic process is:

Step 1: NO + NO $⇌$ N₂O₂ (k₁ and k_-1)
Step 2: N₂O₂ + O₂ → 2 NO₂ (k₂)

1) Write a chemical equation for this reaction
2) Write the rate law for the formation of nitrogen dioxide using the mechanistic proposal assuming the first step is a fast equilibrium
3) Write the rate law for the formation of nitrogen dioxide without assumptions about fast or slow steps

Be sure to eliminate intermediates from the rate expression

Question

Nitric oxide NO reacts with dioxygen to form nitrogen dioxide.

The mechanistic process is:

Step 1: NO + NO

⇌

N₂O₂ (k₁ and k_-1)

Step 2: N₂O₂ + O₂ → 2 NO₂ (k₂)

1) Write a chemical equation for this reaction

2) Write the rate law for the formation of nitrogen dioxide using the mechanistic proposal assuming the first step is a fast equilibrium

3) Write the rate law for the formation of nitrogen dioxide without assumptions about fast or slow steps

Be sure to eliminate intermediates from the rate expression

| General Chemistry 2

Accepted Answer

1) 2 NO + O₂ → 2 NO₂

2) Formation of nitrogen: -

\frac{∆ [{NO}_{2}]}{∆ t}

rate law: -

\frac{1}{2} \frac{∆ [{NO}_{2}]}{∆ t}

= k₂[N₂O₂][O₂]

N₂O₂ is not a reactant or a product: it should be eliminated from the rate law.

Step 1 is a fast equilibrium: k₁[NO]² = k_-1 [N₂O₂]

⇒ [N₂O₂] =

\frac{k_{1}}{k_{- 1}}

[NO]²

-

\frac{1}{2} \frac{∆ [{NO}_{2}]}{∆ t}

= k₂[N₂O₂][O₂]

⇒ -

\frac{∆ [{NO}_{2}]}{∆ t}

= 2 k₂[N₂O₂][O₂]

⇒ -

\frac{∆ [{NO}_{2}]}{∆ t}

= 2

\frac{k_{2} k_{1}}{k_{- 1}}

[NO]²[O₂]

The rate law for the formation of nitrogen dioxide is 2

\frac{k_{2} k_{1}}{k_{- 1}}

[NO]²[O₂]

3) N₂O₂ is an intermediate:

k₁[NO]² – k_-1[N₂O₂] – k₂ [N₂O₂][O₂] = 0

⇒ [N₂O₂] (k_-1 + k₂[O₂]) = k₁[NO]²

⇒ [N₂O₂] =

\frac{k_{1} {[NO]}^{2}}{k_{- 1} + k_{2} [O_{2}]}

-

\frac{∆ [{NO}_{2}]}{∆ t}

= 2 k₂[N₂O₂][O₂]

⇒ -

\frac{∆ [{NO}_{2}]}{∆ t}

= 2

\frac{k_{2} k_{1} {[NO]}^{2} [O_{2}]}{k_{- 1} + k_{2} [O_{2}]}

The rate law for the formation of nitrogen dioxide is 2

Final - Question 4 | General Chemistry 2