What is the difference between the molar mass and the empirical formula mass of a compound? When are these masses the same and when are they different? When different, how is the molar mass related to the empirical formula mass?

Molar mass is the mass of one mole of a substance, which is the mass of 6.022 x 10^23 units (atoms, molecules, or formula units) of that substance. It is usually expressed in grams per mole (g/mol). Empirical formula mass is the mass of one mole of the simplest formula that represents the compound's composition. The empirical formula represents the simplest whole-number ratio of atoms in the compound.

The molar mass and empirical formula mass will be the same when the molecular formula of a compound is the same as its empirical formula, meaning that the compound already exists in its simplest whole-number ratio. This often occurs for ionic compounds. For example, consider table salt, which has the molecular formula NaCl. Since its empirical formula is also NaCl, its molar mass and empirical formula mass are the same.

The molar mass and empirical formula mass will be different when the molecular formula of a compound is not the same as its empirical formula, meaning that the compound does not exist in its simplest whole-number ratio. This frequently occurs for covalent compounds. For example, consider glucose, which has the molecular formula C6H12O6. Its empirical formula is CH2O because the compound's molecular formula can be reduced to a simpler whole-number ratio of atoms. In this case, the molar mass is not equal to the empirical formula mass.

When the molar mass and empirical formula mass are different, they are related by an integer multiple. To find the multiple, divide the molar mass by the empirical formula mass, which should give a whole number result (considering reasonable experimental error). Using the glucose example from Step 3, the empirical formula mass of CH2O is 12.01 g/mol (C) + 2.02 g/mol (H) + 16.00 g/mol (O) = 30.03 g/mol. The molar mass of glucose is approximately 180.16 g/mol. Dividing the molar mass by the empirical formula mass: \[ n = \frac{180.16 \ \text{g/mol}}{30.03 \ \text{g/mol}} \approx 6 \] The whole-number multiple, n, is approximately 6. This means that the molecular formula of glucose (C6H12O6) is approximately six times the empirical formula (CH2O).