Molar Masses of Compounds
The molecular formula of the compound carbon dioxide is \(\ce{CO_2}\). One molecule of carbon dioxide consists of 1 atom of carbon and 2 atoms of oxygen. We can calculate the mass of one molecule of carbon dioxide by adding together the masses of 1 atom of carbon and 2 atoms of oxygen:
\[12.01 \: \text{amu} + 2 \left( 16.00 \: \text{amu} \right) = 44.01 \: \text{amu}\nonumber \]
The molecular mass of a compound is the mass of one molecule of that compound. The molecular mass of carbon dioxide is \(44.01 \: \text{amu}\).
The molar mass of any compound is the mass in grams of one mole of that compound. One mole of carbon dioxide molecules has a mass of \(44.01 \: \text{g}\), while one mole of sodium sulfide formula units has a mass of \(78.04 \: \text{g}\). The molar masses are \(44.01 \: \text{g/mol}\) and \(78.04 \: \text{g/mol}\) respectively. In both cases, that is the mass of \(6.02 \times 10^{23}\) representative particles. The representative particle of \(\ce{CO_2}\) is the molecule, while for \(\ce{Na_2S}\) it is the formula unit.
Example \(\PageIndex{1}\): Molar Mass of a Compound
Calcium nitrate, \(\ce{Ca(NO_3)_2}\), is used as a component in fertilizer. Determine the molar mass of calcium nitrate.
Solution
Step 1: List the known and unknown quantities and plan the problem.
Known
- Formula \(= \ce{Ca(NO_3)_2}\)
- Molar mass \(\ce{Ca} = 40.08 \: \text{g/mol}\)
- Molar mass \(\ce{N} = 14.01 \: \text{g/mol}\)
- Molar mass \(\ce{O} = 16.00 \: \text{g/mol}\)
Unknown
First we need to analyze the formula. Since the \(\ce{Ca}\) lacks a subscript, there is one \(\ce{Ca}\) atom per formula unit. The 2 outside the parentheses means that there are two nitrate ions per formula unit and each nitrate ion consists of one nitrogen atom and three oxygen atoms per formula unit. Thus, \(1 \: \text{mol}\) of calcium nitrate contains \(1 \: \text{mol}\) of \(\ce{Ca}\) atoms, \(2 \: \text{mol}\) of \(\ce{N}\) atoms, and \(6 \: \text{mol}\) of \(\ce{O}\) atoms.
Step 2: Calculate
Use the molar masses of each atom together with the number of atoms in the formula and add together.
\[1 \: \text{mol} \: \ce{Ca} \times \frac{40.08 \: \text{g} \: \ce{Ca}}{1 \: \text{mol} \: \ce{Ca}} = 40.08 \: \text{g} \: \ce{Ca}\nonumber \]
\[2 \: \text{mol} \: \ce{N} \times \frac{14.01 \: \text{g} \: \ce{N}}{1 \: \text{mol} \: \ce{N}} = 28.02 \: \text{g} \: \ce{N}\nonumber \]
\[6 \: \text{mol} \: \ce{O} \times \frac{16.00 \: \text{g} \: \ce{O}}{1 \: \text{mol} \: \ce{O}} = 96.00 \: \text{g} \: \ce{O}\nonumber \]
Molar mass of \(\ce{Ca(NO_3)_2} = 40.08 \: \text{g} + 28.02 \: \text{g} + 96.00 \: \text{g} = 164.10 \: \text{g/mol}\)