Empirical and Molecular Formulas

Table of Contents

Understanding empirical and molecular formulas is essential in chemistry. These formulas tell us which elements are present in a compound and in what proportions they exist. This topic helps us determine the composition of substances, which is fundamental in chemical analysis.

1. Understanding Chemical Formulas #

Chemical formulas represent the elements in a compound and their relative numbers. They show us the building blocks of substances at the molecular level.

Different Types of Chemical Formulas #

Empirical Formula #

  • Shows the simplest whole-number ratio of atoms of each element in a compound
  • The building block or basic unit of a compound
  • Example: CH2O for glucose (whose molecular formula is C6H12O6)

Molecular Formula #

  • Shows the actual number of atoms of each element in a molecule
  • May be the same as or a multiple of the empirical formula
  • Example: C6H12O6 for glucose

A Real-Life Analogy: Recipe Ratios #

Think of the relationship between empirical and molecular formulas like a recipe:

  • Empirical Formula = Basic Ratio: Like saying a recipe needs 1 part flour, 2 parts water, and 1 part sugar (a 1:2:1 ratio).
  • Molecular Formula = Actual Quantities: Like the specific amounts in the full recipe: 100g flour, 200g water, and 100g sugar (maintaining the same 1:2:1 ratio).

For glucose:

  • The empirical formula CH2O tells you the basic ratio: 1 part carbon, 2 parts hydrogen, 1 part oxygen.
  • The molecular formula C6H12O6 tells you exactly how many atoms are in one molecule: 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms.

Both formulas maintain the same 1:2:1 ratio, but the molecular formula tells you the actual size of the molecule.

2. Finding the Empirical Formula #

The empirical formula tells us the simplest ratio of atoms in a compound. Finding it involves converting mass data to mole ratios.

Step-by-Step Method to Calculate Empirical Formula #

  1. Start with percentage or mass of each element in the compound
  2. Convert each mass to moles by dividing by the element’s relative atomic mass
  3. Find the simplest ratio by dividing all values by the smallest number of moles
  4. Convert to whole numbers if necessary by multiplying all values by a suitable factor
  5. Write the empirical formula using the whole number values as subscripts

Example 1: Finding the Empirical Formula from Percentage Composition #

A compound contains: 40.0% Carbon, 6.7% Hydrogen, and 53.3% Oxygen by mass.

Find its empirical formula.

Step 1: Convert percentages to masses (assuming 100g of compound) #

Carbon: 40.0 g

Hydrogen: 6.7 g

Oxygen: 53.3 g

Step 2: Convert masses to moles #

Carbon: 40.0 ÷ 12 = 3.33 mol

Hydrogen: 6.7 ÷ 1 = 6.7 mol

Oxygen: 53.3 ÷ 16 = 3.33 mol

Step 3: Find the simplest ratio by dividing by the smallest value (3.33) #

Carbon: 3.33 ÷ 3.33 = 1

Hydrogen: 6.7 ÷ 3.33 = 2.01 ≈ 2

Oxygen: 3.33 ÷ 3.33 = 1

Step 4: Write the empirical formula #

CH2O

Example 2: Finding the Empirical Formula from Mass Data #

A compound contains: 2.4g of Carbon, 0.4g of Hydrogen, and 3.2g of Oxygen.

Find its empirical formula.

Understanding Moles #

A mole is simply a counting unit in chemistry – similar to how we count eggs in dozens. One mole of any element contains exactly 6.02 × 1023 atoms of that element (known as Avogadro’s constant).

We convert mass to moles by dividing by the relative atomic mass (the mass of one mole of an element in grams):

Number of moles = Mass of element (g) ÷ Relative atomic mass (g/mol)

The relative atomic masses needed are:

  • Carbon (C): 12 g/mol
  • Hydrogen (H): 1 g/mol
  • Oxygen (O): 16 g/mol

Step 1: Convert masses to moles #

Carbon: 2.4 ÷ 12 = 0.2 mol (We divide by 12 because carbon’s relative atomic mass is 12)

Hydrogen: 0.4 ÷ 1 = 0.4 mol (We divide by 1 because hydrogen’s relative atomic mass is 1)

Oxygen: 3.2 ÷ 16 = 0.2 mol (We divide by 16 because oxygen’s relative atomic mass is 16)

