Empirical and Molecular Formulas, The Mole, and Mass Percent in Chemistry

Empirical Formula vs. Molecular Formula

Definitions and Key Differences

Understanding the difference between empirical and molecular formulas is essential in chemistry, as these formulas describe the composition of chemical compounds in terms of their constituent elements.

• Empirical Formula: Represents the simplest whole-number ratio of the elements in a compound.

• Molecular Formula: Shows the actual number of atoms of each element in a molecule of the compound.

By convention, empirical formulas must contain whole numbers for each atom, reflecting the simplest ratio.

Compound	Molecular Formula	Empirical Formula
Glucose	C6H12O6	CH2O
Octane	C8H18	C4H9
Salicylic Acid	C7H6O3	C7H6O3

Calculating the Empirical Formula

The empirical formula can be determined from the mass percent or mass of elements in a compound.

1. Step 1: Write down the mass (in grams) for each element in the question.

2. Step 2: Convert all masses into moles by dividing by the atomic mass of each element.

3. Step 3: Divide each mole number by the smallest value to obtain whole numbers for each element.

4. Step 4: If necessary, multiply by a factor to get whole numbers.

Example: Determine the empirical formula of a compound that is 68.40% chromium and 31.60% oxygen.

Calculating the Molecular Formula

Once the empirical formula is determined, the molecular formula can be found if the molar mass is known.

1. Step 1: Calculate the empirical formula mass.

2. Step 2: Divide the molar mass of the compound by the empirical formula mass to determine the n-factor.

3. Step 3: Multiply the subscripts in the empirical formula by the n-factor to get the molecular formula.

Example: After a workout session, lactic acid (M = 90.08 g/mol) forms in muscle tissue. Elemental analysis shows this compound contains 40% C, 6.7% H, and 53.3% O. Determine the molecular formula.

The Mole Concept

Definition and Applications

The mole is a fundamental unit in chemistry that connects the mass of a substance to the number of particles (atoms, ions, molecules, or formula units).

• Atom: Single element with no charge.

• Ion: Single element with a charge.

• Molecule: Compound with two or more atoms.

• Formula Unit: General term for a compound composed of ions.

Example: Which of the following compounds would not be associated with the term "formula unit"? (Na2CO3, CH3COONa, BF3, MnCl2)

Avogadro's Number and Particles

Avogadro's Number ($6.022 \times 10^{23}$) is the number of particles in one mole of a substance.

• Particles: Can refer to atoms, ions, molecules, or formula units.

Example: How many moles of chlorine gas are there in $8.33 \times 10^{23}$ molecules?

Converting Between Mass and Moles

One mole of a substance is equal to its molar mass in grams.

• Molar Mass: The mass of one mole of a substance, usually in g/mol.

Example: How many grams of chlorine gas are there in 2.34 moles?

Converting Between Mass and Particles

The mole serves as a bridge between mass and number of particles.

• Atoms, Ions, Molecules, Formula Units → Mole → Grams

Example: How many grams of Cl2 contain $9.25 \times 10^{14}$ molecules of Cl2?

Calculating Mass Percent

Definition and Formula

Mass percent (weight percent) is the percentage of a given element in a compound, calculated as follows:

Mass Percent Formula:

$\text{Mass Percent} = \frac{\text{mass of element in 1 mole of compound}}{\text{mass of 1 mole of compound}} \times 100\%$

• It deals with the mass (in grams) of the selected element and 1 mole of the compound.

Example: Calculate the mass percent of carbon within sodium carbonate, Na2CO3.

Practice Problems

Empirical and Molecular Formula Practice

• A compound that contains only carbon, hydrogen, and oxygen is composed of 48.64% C and 43.2% O by mass. What is the empirical formula?

• Elemental analysis of a sample of an ionic compound showed 2.82 g of Na, 4.35 g of Cl, and 7.83 g of O. What is the empirical formula?

• A compound composed of carbon, hydrogen, and chlorine contains $4.19 \times 10^{23}$ hydrogen atoms. If 9.00 g of the compound also contains 55.05% chlorine by mass, what is the empirical formula?

• What is the molecular formula for a compound with empirical formula NPCI2 and molar mass 347.64 g/mol?

• Cortisol (M = 362.47 g/mol), a steroid hormone, contains 69.6% C, 8.34% H, and 22.1% O by mass. What is its molecular formula?

• Elemental analysis of a pure compound indicated 72.2% C, 8.50% H, remainder O. If 0.250 moles of the compound weighs 41.55 g, what is the molecular formula?

The Mole and Particle Calculations Practice

• If a sample of sodium chloride, NaCl, contains 73.1 kg, what is its number of formula units?

• Calculate the number of oxygen atoms found in 783.9 g NiCl2 · 6 H2O.

• If the density of water is 1.00 g/mL at 25°C, calculate the number of water molecules found in $1.50 \times 10^3$ μL of water.

• A cylindrical copper wire is used for fences around a house. The wire has a diameter of 0.0750 in. How many copper atoms are found in a 5.160 cm piece? The density of copper is 8.96 g/cm3. (V = π × r2 × h)

• The density of the sun is 1.41 g/cm3 and its volume is $1.41 \times 10^{27}$ m3. How many hydrogen molecules are in the sun if we assume all the mass is hydrogen gas?

Mass Percent Practice

• Determine the percent composition of nitrogen and oxygen in nitrogen dioxide, NO2.

Additional info: Some steps and definitions have been expanded for clarity and completeness. All equations are provided in LaTeX format for academic accuracy.