Question

Nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) is also called "laughing gas." It can be prepared by the thermal decomposition of ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\). The other product is \(\mathrm{H}_{2} \mathrm{O}\). (a) Write a balanced equation for this reaction. (b) How many grams of \(\mathrm{N}_{2} \mathrm{O}\) are formed if \(0.46 \mathrm{~mol}\) of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) is used in the reaction?

Short answer

The balanced equation is \(\mathrm{NH}_{4} \mathrm{NO}_{3} \rightarrow \mathrm{N}_{2} \mathrm{O} + 2\mathrm{H}_{2} \mathrm{O}\). From 0.46 mol \(\mathrm{NH}_{4} \mathrm{NO}_{3}\), 20.25 g \(\mathrm{N}_{2} \mathrm{O}\) is formed.

Step-by-step solution

Write the Unbalanced Equation

The decomposition of ammonium nitrate (\(\mathrm{NH}_{4} \mathrm{NO}_{3}\)) produces nitrous oxide (\(\mathrm{N}_{2} \mathrm{O}\)) and water (\(\mathrm{H}_{2} \mathrm{O}\)). The unbalanced equation is:\[\mathrm{NH}_{4} \mathrm{NO}_{3} \rightarrow \mathrm{N}_{2} \mathrm{O} + \mathrm{H}_{2} \mathrm{O}\]

Balance the Chemical Equation

Balance the chemical equation by making sure that the number of atoms for each element is equal on both sides. For the given equation:1. Nitrogen atoms: 2 on the right, 2 from \(\mathrm{NH}_{4} \mathrm{NO}_{3}\).2. Hydrogen atoms: 4 on the left, balanced by forming 2 molecules of water.3. Oxygen atoms: 3 on the left, 3 on the right (from \(\mathrm{N}_{2} \mathrm{O}\) and \(\mathrm{H}_{2} \mathrm{O}\)).The balanced equation is:\[\mathrm{NH}_{4} \mathrm{NO}_{3} \rightarrow \mathrm{N}_{2} \mathrm{O} + 2\mathrm{H}_{2} \mathrm{O}\]

Determine Molar Mass of Compounds

Calculate the molar mass for \(\mathrm{N}_{2} \mathrm{O}\) and \(\mathrm{NH}_{4} \mathrm{NO}_{3}\):For \(\mathrm{N}_{2} \mathrm{O}\):- Nitrogen (N): 14.01 g/mol \(\times 2 = 28.02\) g/mol- Oxygen (O): 16.00 g/mol- Total: 28.02 g/mol + 16.00 g/mol = 44.02 g/molFor \(\mathrm{NH}_{4} \mathrm{NO}_{3}\):- Nitrogen (N): 14.01 g/mol \(\times 2 = 28.02\) g/mol- Hydrogen (H): 1.01 g/mol \(\times 4 = 4.04\) g/mol- Oxygen (O): 16.00 g/mol \(\times 3 = 48.00\) g/mol- Total: 28.02 g/mol + 4.04 g/mol + 48.00 g/mol = 80.06 g/mol

Calculate Mass of \(\mathrm{N}_{2} \mathrm{O}\) Formed

Use stoichiometry to find the mass of \(\mathrm{N}_{2} \mathrm{O}\) produced from 0.46 mol of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\). The balanced equation shows a 1:1 molar ratio.1. Moles of \(\mathrm{N}_{2} \mathrm{O}\) = 0.46 mol (same as \(\mathrm{NH}_{4} \mathrm{NO}_{3}\))2. Mass = moles \(\times\) molar mass3. Mass of \(\mathrm{N}_{2} \mathrm{O}\) = 0.46 mol \(\times 44.02\, \mathrm{g/mol} = 20.25\) g

Key concepts

Molar Mass Calculation

Calculating the molar mass is a fundamental skill in chemistry, essential for analyzing chemical reactions. The molar mass of a compound is determined by adding the atomic masses of all the atoms in its formula. For instance, to find the molar mass of nitrous oxide (\(\mathrm{N}_{2} \mathrm{O}\)), you multiply the atomic mass of nitrogen (14.01 g/mol) by 2, because there are two nitrogen atoms. Then, add the atomic mass of oxygen (16.00 g/mol), giving a total molar mass of 44.02 g/mol.

• For \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) (ammonium nitrate), calculate by summing:
  • Nitrogen: 14.01 g/mol \(\times 2 = 28.02\) g/mol
  • Hydrogen: 1.01 g/mol \(\times 4 = 4.04\) g/mol
  • Oxygen: 16.00 g/mol \(\times 3 = 48.00\) g/mol

The molar mass of ammonium nitrate is thereby calculated as 80.06 g/mol. Understanding these calculations allows chemists to predict how substances react and to compare these reactions quantitatively.

Stoichiometry

Stoichiometry is the area of chemistry that involves calculating amounts of reactants and products in chemical reactions. It’s akin to a recipe card that ensures the correct amounts of each ingredient to achieve a desired product.
In the decomposition of ammonium nitrate, the balanced equation provides a 1:1 molar relationship between \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) and \(\mathrm{N}_{2} \mathrm{O}\). This ratio informs us that for every mole of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) decomposed, one mole of \(\mathrm{N}_{2} \mathrm{O}\) is produced, alongside 2 moles of water.
Stoichiometric calculations can be used to determine how much product is formed from a given quantity of reactant or vice versa. In our example, with 0.46 moles of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\), you can predict 0.46 moles of \(\mathrm{N}_{2} \mathrm{O}\) will be formed, leading to the same number of moles being utilized on the reactant side.

Thermal Decomposition

Thermal decomposition refers to the breaking down of a chemical compound due to heat.
For ammonium nitrate (\(\mathrm{NH}_{4} \mathrm{NO}_{3}\)), heating causes the compound to decompose into nitrous oxide (\(\mathrm{N}_{2} \mathrm{O}\)) and water (\(\mathrm{H}_{2} \mathrm{O}\)). This process is common in compounds that are not stable when heated.
In a thermal decomposition reaction, understanding the energy changes is important as the compounds absorb heat until the bonds break down. This reaction not only requires precise control over temperature but also needs a good understanding of safety protocols when handling potential gases evolved during decomposition.

• Reactant: \(\mathrm{NH}_{4} \mathrm{NO}_{3}\)
• Products: \(\mathrm{N}_{2} \mathrm{O}\) and \(\mathrm{H}_{2} \mathrm{O}\)

As a result, understanding thermal decomposition is critical for applications in which temperature control can determine the reaction’s success or could cause safety issues.

Ammonium Nitrate

Ammonium nitrate (\(\mathrm{NH}_{4} \mathrm{NO}_{3}\)) is a compound with various applications, notably in fertilizers and as an explosive. It is a salt formed from ammonia and nitric acid.
Being highly soluble in water and highly reactive, it plays a significant role in delivering nitrogen, a critical nutrient for plant growth.
Its decomposition into nitrous oxide and water by heating is used as a method to produce 'laughing gas' in a controlled setting. This property underscores the compound’s dual nature: beneficial in agriculture due to its nutrient-rich composition, but potentially dangerous if mishandled.

• Structure: NH₄⁺ (ammonium ion) and NO₃⁻ (nitrate ion)
• Uses: Fertilizers, explosives, and as a gas source in laboratories

While it is invaluable in many industries, strict guidelines govern its handling due to its explosive potential. Respect for these handling processes is key to utilizing ammonium nitrate safely.