Step 2: Find the simplest ratio by dividing by the smallest value (0.2) #

Carbon: 0.2 ÷ 0.2 = 1

Hydrogen: 0.4 ÷ 0.2 = 2

Oxygen: 0.2 ÷ 0.2 = 1

Step 3: Write the empirical formula #

CH2O

3. Finding the Molecular Formula #

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

Step-by-Step Method to Calculate Molecular Formula #

  1. First, determine the empirical formula of the compound
  2. Calculate the empirical formula mass by adding the relative atomic masses of all atoms in the empirical formula
  3. Calculate the formula ratio: Divide the relative molecular mass by the empirical formula mass
  4. Calculate the molecular formula: Multiply all subscripts in the empirical formula by the formula ratio

Example 3: Finding the Molecular Formula from the Empirical Formula and Relative Molecular Mass #

A compound has an empirical formula of CH2O and a relative molecular mass of 180.

Find its molecular formula.

Step 1: Calculate the empirical formula mass #

C: 1 × 12 = 12

H: 2 × 1 = 2

O: 1 × 16 = 16

Empirical formula mass = 12 + 2 + 16 = 30

Step 2: Calculate the formula ratio #

Formula ratio = Relative molecular mass ÷ Empirical formula mass

Formula ratio = 180 ÷ 30 = 6

Step 3: Calculate the molecular formula #

Molecular formula = Empirical formula × Formula ratio

Molecular formula = (CH2O) × 6 = C6H12O6

Example 4: Finding the Molecular Formula from Percentage Composition and Relative Molecular Mass #

A compound contains: 85.7% Carbon and 14.3% Hydrogen by mass. Its relative molecular mass is 42.

Find its molecular formula.

Step 1: Calculate the empirical formula #

Carbon: 85.7 ÷ 12 = 7.14 mol

Hydrogen: 14.3 ÷ 1 = 14.3 mol

Dividing both by the smaller value (7.14):

Carbon: 7.14 ÷ 7.14 = 1

Hydrogen: 14.3 ÷ 7.14 = 2

Empirical formula = CH2

Step 2: Calculate the empirical formula mass #

C: 1 × 12 = 12

H: 2 × 1 = 2

Empirical formula mass = 12 + 2 = 14

Step 3: Calculate the formula ratio #

Formula ratio = Relative molecular mass ÷ Empirical formula mass

Formula ratio = 42 ÷ 14 = 3

Step 4: Calculate the molecular formula #

Molecular formula = Empirical formula × Formula ratio

Molecular formula = (CH2) × 3 = C3H6

4. Calculating Relative Molecular Mass #

The relative molecular mass (Mr) is the sum of the relative atomic masses of all atoms in a molecule.

How to Calculate Relative Molecular Mass #

  1. Identify the number of atoms of each element in the molecular formula
  2. Multiply each by its relative atomic mass (from the periodic table)
  3. Add up all values to get the relative molecular mass

Example 5: Calculating the Relative Molecular Mass #

Calculate the relative molecular mass of ethanoic acid (CH3COOH).

Element Number of atoms Relative atomic mass Total mass contribution
Carbon (C) 2 12 2 × 12 = 24
Hydrogen (H) 4 1 4 × 1 = 4
Oxygen (O) 2 16 2 × 16 = 32
Relative molecular mass (Mr) 60

The relative molecular mass of ethanoic acid (CH3COOH) is 60.

5. Practice Problems #

Here are some practice problems to test your understanding of empirical and molecular formulas.

Problem 1: Finding Empirical Formula from Percentage Composition #

An ester Y has the following composition by mass: 48.6% carbon, 8.1% hydrogen, and 43.3% oxygen. Calculate its empirical formula.

Problem 2: Calculating Relative Molecular Mass #

Ethylbutanoic acid has the molecular formula C6H12O2. Complete the following table to calculate its relative molecular mass:

Element Number of atoms Relative atomic mass Total mass contribution
Carbon 6 12 ?
Hydrogen 12 1 ?
Oxygen 2 16 ?
Relative molecular mass (Mr) ?

Problem 3: Finding Molecular Formula #

An ester Z has the empirical formula C2H4O and a relative molecular mass of 88. Determine its molecular formula.

Key Points to Remember #

  • Empirical formula shows the simplest whole-number ratio of atoms
  • Molecular formula shows the actual number of atoms in the molecule
  • Molecular formula = Empirical formula × n (where n is a whole number)
  • To find the empirical formula, convert masses to moles and find the simplest ratio
  • To find the molecular formula, you need both the empirical formula and the relative molecular mass
  • Relative molecular mass is calculated by adding up the masses of all atoms in the molecule
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