Molecular formulas Knowledge-Based Study

Study notes

1. In chemistry, chemical formulas represent the elemental composition of compounds. Two fundamental representations are the empirical formula and the molecular formula.

   • Empirical Formula: The simplest whole-number ratio of atoms of each element in a compound (for example, $\text{CH}$ or $\text{NO}_2$).
   • Molecular Formula: The actual number of atoms of each element present in a single molecule of the compound (for example, $\text{C}_6\text{H}_6$ or $\text{N}_2\text{O}_4$).

   For many substances, such as water ($\text{H}_2\text{O}$) or carbon dioxide ($\text{CO}_2$), the empirical formula and the molecular formula are identical. For others, the molecular formula is an integer multiple of the empirical formula.

   The molecular formula of a covalent compound is directly related to its empirical formula by an integer multiplier, $n$:

   $$\text{Molecular Formula} = (\text{Empirical Formula})_n$$

   Because the molecular formula consists of $n$ empirical units, the actual molar mass (molecular mass) is $n$ times the empirical formula mass:

   $$n = \frac{\text{Molar Mass of Compound}}{\text{Empirical Formula Mass}}$$

   The value of $n$ must always be a whole number (1, 2, 3, etc.). If an experimental calculation yields a decimal very close to an integer, it is rounded to that nearest whole number.

   To find the molecular formula of an unknown compound from experimental data, follow this structured procedure:

   1. Determine the Empirical Formula: Convert mass data or percentage composition to moles for each element, and divide by the smallest molar quantity to find the simplest whole-number atom ratio.
   2. Calculate the Empirical Formula Mass: Sum the atomic masses of all atoms present in the empirical formula.
   3. Determine the Multiplier ($n$): Divide the experimentally determined molar mass by the empirical formula mass: $$n = \frac{\text{Molar Mass}}{\text{Empirical Formula Mass}}$$
   4. Multiply the Subscripts: Multiply each subscript in the empirical formula by the integer $n$ to establish the molecular formula.

   Problem: Chemical analysis of a carbohydrate shows an empirical formula of $\text{CH}_2\text{O}$. A mass spectrometer determines that the molar mass of the compound is $180.16\text{ g/mol}$. What is its molecular formula?

   Solution:

   1. Calculate the empirical formula mass of $\text{CH}_2\text{O}$:

   • Carbon: $1 \times 12.01\text{ g/mol} = 12.01\text{ g/mol}$
   • Hydrogen: $2 \times 1.008\text{ g/mol} = 2.016\text{ g/mol}$
   • Oxygen: $1 \times 16.00\text{ g/mol} = 16.00\text{ g/mol}$
   • Total Empirical Formula Mass: $30.03\text{ g/mol}$

   2. Calculate the integer multiplier $n$:

   $$n = \frac{180.16\text{ g/mol}}{30.03\text{ g/mol}} \approx 6$$

   3. Apply the multiplier to the empirical formula:

   $$(\text{CH}_2\text{O})_6 = \text{C}_6\text{H}_{12}\text{O}_6$$

   The molecular formula of the compound is $\text{C}_6\text{H}_{12}\text{O}_6$.