Problem 103 - Chemistry: The Central Science in SI Units, Global Edition

Question

A mixture of \(\mathrm{N}_{2}(g)\) and \(\mathrm{H}_{2}(g)\) reacts in a closed container to form ammonia, \(\mathrm{NH}_{3}(g)\). The reaction ceases before either reactant has been totally consumed. At this stage \(3.0 \mathrm{~mol} \mathrm{~N}_{2}, 3.0 \mathrm{~mol} \mathrm{H}_{2}\), and \(3.0 \mathrm{~mol} \mathrm{NH}_{3}\) are present. How many moles of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) were present originally?

Step-by-Step Solution

Answer

There were initially \(4.5 \mathrm{~moles}\) of \(\mathrm{N}_{2}\) and \(7.5 \mathrm{~moles}\) of \(\mathrm{H}_{2}\) present in the container.

Step 1: Write the balanced chemical equation

Write down the balanced chemical equation for the reaction between nitrogen gas and hydrogen gas to form ammonia gas: N2(g) + 3H2(g) → 2NH3(g) We can see the stoichiometry of the reaction is 1:3:2 for N2, H2, and NH3 respectively.

Step 2: Identify the moles of N2 and H2 consumed by the reaction

According to the stoichiometry of the reaction, for every 2 moles of NH3 produced, 1 mole of N2 and 3 moles of H2 are consumed. We are given that 3 moles of NH3 have been formed, which means: \(Moles \quad of \quad \mathrm{N}_{2} \quad consumed = \frac{1}{2} × Moles \quad of \quad \mathrm{NH}_{3} = \frac{1}{2} × 3 = 1.5 \quad moles\) \(Moles \quad of \quad \mathrm{H}_{2} \quad consumed = \frac{3}{2} × Moles \quad of \quad \mathrm{NH}_{3} = \frac{3}{2} × 3 = 4.5 \quad moles\)

Step 3: Determine the initial moles of N2 and H2

Now that we know the moles of N2 and H2 consumed in the reaction, we can determine the initial moles by adding them to the moles present at the equilibrium state. Moles of N2 initially: \(3.0 \, moles \, (equilibrium) + 1.5 \, moles \, (consumed) = 4.5 \, moles\) Moles of H2 initially: \(3.0 \, moles \, (equilibrium) + 4.5 \, moles \, (consumed) = 7.5 \, moles\) So, there were 4.5 moles of N2 and 7.5 moles of H2 present initially.

Key Concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves calculating the quantitative relationships between the reactants and products in a chemical reaction. Simply put, it helps us understand how much of each chemical is needed or produced in a reaction. Stoichiometry is rooted in the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.

In our example, stoichiometry is used to calculate how many moles of nitrogen (\(\mathrm{N}_{2}\)) and hydrogen (\(\mathrm{H}_{2}\)) react to form a certain amount of ammonia (\(\mathrm{NH}_{3}\)). The balanced chemical equation acts as a map to navigate these quantitative relationships.

• Helps calculate amounts of reactants and products
• Based on the balanced chemical equation
• Essential for understanding chemical reactions

Balanced Chemical Equation

A balanced chemical equation is crucial for understanding a chemical reaction. It ensures the correct correspondence of reactants and products, reflecting the conservation of atoms in a reaction.

For the ammonia formation, the balanced equation is \(\mathrm{N}_{2}(g) + 3\mathrm{H}_{2}(g) \rightarrow 2\mathrm{NH}_{3}(g)\). This equation illustrates that one molecule of nitrogen reacts with three molecules of hydrogen to produce two molecules of ammonia. Balancing chemical equations focuses on maintaining equal numbers of each type of atom on both sides of the equation, reinforcing the conservation of mass.

• Shows detailed atom conservation
• Provides a basis for stoichiometric calculations
• Essential for reaction predictions

Reaction Stoichiometry

Reaction stoichiometry focuses specifically on the quantitative aspects of reactants and products in a chemical reaction. Using stoichiometry, we can calculate how much of each substance will react or be produced. This is guided by the coefficients in the balanced chemical equation.

In the formation of ammonia, the stoichiometry tells us that:

• 1 mole of \(\mathrm{N}_{2}\) reacts with 3 moles of \(\mathrm{H}_{2}\)
• To produce 2 moles of \(\mathrm{NH}_{3}\)

Given this ratio, we can determine how much \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) are required for the formation of a specified amount of ammonia, and how much remains at equilibrium.

• Explains mole-to-mole relationships
• Guides calculation of unknown quantities
• Central to analyzing chemical systems

Ammonia Formation

Ammonia is a significant chemical in agriculture and industry, synthesized through the reaction of nitrogen and hydrogen gases. This reaction is represented by the balanced chemical equation \(\mathrm{N}_{2}(g) + 3\mathrm{H}_{2}(g) \rightarrow 2\mathrm{NH}_{3}(g)\).

Ammonia's formation is vital for producing fertilizers, which supports global food production. In the context of chemical reactions, understanding the stoichiometry of ammonia formation allows chemists to optimize conditions for maximum yield. In our reaction sequence, even when the reaction ceases before all reactants are consumed, knowing the balanced equation helps determine how reactants were initially mixed.

• Key compound in fertilizers
• Understanding formation aids in efficient production
• Illustrates practical application of stoichiometry