Question

Nitrogen and hydrogen react in a 1:3 ratio by volume. Assuming nitrogen and hydrogen are diatomic, how many liters of ammonia, \(\mathrm{NH}_{3}\), should be formed from the reaction of \(1 \mathrm{~L}\) of nitrogen, \(\mathrm{N}_{2}\), with \(3 \mathrm{~L}\) of hydrogen, \(\mathrm{H}_{2}\) ?

Short answer

2 liters of ammonia are formed.

Step-by-step solution

Write the balanced chemical equation

The reaction occurs between nitrogen ( \( \mathrm{N}_2 \) ) and hydrogen ( \( \mathrm{H}_2 \) ) to form ammonia ( \( \mathrm{NH}_3 \) ). The balanced chemical equation is: \[ \mathrm{N}_2(g) + 3\mathrm{H}_2(g) \rightarrow 2\mathrm{NH}_3(g) \] This means one mole of nitrogen reacts with three moles of hydrogen to produce two moles of ammonia.

Use the volume ratio for gases

Since gases combine in volumes that are proportional to their mole ratios (under the same conditions of temperature and pressure), we can directly use the equation's coefficients as volume ratios: 1 L of \( \mathrm{N}_2 \) reacts with 3 L of \( \mathrm{H}_2 \) to form 2 L of \( \mathrm{NH}_3 \).

Determine the volume of ammonia produced

Given that you have 1 L of \( \mathrm{N}_2 \) and 3 L of \( \mathrm{H}_2 \), which are exactly in the stoichiometric ratio, all of both reactants will be completely used to produce ammonia. From the balanced equation, 1 L of \( \mathrm{N}_2 \) and 3 L of \( \mathrm{H}_2 \) will produce 2 L of \( \mathrm{NH}_3 \).

Key concepts

Balanced Chemical Equation

A balanced chemical equation is crucial for understanding chemical reactions. It shows the relationship between reactants and products. In our example, nitrogen (\( \mathrm{N}_2 \)) and hydrogen (\( \mathrm{H}_2 \)) react to form ammonia (\( \mathrm{NH}_3 \)). The balanced equation for this reaction is:\[\mathrm{N}_2(g) + 3\mathrm{H}_2(g) \rightarrow 2\mathrm{NH}_3(g)\]This equation tells us that one molecule of nitrogen gas reacts with three molecules of hydrogen gas to create two molecules of ammonia gas. It shows how mass is conserved in the reaction. All atoms present on the reactant side must appear in the same number on the product side. This balance helps predict how much of each substance is involved in the reaction, ensuring proper stoichiometry.

Gas Volume Ratios

Gas volume ratios are pivotal in reactions involving gases. For gases, the ratios of volumes directly relate to the ratios of moles, as long as the temperature and pressure are constant. In our case, the reaction between nitrogen and hydrogen follows this principle.

• 1 volume of nitrogen (\( \mathrm{N}_2 \)) reacts with 3 volumes of hydrogen (\( \mathrm{H}_2 \)).
• This reaction produces 2 volumes of ammonia (\( \mathrm{NH}_3 \)).

This direct correlation between volume and mole ratios simplifies calculations without needing to convert volumes to moles. In our specific example, these volumes align with the coefficients in the chemical equation, allowing us to predict the resulting volume of ammonia.

Diatomic Molecules

Diatomic molecules are substances consisting of two atoms. Important examples include nitrogen (\( \mathrm{N}_2 \)) and hydrogen (\( \mathrm{H}_2 \)). These gases naturally exist as pairs of atoms rather than singles. This molecular structure is significant in understanding reactions and calculating reactant and product quantities.

• Nitrogen and hydrogen do not exist as single atoms in their natural gaseous states.
• They are bound as diatomic molecules, making them stable under normal conditions.

For this reason, when calculating volumes or moles, the diatomic nature must be considered, ensuring accurate stoichiometric calculations. Recognizing this helps in correctly balancing the chemical equations and predicting outcomes in reactions like the formation of ammonia.

Reaction Stoichiometry

Reaction stoichiometry involves calculating the quantities of reactants and products in a chemical reaction. It is based on the balanced chemical equation. For the formation of ammonia, understanding stoichiometry allows us to determine how much ammonia can be formed from given amounts of nitrogen and hydrogen.

• The balanced equation \( \mathrm{N}_2(g) + 3\mathrm{H}_2(g) \rightarrow 2\mathrm{NH}_3(g) \) gives us an exact mole-to-mole relationship.
• For every 1 mole of nitrogen, 3 moles of hydrogen are needed to form 2 moles of ammonia.

Stoichiometry ensures we use reactants efficiently and predict how much product will result. With reaction stoichiometry, we can say precisely that using 1 liter of \( \mathrm{N}_2 \) and 3 liters of \( \mathrm{H}_2 \) should yield 2 liters of \( \mathrm{NH}_3 \), following the volume ratios derived from the stoichiometric coefficients.