Simplest and Actual Ratios: Empirical and Molecular Formulas
- You’re a detective in a chemistry lab, analyzing a mysterious compound.
- You know its elements and their relative amounts, but what does the compound look like at the molecular level? Is it a simple molecule, or does it consist of repeating units?
To uncover the full picture, you’ll need two essential tools: the empirical formula and the molecular formula.
The Empirical Formula: The Simplest Ratio
Empirical formula
The empirical formula represents the simplest whole-number ratio of atoms of each element in a compound.
It doesn’t indicate the exact number of atoms in a molecule, just their relative proportions.Example
- The empirical formula of hydrogen peroxide (H₂O₂) is HO because the ratio of hydrogen to oxygen atoms is 1:1.
- For glucose (C₆H₁₂O₆), the empirical formula is CH₂O, as the ratio of carbon, hydrogen, and oxygen atoms simplifies to 1:2:1.
Why is the empirical formula useful?
- The empirical formula is especially valuable when analyzing experimental data, such as percentage composition.
- It serves as a stepping stone for determining the molecular formula, which provides more detailed information.
- The empirical formula is often used to describe ionic compounds, as it reflects their simplest ratio of ions.
- For example, the empirical formula of sodium chloride is NaCl, even though it forms a lattice structure rather than discrete molecules.
The Molecular Formula: The Actual Number of Atoms
Molecular formula
The molecular formula specifies the exact number of atoms of each element in a molecule.
It is either identical to the empirical formula or an integer multiple of it.Example
- The molecular formula of hydrogen peroxide is H₂O₂, which is the empirical formula multiplied by 2.
- For glucose, the molecular formula is C₆H₁₂O₆, which is the empirical formula multiplied by 6.
To determine the molecular formula, additional information is required: the molar mass of the compound.
From Formulas to Percentages: Step-by-Step Calculations
Percentage composition
The percentage composition of an element in a compound describes the proportion of the compound's mass contributed by that element.
It can be calculated using the formula:
$$\% \text{Element} = \frac{\text{Mass of element in 1 mole of compound}}{\text{Molar mass of compound}} \times 100$$
Calculate the percentage of oxygen in water ($H_2O$).
Solution
Step 1: Identify the Molar Mass of the Compound
- Hydrogen: $2 \times 1.008 = 2.016 \, \text{g mol}^{-1}$
- Oxygen: $16.00\, \text{g mol}^{-1}$
- Molar mass of water: $M = 2.016 + 16.00 = 18.016 \, \text{g mol}^{-1}$
Step 2: Apply the Formula
For oxygen: $$\% \text{Oxygen} = \frac{16.00}{18.016} \times 100$$
Step 3: Perform the Calculation
$$\% \text{Oxygen} = \frac{16.00}{18.016} \times 100 \approx 88.81 \%$$
Final Answer:
The percentage composition of oxygen in water is approximately 88.81%.
The sum of the percentage compositions of all elements in a compound should equal 100% (within rounding error).
From Percentages to Formulas: Step-by-Step Calculations
Now that you understand the difference between empirical and molecular formulas, let’s explore how to calculate them using experimental data.
1. Calculating the Empirical Formula from Percentage Composition
Suppose you’re given the percentage composition of a compound. Follow these steps:
- Convert percentages to masses:
- Assume you have 100 g of the compound.
- This makes the percentages equivalent to masses in grams.
