Problem 128 - Introductory Chemistry Atoms First

Question

Nitrous oxide, \(\mathrm{N}_{2} \mathrm{O}\), is produced when ammonium nitrate, \(\mathrm{NH}_{4} \mathrm{NO}_{3}\), is heated gently. Water is also produced in the reaction. Write the balanced equation for the reaction.

Step-by-Step Solution

Answer

The balanced equation for the reaction is: \[\mathrm{NH}_{4} \mathrm{NO}_{3} \rightarrow \mathrm{N}_{2} \mathrm{O} + 2\,\mathrm{H}_{2}\mathrm{O}\]

Step 1: Write the unbalanced equation with formulas of reactants and products

Based on the problem, we know the reactant is ammonium nitrate (\(\mathrm{NH}_{4} \mathrm{NO}_{3}\)) and the two products are nitrous oxide (\(\mathrm{N}_{2} \mathrm{O}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)): \[\mathrm{NH}_{4} \mathrm{NO}_{3} \rightarrow \mathrm{N}_{2} \mathrm{O} + \mathrm{H}_{2}\mathrm{O}\] Now we need to balance the equation.

Step 2: Count and compare atoms in reactants and products

Count the atoms on both sides of the equation, and compare their numbers: Reactant side (\(\mathrm{NH}_{4} \mathrm{NO}_{3}\)): - 2 Nitrogen atoms - 4 Hydrogen atoms - 3 Oxygen atoms Product side (\(\mathrm{N}_{2} \mathrm{O} + \mathrm{H}_{2}\mathrm{O}\)): - 2 Nitrogen atoms - 2 Hydrogen atoms - 3 Oxygen atoms We can see that the nitrogen and oxygen atoms are already balanced, but the hydrogen atoms are not.

Step 3: Balance the hydrogen atoms

To balance the hydrogen atoms, we'll multiply \(\mathrm{H}_{2}\mathrm{O}\) by 2: \[\mathrm{NH}_{4} \mathrm{NO}_{3} \rightarrow \mathrm{N}_{2} \mathrm{O} + 2\,\mathrm{H}_{2}\mathrm{O}\] Now, let's re-check the balance of the atoms: Reactant side (\(\mathrm{NH}_{4} \mathrm{NO}_{3}\)): - 2 Nitrogen atoms - 4 Hydrogen atoms - 3 Oxygen atoms Product side (\(\mathrm{N}_{2} \mathrm{O} + 2\,\mathrm{H}_{2}\mathrm{O}\)): - 2 Nitrogen atoms - 4 Hydrogen atoms - 3 Oxygen atoms All the atoms are balanced.

Step 4: Verify and write the final balanced equation

Double-checking the balanced equation, we can confirm that all the atoms are equal on both sides, so the balanced equation is: \[\mathrm{NH}_{4} \mathrm{NO}_{3} \rightarrow \mathrm{N}_{2} \mathrm{O} + 2\,\mathrm{H}_{2}\mathrm{O}\]

Key Concepts

Chemical Reaction

When substances undergo a chemical reaction, they are transformed into different substances with new properties. This change involves making or breaking chemical bonds and the rearrangement of atoms. The process of heating ammonium nitrate to produce nitrous oxide and water is an example of a chemical reaction. These transformations follow specific rules, such as the law of conservation of mass, and require careful balancing to reflect the reorganization of atoms.

In teaching chemical reactions, it's important to emphasize the visualization of atoms and molecules before and after the reaction. Using models or drawings can help students conceptualize these invisible processes. Additionally, demonstrations or interactive simulations can foster a deeper understanding of the dynamic nature of these reactions.

Stoichiometry

The field of stoichiometry involves the calculation of the quantities of reactants and products in a chemical reaction. It's like a recipe for a chemical reaction, telling you how much of each substance you need and can expect to produce. Stoichiometry is based on the balanced chemical equation, where the coefficients represent the ratio of moles of each compound involved in the reaction.

When explaining stoichiometry to students, it's useful to start with the familiar concept of a recipe and measure out ingredients physically to demonstrate the stoichiometric principles. This hands-on approach aids comprehension and retention.

Chemical Formula

A chemical formula is a symbolic representation of a chemical substance using letters and numbers. For example, the chemical formula for ammonium nitrate is \(\mathrm{NH}_{4} \mathrm{NO}_{3}\), which tells us the molecule consists of ammonium ions (\(\mathrm{NH}_{4}^{+}\)) and nitrate ions (\(\mathrm{NO}_{3}^{-}\)). Chemical formulas are crucial for communicating the composition of molecules and the stoichiometry of reactions.

When teaching this concept, it's helpful to explain the meaning behind the symbols and subscripts. Interactive activities that involve building molecules using molecular model kits or drawing them can enhance understanding by making the abstract concept of chemical formulas tangible.

Law of Conservation of Mass

The law of conservation of mass states that mass is neither created nor destroyed in a chemical reaction. This principle is fundamental to understanding why it is necessary to balance chemical equations. When balancing the reaction of ammonium nitrate decomposing into nitrous oxide and water, we have to make sure the number of atoms of each element is equal on both sides of the equation, consistent with this law.

To help students internalize this law, use illustration of mass balance scales, showing that the mass of reactants equals the mass of the products. Problem-solving exercises that involve predicting the mass of products given the mass of reactants can provide practical application of this concept.