Chapter 6: Chemical Composition – The Mole, Molar Mass, and Chemical Formulas

Chapter 6: Chemical Composition

Introduction to Chemical Composition

Chemical composition is a fundamental concept in general chemistry, describing the relative amounts of elements in compounds and mixtures. Understanding chemical composition allows chemists to relate the mass of substances to the number of atoms, molecules, or ions present, and to interpret chemical formulas quantitatively.

The Mole Concept

Definition and Importance of the Mole

The mole is a counting unit used by chemists to express amounts of a chemical substance. It allows for the conversion between the number of particles (atoms, molecules, ions) and measurable mass.

• Avogadro's Number: $6.022 \times 10^{23}$ particles per mole.

• One mole of any substance contains $6.022 \times 10^{23}$ units of that substance.

• The mole bridges the gap between the atomic scale and the macroscopic scale.

Example: 1 mole of copper atoms contains $6.022 \times 10^{23}$ copper atoms.

Counting by Weighing: From Nails to Atoms

Just as hardware stores sell nails by weight, chemists count atoms by weighing samples. Because atoms are extremely small and numerous, the mole is used as a convenient counting unit.

• For nails: 1 dozen = 12 nails; for atoms: 1 mole = $6.022 \times 10^{23}$ atoms.

• Conversion factors are used to relate mass to number of items.

Example: To find the number of nails in 2.60 lb, use the conversion factors for weight per dozen and number per dozen.

Molar Mass and Atomic Mass

Atomic Mass Unit (amu) and Molar Mass

The atomic mass unit (amu) is defined as one-twelfth the mass of a carbon-12 atom. The molar mass of an element is the mass of one mole of its atoms, numerically equal to its atomic mass in grams.

• Atomic mass: Mass of a single atom (in amu).

• Molar mass: Mass of 1 mole of atoms (in g/mol).

Example: Copper has an atomic mass of 63.55 amu; its molar mass is 63.55 g/mol.

Converting Between Grams, Moles, and Number of Atoms

Conversions between mass, moles, and number of atoms are essential in chemical calculations.

• To convert grams to moles: $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

• To convert moles to number of atoms: $\text{number of atoms} = \text{moles} \times 6.022 \times 10^{23}$

• To convert number of atoms to moles: $\text{moles} = \frac{\text{number of atoms}}{6.022 \times 10^{23}}$

Example: How many moles are in 0.589 g of carbon? $\frac{0.589\,\text{g}}{12.01\,\text{g/mol}} = 0.049\,\text{mol}$

Molar Mass of Compounds

Calculating Molar Mass of Compounds

The molar mass of a compound is the mass of one mole of its molecules or formula units. It is calculated by summing the atomic masses of all atoms in the chemical formula.

• Formula mass: Sum of atomic masses in a chemical formula (in amu).

• Molar mass: Formula mass expressed in g/mol.

Example: Water ($\mathrm{H_2O}$): $2 \times 1.01 + 16.00 = 18.02$ g/mol.

Conversions Involving Compounds

• Grams to moles: $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$

• Moles to grams:

• Moles to molecules: $\text{number of molecules} = \text{moles} \times 6.022 \times 10^{23}$

Example: What is the mass of 1.75 mol of water? $1.75 \times 18.02 = 31.54$ g

Chemical Formulas as Conversion Factors

Using Chemical Formulas to Relate Elements and Compounds

Chemical formulas indicate the ratio of atoms in a compound, which can be used as conversion factors in calculations.

• Example: $\mathrm{CO_2}$ has 2 O atoms per 1 CO2 molecule.

• Conversion factor: $2\,\text{mol O} : 1\,\text{mol CO}_2$

Converting Between Moles of Compound and Moles of Element

• Example: How many moles of O are in 1.7 mol of CaCO3? $1.7 \times \frac{3\,\text{mol O}}{1\,\text{mol CaCO}_3} = 5.1\,\text{mol O}$

Converting Between Grams of Compound and Grams of Element

• Example: What is the mass of sodium in 15 g of NaCl?

