Question

How many moles of nitrogen, \(\mathrm{N},\) are in \(0.556 \mathrm{~mol}\) of ammonium nitrate? How many grams of this compound supply this much nitrogen?

Short answer

There are 1.112 moles of nitrogen in 0.556 mol of ammonium nitrate. To find the mass in grams, multiply 0.556 mol of ammonium nitrate by its molar mass, which is approximately 80.052 grams/mol.

Step-by-step solution

Calculate Moles of Nitrogen

Ammonium nitrate is a compound with the formula \( \mathrm{NH}_4\mathrm{NO}_3 \). It contains two nitrogen atoms per formula unit. To find the moles of nitrogen, we multiply the moles of ammonium nitrate by 2, the number of nitrogen atoms per molecule of ammonium nitrate.

Convert Moles of Nitrogen to Grams of Ammonium Nitrate

First, calculate the molar mass of \( \mathrm{NH}_4\mathrm{NO}_3 \) by adding the atomic masses of all the atoms in the formula: \( (2 \times 14.007) + (4 \times 1.008) + (3 \times 16.00) \). Then, use the molar mass to convert the original moles of ammonium nitrate to grams.

Calculate the Mass of Ammonium Nitrate

Multiply the moles of ammonium nitrate by its molar mass to get the mass in grams.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. Understanding stoichiometry is essential for a range of tasks, from predicting the yields of reactions to figuring out reactant quantitates needed for desired product amounts.

An important application of stoichiometry is in the calculation of mole ratios in chemical formulas, as seen in the exercise involving ammonium nitrate (\(NH_4NO_3\)). In this context, the stoichiometry tells us that each formula unit contains two nitrogen atoms. If asked to find the amount of nitrogen in \(0.556 mol\) of ammonium nitrate, stoichiometry lets us use the mole ratio directly in our calculations to determine that there are twice the moles of nitrogen atoms.

Molar Mass

Molar mass is the mass of one mole of a substance, typically measured in grams per mole (\(g/mol\)). This property is pivotal when converting between grams and moles, as it essentially functions as a conversion factor. The molar mass of a compound can be calculated by adding the molar masses of each atom that makes up the compound.

For example, in the given exercise involving ammonium nitrate (\(NH_4NO_3\)), the molar mass calculation would factor in the mass of nitrogen, hydrogen, and oxygen atoms as per the chemical formula. Once the molar mass is known, it's straightforward to convert moles of a compound into grams, as seen in the solution steps where we multiply the moles of ammonium nitrate by its molar mass to find the resultant mass in grams.

Chemical Formula

A chemical formula provides essential information about the composition of a compound, describing the types and numbers of atoms present. The chemical formula for ammonium nitrate, \(NH_4NO_3\), tells us that each formula unit contains one nitrogen atom in the ammonium ion (\(NH^+_4\)) and one in the nitrate ion (\(NO^-_3\)).

Understanding a compound's chemical formula is crucial when solving related stoichiometry problems. For instance, to calculate the moles of nitrogen in a given amount of ammonium nitrate, we use the chemical formula to ascertain that there are two nitrogen atoms per formula unit, leading to a direct multiplication of the number of moles of the compound by two to find the moles of nitrogen.