Question

Ammonia is a principal nitrogen fertilizer. It is prepared by the reaction between hydrogen and nitrogen: $$ 3 \mathrm{H}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ In a particular reaction, \(6.0 \mathrm{~mol}\) of \(\mathrm{NH}_{3}\) were produced. How many moles of \(\mathrm{H}_{2}\) and how many moles of \(\mathrm{N}_{2}\) were consumed to produce this amount of \(\mathrm{NH}_{3}\) ?

Short answer

9.0 moles of \(\text{H}_2\) and 3.0 moles of \(\text{N}_2\) were consumed.

Step-by-step solution

Understand the Reaction

The balanced chemical equation for the formation of ammonia (\(\text{NH}_3\)) from hydrogen (\(\text{H}_2\)) and nitrogen (\(\text{N}_2\)) is given by:\[3 \mathrm{H}_2(g) + \mathrm{N}_2(g) \rightarrow 2 \mathrm{NH}_3(g)\]This means 3 moles of \(\text{H}_2\) react with 1 mole of \(\text{N}_2\) to produce 2 moles of \(\text{NH}_3\).

Set Up the Mole Ratio

From the balanced equation, the molar ratio between \(\text{H}_2\) and \(\text{NH}_3\) is 3:2, and between \(\text{N}_2\) and \(\text{NH}_3\) is 1:2.

Calculate Moles of H2 Consumed

Since the ratio of \(\text{H}_2\) to \(\text{NH}_3\) is 3:2, you can set up the proportion:\[ \frac{3 \, \text{mol} \; \text{H}_2}{2 \, \text{mol} \; \text{NH}_3} = \frac{x \, \text{mol} \; \text{H}_2}{6.0 \, \text{mol} \; \text{NH}_3} \]Solving for \(x\), \(3/2 = x/6.0\) gives:\[x = \frac{3}{2} \times 6.0 = 9.0 \, \text{mol} \; \text{H}_2\]

Calculate Moles of N2 Consumed

Since the ratio of \(\text{N}_2\) to \(\text{NH}_3\) is 1:2, you use:\[ \frac{1 \, \text{mol} \; \text{N}_2}{2 \, \text{mol} \; \text{NH}_3} = \frac{y \, \text{mol} \; \text{N}_2}{6.0 \, \text{mol} \; \text{NH}_3} \]Solving for \(y\), \(1/2 = y/6.0\) gives:\[y = \frac{1}{2} \times 6.0 = 3.0 \, \text{mol} \; \text{N}_2\]

Key concepts

Mole Ratio

In the study of chemical reactions, understanding the concept of mole ratio is essential. Mole ratio is derived from the coefficients of a balanced chemical equation. It represents the proportions of reactants and products involved in a chemical reaction. For example, in the reaction:

• 3 moles of hydrogen (\[\text{H}_2\]) react with 1 mole of nitrogen (\[\text{N}_2\]) to produce 2 moles of ammonia (\[\text{NH}_3\]).

This means for every 2 units of ammonia formed, 3 units of hydrogen and 1 unit of nitrogen are needed. Mole ratios help in solving problems related to the amounts of substances consumed or produced in a reaction.
To apply mole ratio in calculations, you can set up a proportion based on the balanced equation. This allows you to calculate the unknown quantity if you have one known quantity related to the substances involved. This method was used in calculating the moles of \[ \text{H}_2 \] and \[ \text{N}_2 \] consumed.

Balanced Chemical Equation

A balanced chemical equation is a fundamental tool in chemistry. It not only represents what happens in a reaction but also ensures the law of conservation of mass is adhered to. This law states that matter cannot be created or destroyed.
In simple terms, atoms and molecules present at the start of a reaction must still be present at the end of it. Thus, a balanced equation has the same number of each type of atom on both sides of the reaction. In the ammonia synthesis equation:

• \[ 3 \mathrm{H}_2(g) + \mathrm{N}_2(g) \rightarrow 2 \mathrm{NH}_3(g) \]

This equation shows that three molecules of hydrogen gas react with one molecule of nitrogen gas to form two molecules of ammonia. Balancing an equation is crucial for accurate stoichiometric calculations. Without it, determining the correct mole ratios would be impossible. Always ensure the chemical equation is balanced before performing calculations.

Ammonia Synthesis

Ammonia synthesis, often carried out through the Haber-Bosch process, is a vital industrial chemical reaction. This process is crucial for producing ammonia, a key ingredient in fertilizers that supports agricultural productivity worldwide.
The reaction involves nitrogen from the air and hydrogen derived from natural gas or water electrolysis. The balanced equation for ammonia synthesis is:

• \[ 3 \mathrm{H}_2(g) + \mathrm{N}_2(g) \rightarrow 2 \mathrm{NH}_3(g) \]

This synthesis requires high temperatures and pressures to achieve significant conversion rates of nitrogen and hydrogen into ammonia. The process is designed to ensure optimal reactor efficiency while minimizing energy consumption. Understanding the stoichiometry of this reaction helps optimize conditions and calculate the necessary reactant quantities for desired product amounts.

Chemical Reaction

A chemical reaction involves rearrangement of molecules to form new substances. It is a process characterized by the interaction of reactants to form products with different properties. In the context of the ammonia synthesis reaction:

• Hydrogen (\[ \text{H}_2 \]) and nitrogen (\[ \text{N}_2 \]) interact to form ammonia (\[ \text{NH}_3 \]).

Chemical reactions can be exothermic or endothermic. Ammonia synthesis is exothermic, releasing energy due to the formation of strong nitrogen-hydrogen bonds in ammonia. Analysis of chemical reactions involves understanding changes at the molecular level, usually afforded by a balanced equation.
These reactions are central to various industries, including agriculture, pharmaceuticals, and environmental management. Knowing how reactions work allows chemists and engineers to manipulate them for desired outcomes, including the design of sustainable processes and resources.