Understanding the Ammonia Synthesis Reaction

The question asks about the volume relationship when nitrogen gas reacts with hydrogen gas to form ammonia gas. This reaction is a classic example of chemical synthesis, specifically the Haber process, which is used industrially to produce ammonia.

The chemical reaction between nitrogen and hydrogen to form ammonia is represented by the following balanced equation:

$ \text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} \rightarrow 2\text{NH}_3\text{(g)} $

This equation tells us the stoichiometric ratio of the reactants and product. For gaseous reactants and products at constant temperature and pressure, the coefficients in the balanced equation also represent the relative volumes involved in the reaction. This principle is known as Gay-Lussac's Law of Gaseous Volumes.

Applying Gay-Lussac's Law to Gas Volumes

According to the balanced chemical equation:

• One molecule of nitrogen ($\text{N}_2$) reacts with three molecules of hydrogen ($\text{H}_2$).
• This produces two molecules of ammonia ($\text{NH}_3$).

Based on Gay-Lussac's Law, the ratio of the volumes of reacting gases and products (at the same temperature and pressure) is equal to the ratio of their coefficients in the balanced equation.

Therefore, the volume relationship is:

• 1 volume of $\text{N}_2$ reacts with
• 3 volumes of $\text{H}_2$ to produce
• 2 volumes of $\text{NH}_3$.

Determining the Volume of Ammonia Produced

The question specifically states that one volume of nitrogen reacts with three volumes of hydrogen.

Given:

• Volume of Nitrogen ($\text{N}_2$) = 1 volume
• Volume of Hydrogen ($\text{H}_2$) = 3 volumes

From the balanced equation and Gay-Lussac's Law, this is exactly the stoichiometric ratio required for the reaction to go to completion with both reactants being consumed (assuming ideal conditions).

According to the stoichiometry:

$ 1 \text{ volume } \text{N}_2 + 3 \text{ volumes } \text{H}_2 \rightarrow 2 \text{ volumes } \text{NH}_3 $

Thus, when one volume of nitrogen combines with three volumes of hydrogen, two volumes of ammonia are produced.

Revision Table: Ammonia Synthesis Volumes

Additional Information: The Haber Process

The synthesis of ammonia from nitrogen and hydrogen is known as the Haber process. While the volume relationships discussed here are based on the ideal gas law and stoichiometry at constant temperature and pressure, the actual industrial Haber process is carried out at high temperatures (around 400-450 °C) and very high pressures (150-250 atmospheres) in the presence of an iron catalyst. High pressure favors the side with fewer moles of gas (the product side, ammonia), helping to increase the yield. The volume relationships derived from the stoichiometry apply to gases at the same temperature and pressure conditions.

This question demonstrates a fundamental application of stoichiometry and Gay-Lussac's Law to reactions involving gases.