## Structure 1.4.4—The empirical formula of a compound gives the simplest ratio of atoms of each element present in that compound. The molecular formula gives the actual number of atoms of each element present in a molecule.

Structure 1.4.4—The empirical formula of a compound gives the simplest ratio of atoms of each element present in that compound. The molecular formula gives the actual number of atoms of each element present in a molecule.

What You’ll Learn:

• Interconvert the percentage composition by mass and the empirical formula.
• Determine the molecular formula of a compound from its empirical formula and molar mass.

Keywords

Tool 1—What are the considerations in the choice of glassware used in preparing a standard solution and a serial dilution?
Tool 1, Inquiry 2—How can a calibration curve be used to determine the concentration of a solution?

## Empirical Formula

The empirical formula of a compound represents the simplest whole number ratio of the atoms present in the compound. It is the formula that provides the relative number of atoms of each element in a compound in the smallest possible integer ratio. The empirical formula is important because it helps to determine the chemical formula of a compound.

The empirical formula can be used to:

1. Identify the simplest whole number ratio of atoms in a compound. This information can be used to determine the chemical formula of the compound.
2. Calculate the percentage composition of a compound. Once the empirical formula is known, the percentage composition of the compound can be determined by finding the total molar mass of the empirical formula and dividing the mass of each element by the total molar mass.

To calculate the empirical formula, you can follow these steps:

1. Convert the mass of each element in the compound to moles using its molar mass.
2. Divide the number of moles of each element by the smallest number of moles to obtain the simplest whole number ratio of the atoms present in the compound.
3. Write the empirical formula using the whole number ratios obtained in step 2.

Here is an example:

Question: Determine the empirical formula of a compound that is composed of 30.4% nitrogen and 69.6% oxygen by mass.

Solution: Given the mass percentages, assume 100 g of the compound, which contains 30.4 g of nitrogen and 69.6 g of oxygen.

Calculate the number of moles of each element:

• Moles of nitrogen = 30.4 g / 14.01 g/mol = 2.17 mol
• Moles of oxygen = 69.6 g / 16.00 g/mol = 4.35 mol

Divide each of the mole values by the smallest mole value, which is 2.17 mol:

• Nitrogen: 2.17 mol / 2.17 mol = 1
• Oxygen: 4.35 mol / 2.17 mol = 2

Write the empirical formula using the whole number ratio obtained in step 3. The empirical formula is NO2.

Therefore, the empirical formula of the compound with 30.4% nitrogen and 69.6% oxygen by mass is NO2.

## Molecular formula

The empirical formula represents the simplest whole-number ratio of atoms in a compound. However, a compound can have multiple molecular formulas that correspond to the same empirical formula. Therefore, the empirical formula alone cannot determine the exact molecular formula of a compound.

To find the molecular formula, you need additional information, such as the molar mass of the compound.

Once you have the empirical formula, you can calculate the empirical formula mass by summing up the atomic masses of each element in the empirical formula. The empirical formula mass represents the mass of one empirical formula unit of the compound.

Next, you need to determine the molar mass of the compound by measuring the actual mass of one mole of the compound. This can be done experimentally or by adding up the masses of all the atoms in one molecular formula unit.

Finally, you can calculate the molecular formula of the compound by dividing the molar mass of the compound by the empirical formula mass. The resulting value represents the ratio of the actual molecular mass of the compound to the empirical formula mass.

To summarize:

1. Calculate the empirical formula mass by adding up the atomic masses of the elements in the empirical formula.
2. Determine the molar mass of the compound experimentally or by adding up the masses of all the atoms in one molecular formula unit.
3. Divide the molar mass of the compound by the empirical formula mass to obtain a whole number, which represents the factor by which the empirical formula should be multiplied to obtain the molecular formula.
4. Multiply the empirical formula by the factor obtained in step 3 to obtain the molecular formula.

Here’s an example:

The empirical formula of a compound is C2H5O and its experimental molar mass is 90 g/mol. Determine the molecular formula of the compound.

1. Calculate the empirical formula mass:
• Carbon: 2 × 12.01 g/mol = 24.02 g/mol
• Hydrogen: 5 × 1.01 g/mol = 5.05 g/mol
• Oxygen: 1 × 16.00 g/mol = 16.00 g/mol
• Empirical formula mass = 24.02 + 5.05 + 16.00 = 45.07 g/mol
1. Determine the experimental molar mass of the compound, which is 90 g/mol.
2. Divide the molar mass of the compound by the empirical formula mass to obtain a whole number factor:
• 90 g/mol / 45.07 g/mol ≈ 2
1. Multiply the empirical formula by the factor obtained in step 3 to obtain the molecular formula:
• C2H5O × 2 = C4H10O2

Therefore, the molecular formula of the compound with empirical formula C2H5O and experimental molar mass 88 g/mol is C4H10O2.

Questions

1. What is the empirical formula of a compound that contains 40% carbon, 6.67% hydrogen, and 53.33% oxygen by mass?
2. A compound with the empirical formula CH2O has a molar mass of 90 g/mol. What is its molecular formula?
3. A compound contains 28.6% nitrogen and 71.4% oxygen by mass. What is its empirical formula?
4. The empirical formula of a compound is CH2Cl. Its molar mass is 99 g/mol. What is its molecular formula?
5. A compound contains 53.33% carbon, 15.56% hydrogen, and 31.11% oxygen by mass. What is its empirical formula?
6. The empirical formula of a compound is NH3. Its molar mass is 34 g/mol. What is its molecular formula?
7. A compound with the empirical formula C3H5BrO has a molar mass of 200 g/mol. What is its molecular formula?
8. What is the empirical formula of a compound that contains 27.3% sodium, 16.3% sulfur, and 56.4% oxygen by mass?
9. The empirical formula of a compound is CH2. Its molar mass is 84 g/mol. What is its molecular formula?
10. A compound contains 18.9% nitrogen and 81.1% oxygen by mass. What is its empirical formula?