Problem 28 - Chemistry: The Central Science

Question

Nitrogen and hydrogen gases react to form ammonia gas as follows: $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ At a certain temperature and pressure, \(1.2 \mathrm{~L}\) of \(\mathrm{N}_{2}\) reacts with \(3.6 \mathrm{~L}_{2}\) of \(\mathrm{H}_{2}\). If all the \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) are consumed, what volume of \(\mathrm{NH}_{3}\), at the same temperature and pressure, wi

Step-by-Step Solution

Answer

The volume of ammonia gas (NH₃) produced from the given volumes of nitrogen (N₂) and hydrogen (H₂) at the same temperature and pressure is \(2.4 L\).

Step 1: Find the stoichiometric ratio of given reactants

According to the balanced chemical equation: $$\mathrm{N}_{2} (g) + 3\mathrm{H}_{2} (g) \longrightarrow 2\mathrm{NH}_{3} (g)$$ The stoichiometric mole ratio for the reaction is: $$\frac{1}{\mathrm{N_2}} = \frac{3}{\mathrm{H_2}} = \frac{2}{\mathrm{NH_3}}$$

Step 2: Determine the given volume ratio of the reactants

The volume ratio of reactants \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) is: $$\frac{\mathrm{N}_{2}}{\mathrm{H}_{2}} = \frac{1.2L}{3.6L} = \frac{1}{3}$$

Step 3: Compare the given volume ratio with the stoichiometric volume ratio

From the balanced chemical equation, the stoichiometric ratio for \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) is: $$\frac{\mathrm{N}_{2}}{\mathrm{H}_{2}} = \frac{1}{3}$$ Since the stoichiometric volume ratio matches the given volume ratio, it shows that both reactants are in the correct proportion and therefore, both are completely consumed.

Step 4: Use the stoichiometric mole ratio of product to find the volume of product

Since we've determined that both reactants are consumed, we can use the stoichiometric mole ratio to find the volume of \(\mathrm{NH}_{3}\) produced. The stoichiometric ratio of \(\mathrm{NH}_{3}\) to \(\mathrm{N}_{2}\) is: $$\frac{2}{1}$$ $$\mathrm{NH}_3 = 2 * 1.2 L = 2.4 L$$

Step 5: Write the final answer

The volume of ammonia gas (NH₃) produced from the given volumes of nitrogen (N₂) and hydrogen (H₂) at the same temperature and pressure is 2.4 L.

Key Concepts

Chemical Equations

Chemical equations are the symbolic representation of chemical reactions. They show the reactants and products involved in a chemical reaction along with their respective quantities. In a balanced chemical equation, the number of atoms for each element is the same on both sides, which reflects the conservation of mass.
In our example, the chemical equation for the reaction between nitrogen (\(\mathrm{N}_{2}\)) and hydrogen (\(\mathrm{H}_{2}\)) to form ammonia (\(\mathrm{NH}_{3}\)) is:

• \(\mathrm{N}_{2}(g) + 3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\)

This balanced equation tells us that one molecule of nitrogen reacts with three molecules of hydrogen to produce two molecules of ammonia. This stoichiometric relationship is critical when calculating the quantities of reactants or products involved in the reaction.

Volume Ratios

When dealing with gases in a chemical reaction, the volume ratios of the gases are equivalent to the mole ratios. This is true under the same conditions of temperature and pressure, according to Avogadro's law.
In the given reaction \(\mathrm{N}_{2} + 3\mathrm{H}_{2} \longrightarrow 2\mathrm{NH}_{3}\), we observe that the volume of nitrogen to hydrogen must be in a ratio of 1:3.

• Given volumes: \(1.2\, \mathrm{L} \) of nitrogen and \(3.6 \, \mathrm{L} \) of hydrogen, thus the ratio is \( \frac{1.2}{3.6} = \frac{1}{3} \)

This matches the stoichiometric ratio from the equation, indicating that both gases are present in the correct amounts to fully react with each other. No excess of either reactant is left over, making the reaction efficient.

Nitrogen and Hydrogen Reaction

The reaction between nitrogen \((\mathrm{N}_{2})\) and hydrogen \((\mathrm{H}_{2})\) is an example of a synthesis reaction, where multiple reactants combine to form a single product. This specific reaction results in the production of ammonia \((\mathrm{NH}_{3})\), which is crucial for various industrial applications, especially in fertilizers.
The balanced chemical equation tells us that:

• One volume of nitrogen reacts with three volumes of hydrogen.
• This forms two volumes of ammonia.

It's noteworthy that before beginning the reaction, ensuring that the reactants are in the correct volume ratio is key to optimizing the amount of ammonia produced. This checks that both reactants are fully consumed in producing the desired product.

Ammonia Production

Ammonia (\(\mathrm{NH}_{3}\)) is widely produced for fertilizers, cleaning products, and other industrial uses. Understanding stoichiometry helps in optimizing the amount of ammonia that can be produced from given reactants.
In the context of our example, at constant temperature and pressure:

• 1.2 L of nitrogen and 3.6 L of hydrogen react completely.
• According to the stoichiometric mole ratio, they produce 2.4 L of ammonia.

This reaction is efficient under the conditions where the combined gases fully convert to ammonia, demonstrating an excellent application of chemical principles to real-world manufacturing and chemical processes. Mastery of these concepts can significantly aid students in understanding and predicting the outcomes of other chemical reactions as well.