Question

Consider the following reaction: $$ 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ If a container were to have 10 molecules of \(\mathrm{O}_{2}\) and 10 molecules of \(\mathrm{NH}_{3}\) initially, how many total molecules (reactants plus products) would be present in the container after this reaction goes to completion?

Short answer

The limiting reactant in the given reaction is O₂. When the reaction goes to completion, there will be 8 molecules of NO, 12 molecules of H₂O, and 2 remaining molecules of NH₃. So, the total number of molecules present in the container will be 22.

Step-by-step solution

Identify the limiting reactant

To identify the limiting reactant, compare the mole ratios of the given reactants to the balanced equation. Using the balanced equation: 4 NH₃ + 5 O₂ → 4 NO + 6 H₂O We have 10 molecules of NH₃ and 10 molecules of O₂. To find out which reactant will run out first, let's divide the number of molecules by their respective coefficients from the balanced equation. For NH₃: \( \frac{10}{4} \) = 2.5 For O₂: \( \frac{10}{5} \) = 2 Since the value for O₂ is smaller, it will be the limiting reactant and will determine the amount of products formed.

Determine the moles of products formed

Using the mole ratios in the balanced equation, we will calculate the amount of NO and H₂O produced when all the O₂ molecules react: For NO The mole ratio of O₂ to NO is \( \frac{5}{4} \). So, using the limiting reactant O₂, we can calculate the number of NO molecules formed: \(NO\, molecules = \frac{4}{5} \times 10 = 8\, molecules\) For H₂O The mole ratio of O₂ to H₂O is \( \frac{5}{6} \). So, using the limiting reactant O₂, we can calculate the amount of H₂O molecules formed: \(H_2O\, molecules = \frac{6}{5} \times 10 = 12\, molecules\)

Determine the remaining moles of NH₃

Now, we need to determine how many NH₃ molecules are left after the reaction goes to completion. To do this, we will use the mole ratio of NH₃ to O₂ from the balanced equation, which is \( \frac{4}{5} \): \(Used\, NH_3\, molecules = \frac{4}{5} \times 10 = 8\, molecules\) Thus, the remaining NH₃ molecules: \(Remaining\, NH_3\, molecules = 10 - 8 = 2\, molecules\)

Calculate the total number of molecules present after the reaction

Finally, we can calculate the total number of molecules present in the container after the reaction goes to completion by adding the moles of the remaining reactant (NH₃) and the products formed (NO and H₂O): Total molecules = Remaining NH₃ molecules + NO molecules + H₂O molecules Total molecules = 2 + 8 + 12 Total molecules = 22 Therefore, there will be 22 total molecules present in the container after the reaction goes to completion.

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that helps us understand the relationships between the amounts of reactants and products in chemical reactions. It is all about the quantitative relationships.
These relationships are derived from the balanced chemical equation, giving us the tools to calculate how much of each substance is needed or produced.

By using stoichiometry:

• We can identify limiting reactants, which are the reactants that will be consumed first in the reaction, therefore determining the amount of products formed.
• We can predict the amounts of products from given quantities of reactants using mole ratios derived from the balanced equation.
• It ensures that mass is conserved in chemical reactions, as we can track the number of moles and subsequently the number of molecules for each substance involved.

Understanding stoichiometry is key for anyone working in chemistry fields, as it is a cornerstone for predicting reaction outcomes and designing experiments.

Balanced Chemical Equation

A balanced chemical equation provides a recipe for a chemical reaction. It shows the reactants (starting materials) and products (end materials), as well as their respective quantities. The coefficients in front of each substance demonstrate how many units, such as atoms or molecules, are involved.

For instance, the chemical equation in our exercise:

• \[4 \mathrm{NH}_3(g) + 5 \mathrm{O}_2(g) \rightarrow 4 \mathrm{NO}(g) + 6 \mathrm{H}_2O(g)\]

denotes that 4 molecules of \( \mathrm{NH}_3 \) react with 5 molecules of \( \mathrm{O}_2 \) to produce 4 molecules of \( \mathrm{NO} \) and 6 molecules of \( \mathrm{H}_2O \).

Balancing equations is crucial because it ensures the law of conservation of mass is satisfied in the reaction.

• The total number of each type of atom must be the same before and after the reaction.
• It helps in calculating the reactants and products using stoichiometry, as you need the correct mole ratios to perform these calculations.
• It provides a clear and concise way to communicate chemical changes.

Mole Ratios

Mole ratios are the heart of stoichiometry and chemical calculations. They are derived from the coefficients of a balanced chemical equation and tell us the relative quantities of reactants and products in a chemical reaction.

To find a mole ratio, simply compare the coefficients from the balanced equation. In the given exercise:

• The mole ratio of \( \mathrm{O}_2 \) to \( \mathrm{NH}_3 \) is \( \frac{5}{4} \).
• The mole ratio of \( \mathrm{O}_2 \) to \( \mathrm{NO} \) is \( \frac{5}{4} \).
• The mole ratio of \( \mathrm{O}_2 \) to \( \mathrm{H}_2O \) is \( \frac{5}{6} \).

Mole ratios are essential for:

• Determining the limiting reactant, which is the reactant that will be completely consumed first in the reaction, limiting the amount of product formed.
• Calculating the amounts of other substances needed or produced in a reaction based on the given or required quantity of one substance.
• Converting between moles and grams of different substances using molar mass.

With mole ratios, chemists can accurately predict the outcomes of chemical reactions, whether in laboratories or industrial processes.