Problem 28 - Chemistry An Atoms First Approach

Question

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?

Step-by-Step Solution

Answer

The molar mass is the mass of one mole of a substance, while the empirical formula mass is the mass of the simplest whole-number ratio of elements in a compound, both expressed in g/mol. The two masses are the same when the empirical formula is the same as the molecular formula (e.g., H₂O, CO₂, NaCl). They are different when the molecular formula is a multiple of the empirical formula (e.g., glucose C₆H₁₂O₆, benzene C₆H₆). In this case, the molar mass is a whole-number multiple of the empirical formula mass: \( \text{Whole-number multiple} = \dfrac{\text{Molar mass}}{\text{Empirical formula mass}} \).

Step 1: Definitions: Molar Mass and Empirical Formula Mass

Molar mass is the mass (in grams) of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by finding the sum of the atomic masses of all the atoms in a molecule. Empirical formula mass, on the other hand, is the mass of the simplest whole number ratio of elements in a compound, also expressed in g/mol. It is calculated by finding the sum of the atomic masses of the elements in the empirical formula.

Step 2: When Molar Mass and Empirical Formula Mass are the Same

The molar mass and empirical formula mass are the same when the empirical formula is the same as the molecular formula. In other words, when the compound already exists in its simplest whole-number ratio, the two masses will be equal. Examples of such compounds include water (H₂O), carbon dioxide (CO₂), and sodium chloride (NaCl).

Step 3: When Molar Mass and Empirical Formula Mass are Different

The molar mass and empirical formula mass are different when the molecular formula is a multiple of the empirical formula. This means that the molecular formula represents a compound with more than the simplest whole-number ratio of its elements. Examples of such compounds include glucose (C₆H₁₂O₆) with an empirical formula of CH₂O and benzene (C₆H₆) with an empirical formula of CH.

Step 4: Relationship between Molar Mass and Empirical Formula Mass

When the molar mass and empirical formula mass are different, the molar mass of the compound is usually a whole number multiple of the empirical formula mass. This is because the molecular formula is a multiple of the empirical formula. To find this whole number multiple, simply divide the molar mass by the empirical formula mass: \( \text{Whole-number multiple} = \dfrac{\text{Molar mass}}{\text{Empirical formula mass}} \) In conclusion, the molar mass and empirical formula mass of a compound can be the same or different based on the whole-number ratio of elements in the compound. When the empirical formula is the same as the molecular formula, the masses are the same; when it is not, the molar mass is a whole number multiple of the empirical formula mass.