• Calculate moles of NaCl, then moles of Na, then mass of Na.

Mass Percent Composition

Definition and Calculation

Mass percent composition expresses the percentage by mass of each element in a compound.

• Formula: $\text{Mass percent of X} = \frac{\text{mass of X in sample}}{\text{mass of sample}} \times 100\%$

Example: In a 0.358-g sample of chromium oxide (0.358 g Cr, 0.523 g oxide): $\frac{0.358}{0.523} \times 100\% = 68.5\%$ Cr

Using Mass Percent as a Conversion Factor

• Mass percent can be used to convert between grams of element and grams of compound.

• Example: NaCl is 39% Na by mass: $39\,\text{g Na} : 100\,\text{g NaCl}$

Calculating Mass Percent from Chemical Formula

• Formula: $\text{Mass percent of X} = \frac{\text{mass of X in 1 mol compound}}{\text{molar mass of compound}} \times 100\%$

• Example: For CCl4: $\frac{4 \times \text{molar mass Cl}}{\text{molar mass CCl}_4} \times 100\%$

Empirical and Molecular Formulas

Empirical Formula

The empirical formula gives the simplest whole-number ratio of atoms in a compound. The molecular formula is a whole-number multiple of the empirical formula.

• Example: Hydrogen peroxide: Empirical formula HO, molecular formula H2O2

• $\text{Molecular formula} = \text{Empirical formula} \times n$

Calculating Empirical Formula from Experimental Data

1. Write down masses of each element.

2. Convert masses to moles using molar mass.

3. Write a pseudo-formula using mole values as subscripts.

4. Divide all subscripts by the smallest value to get whole numbers.

5. If subscripts are not whole numbers, multiply by a small integer to obtain whole numbers.

Example: Decomposition of water yields 3.0 g H and 24 g O. Convert to moles: $\frac{3.0}{1.01} = 3.0$ mol H, $\frac{24}{16.00} = 1.5$ mol O. Empirical formula: HO.

Calculating Molecular Formula from Empirical Formula and Molar Mass

• Find $n$ using: $n = \frac{\text{molar mass}}{\text{empirical formula molar mass}}$

• Multiply subscripts in empirical formula by $n$.

Example: Fructose has empirical formula CH2O and molar mass 180.2 g/mol. Empirical formula mass = 30.03 g/mol. $n = \frac{180.2}{30.03} = 6$. Molecular formula = C6H12O6.

Summary Table: Key Conversion Relationships

Conversion	Equation
Grams to Moles	$\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$
Moles to Number of Particles	$\text{number of particles} = \text{moles} \times 6.022 \times 10^{23}$
Moles of Compound to Moles of Element	$\text{moles of element} = \text{moles of compound} \times \frac{\text{number of element atoms}}{\text{number of compound units}}$
Mass Percent Composition	$\text{mass percent} = \frac{\text{mass of element}}{\text{mass of compound}} \times 100\%$
Molecular Formula	$\text{molecular formula} = \text{empirical formula} \times n$

Chemistry and Health: Fluoridation of Drinking Water

Fluoride in Water

Fluoride strengthens tooth enamel and helps prevent tooth decay. However, excessive fluoride can cause dental and skeletal fluorosis. The recommended intake for adults is about 1–4 mg/day, typically obtained from drinking water.

• Fluoride is often added as sodium fluoride (NaF).

• Mass percent composition can be used to calculate how much NaF to add to water to achieve a desired fluoride concentration.

Chapter Review and Learning Objectives

• Convert between moles and number of atoms.

• Convert between grams and moles.

• Convert between grams and number of atoms or molecules.

• Convert between moles of a compound and moles of a constituent element.

• Convert between grams of a compound and grams of a constituent element.

• Use mass percent composition as a conversion factor.

• Determine mass percent composition from a chemical formula.

• Determine an empirical formula from experimental data.

• Calculate a molecular formula from an empirical formula and molar mass.