Question

At elevated temperatures in an automobile engine, \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) can react to yield NO, an important cause of air pollution. (a) Write a balanced equation for the reaction. (b) How many moles of \(\mathrm{N}_{2}\) are needed to react with \(7.50 \mathrm{~mol}\) of \(\mathrm{O}_{2} ?\) (c) How many moles of \(\mathrm{NO}\) can be formed when \(3.81 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) reacts? (d) How many moles of \(\mathrm{O}_{2}\) must react to produce \(0.250 \mathrm{~mol}\) of \(\mathrm{NO} ?\)

Short answer

(a) \(\mathrm{N}_{2} + \mathrm{O}_{2} \rightarrow 2\mathrm{NO}\); (b) 7.50 mol; (c) 7.62 mol; (d) 0.125 mol.

Step-by-step solution

Write the Balanced Equation

The reaction between nitrogen gas \( \mathrm{N}_{2} \) and oxygen gas \( \mathrm{O}_{2} \) to form nitrogen monoxide \( \mathrm{NO} \) can be represented as follows: \[ \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow 2\mathrm{NO}(g) \] This equation is balanced as there are 2 nitrogen atoms and 2 oxygen atoms on both sides of the equation.

Calculate Moles of \( \mathrm{N}_{2} \) Needed for \( \mathrm{O}_{2} \)

From the balanced equation, we have \(1\) mole of \(\mathrm{N}_{2}\) reacting with \(1\) mole of \(\mathrm{O}_{2}\). We have been given \(7.50 \ \mathrm{mol} \) of \(\mathrm{O}_{2}\). Therefore, the moles of \(\mathrm{N}_{2}\) needed is also \(7.50 \ \mathrm{mol}\).

Calculate Moles of \( \mathrm{NO} \) Formed from \( \mathrm{N}_{2} \)

According to the balanced equation, \(1\) mole of \(\mathrm{N}_{2}\) produces \(2\) moles of \(\mathrm{NO}\). Given \(3.81 \ \mathrm{mol} \) of \(\mathrm{N}_{2}\), the moles of \(\mathrm{NO}\) produced will be:\[ 3.81 \ \mathrm{mol} \times 2 = 7.62 \ \mathrm{mol} \]

Calculate Moles of \( \mathrm{O}_{2} \) Needed for \( \mathrm{NO} \)

From the balanced equation, \(1\) mole of \(\mathrm{O}_{2}\) produces \(2\) moles of \(\mathrm{NO}\). Therefore, \(0.250 \ \mathrm{mol} \) of \(\mathrm{NO}\) requires:\[ \frac{0.250 \ \mathrm{mol}}{2} = 0.125 \ \mathrm{mol} \] of \(\mathrm{O}_{2}\).

Key concepts

Balanced Chemical Equation

In chemical reactions, having a balanced equation is crucial. It ensures that the same number of each type of atom appears on both sides of the equation. This is important because matter is neither created nor destroyed in a chemical reaction. For example, in the reaction between nitrogen (\(\mathrm{N}_2\)) and oxygen (\(\mathrm{O}_2\)) to form nitrogen monoxide (\(\mathrm{NO}\)), we have:

• 1 molecule of \(\mathrm{N}_2\) reacts with 1 molecule of \(\mathrm{O}_2\)
• Produces 2 molecules of \(\mathrm{NO}\)

So, the balanced chemical equation becomes:\[\mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow 2\mathrm{NO}(g)\]In this equation, the number of nitrogen and oxygen atoms are equal on both sides. This balance reflects the law of conservation of mass, which is essential in chemical reactions.

Mole Calculations

Moles are a simple way to count atoms, using a number known as Avogadro’s number (\(6.022 \times 10^{23}\)). When dealing with chemical equations, moles help us calculate the actual amounts of substances involved. For instance:

• If we know 7.50 moles of \(\mathrm{O}_2\) is available, we use the equation’s ratio: 1 mole of \(\mathrm{N}_2\) reacts with 1 mole of \(\mathrm{O}_2\).
• Thus, 7.50 moles of \(\mathrm{N}_2\) are needed.

Similarly, understanding the formation of products:

• 1 mole of \(\mathrm{N}_2\) yields 2 moles of \(\mathrm{NO}\), hence 3.81 moles of \(\mathrm{N}_2\) produce:\[3.81 \times 2 = 7.62 \text{ moles of } \mathrm{NO}\]

Mole calculations are fundamental to predict and quantify outcomes of chemical reactions.

Chemical Reactions

Chemical reactions transform reactants into products. In our case, nitrogen (\(\mathrm{N}_2\)) and oxygen (\(\mathrm{O}_2\)) react to form nitrogen monoxide (\(\mathrm{NO}\)). These reactions may appear straightforward but involve breaking and forming of chemical bonds.Key points:

• Reactions are often driven by conditions such as temperature and pressure.
• This specific reaction occurs at high temperatures, like those in car engines.
• Products like \(\mathrm{NO}\) can be pollutants.

Understanding chemical reactions allows scientists to control and utilize them effectively in various fields, from producing materials to minimizing pollutants.

Environmental Chemistry

Environmental chemistry studies how chemical processes impact the environment. In this context, the formation of nitrogen monoxide (\(\mathrm{NO}\)) in car engines is significant.Key aspects include:

• \(\mathrm{NO}\) is a primary pollutant from combustion engines, contributing to smog and acid rain.
• Controlling emissions is crucial for reducing \(\mathrm{NO}_x\) levels in the atmosphere.
• Technologies like catalytic converters are used to transform \(\mathrm{NO}\) into less harmful compounds.

By understanding the chemistry behind these pollutants, strategies can be developed to mitigate their environmental impact.