Quick Menu

Determining Empirical and Molecular Formula

3.2 Determining Empirical and Molecular Formulas

A chemical formula isn't just a label; it’s a ratio. In this section, we move from the laboratory (where we measure mass) to the chemical formula (where we count atoms).

1. Percent Composition

In clinical chemistry, understanding the mass percentage of an element is vital for analyzing things like the iron content in a hemoglobin molecule or the concentration of active ingredients in a pharmaceutical compound.

The Two-Step Calculation Process

Step 1: Determine the Molar Mass of the Compound
The molar mass is the sum of the masses of all atoms in one mole of the compound. You find the mass of each element on the Periodic Table and add them based on their subscripts in the formula.

Step 2: Calculate the Percent Composition
Divide the total mass of each specific element by the molar mass of the entire compound and multiply by 100%.

Percent Composition = (Total Mass of Element in Compound / Molar Mass of Compound) × 100%

Introductory Example: Water (H2O)

1. Molar Mass Calculation:
H: 2 × 1.01 g/mol = 2.02 g/mol
O: 1 × 16.00 g/mol = 16.00 g/mol
Molar Mass of H2O = 18.02 g/mol

2. Percent Composition:
% H = (2.02 / 18.02) × 100% = 11.21%
% O = (16.00 / 18.02) × 100% = 88.79%

Advanced Clinical Case: Penicillin V

Penicillin V (C16H18N2O5S) is a common antibiotic. Suppose a forensic lab needs to verify the identity of a sample by checking its sulfur content.

✏️ Advanced Practice Challenge: Calculate the percent composition of Sulfur (S) in Penicillin V (C16H18N2O5S).

Atomic Masses: C=12.01, H=1.008, N=14.01, O=16.00, S=32.06 Click for Step-by-Step Solution
Step 1: Calculate Total Molar Mass
  • C: 16 × 12.01 = 192.16
  • H: 18 × 1.008 = 18.14
  • N: 2 × 14.01 = 28.02
  • O: 5 × 16.00 = 80.00
  • S: 1 × 32.06 = 32.06
Molar Mass = 350.38 g/mol

Step 2: Calculate % Sulfur

% S = (32.06 / 350.38) × 100% = 9.15%

Interpretation: This means that in any dose of Penicillin V, only about 9% of the weight of the molecule comes from the Sulfur atom.

 

Clinical Connection: Electrolyte Purity

In a hospital pharmacy, percent composition is used to verify the purity of intravenous salts. For example, if a batch of Magnesium Sulfate ($MgSO_4$) shows a significantly higher mass percentage of Magnesium than the theoretical 20.19%, it indicates the sample may be contaminated or improperly hydrated, which could lead to dangerous dosing errors.

 

The Formula:
% Element = (Mass of element in 1 mol of compound / Molar mass of compound) × 100%
✏️ Practice Problem 1: A common supplement contains a compound with a molar mass of 100.0 g/mol. If one mole of the compound contains 40.0 g of Calcium, what is the percent composition of Calcium? Click for Solution

(40.0 g Ca / 100.0 g total) × 100 = 40% Calcium

2. Determining Empirical Formulas

The empirical formula is the simplest whole-number ratio of atoms in a compound. To find it from mass data, follow these four steps:

  1. Grams to Moles: Convert the mass of each element to moles.
  2. Divide by Smallest: Divide all mole values by the smallest mole value obtained.
  3. Round to Whole Numbers: If the results are within 0.1 of a whole number, round them.
  4. Multiply if Necessary: If you have fractions (like 0.5 or 0.33), multiply all numbers by a factor to get whole numbers.
✏️ Practice Problem 2: A sample of a compound is found to contain 1.0 mole of Nitrogen and 2.0 moles of Oxygen. What is its empirical formula? Click for Solution

The ratio is 1 N : 2 O.
The empirical formula is NO2.

3. Determining Molecular Formulas

The molecular formula is the actual number of atoms in a molecule. It is always a whole-number multiple of the empirical formula.

To find the molecular formula, you need the Molar Mass (actual weight) and the Empirical Formula Mass.

Multiplier (n) = Molar Mass / Empirical Formula Mass

[Image comparing the empirical formula and molecular formula of benzene and acetylene]

✏️ Practice Problem 3: A compound has the empirical formula CH2 (mass = 14 g/mol). Its actual molar mass is 42 g/mol. What is its molecular formula? Click for Solution

n = 42 / 14 = 3
Multiply the empirical formula (CH2) by 3:
Molecular Formula = C3H6

Clinical Connection: Toxicology and Drug ID

In forensic toxicology, when an unknown powder or substance is found, scientists use "combustion analysis" to find the mass of Carbon, Hydrogen, and Nitrogen. They use the steps in this section to identify the empirical formula. By comparing that formula and its molar mass to a database, they can identify whether the substance is a life-saving medication or a dangerous toxin.