Moles, Molar Mass, and Chemical Equations: Study Notes for General Chemistry

7.4 The Mole

Definition and Importance of the Mole

The mole is a fundamental unit in chemistry used to express amounts of a chemical substance. It allows chemists to count particles (atoms, molecules, ions) by weighing them.

• Definition: One mole contains exactly $6.022 \times 10^{23}$ particles (Avogadro's number).

• Application: Used to relate mass, number of particles, and chemical reactions.

• Example: 1 mole of H2O contains $6.022 \times 10^{23}$ water molecules.

Avogadro's Number

Understanding Avogadro's Number

Avogadro's number ($N_A$) is the number of particles in one mole of a substance.

• Value: $N_A = 6.022 \times 10^{23}$ particles/mole

• Significance: Links the macroscopic scale (grams) to the microscopic scale (atoms/molecules).

• Example: 1 mole of carbon atoms = $6.022 \times 10^{23}$ carbon atoms.

Mole of Atoms and Molecules

Counting Particles Using Moles

The mole concept allows conversion between mass, moles, and number of particles.

• Atoms: 1 mole of any element contains $6.022 \times 10^{23}$ atoms.

• Molecules: 1 mole of a compound contains $6.022 \times 10^{23}$ molecules.

• Example: 1 mole of NaCl contains $6.022 \times 10^{23}$ formula units of NaCl.

Particles in One-Mole Samples

Examples of One-Mole Quantities

Substance	1 Mole Contains
Carbon (C)	$6.022 \times 10^{23}$ atoms
Water (H2O)	$6.022 \times 10^{23}$ molecules
Sodium chloride (NaCl)	$6.022 \times 10^{23}$ formula units

Conversion Factors: Avogadro's Number

Using Avogadro's Number in Calculations

Avogadro's number is used as a conversion factor between moles and number of particles.

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

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

Calculating Atoms or Molecules

Stepwise Guide

• Step 1: Write the given quantity (moles or particles).

• Step 2: Use Avogadro's number as a conversion factor.

• Step 3: Set up the calculation so units cancel appropriately.

• Step 4: Solve for the desired quantity.

Converting Moles to Molecules

Worked Example

• Example: How many molecules are in 2.5 moles of CO2?

• Calculation: $2.5 \text{ mol} \times 6.022 \times 10^{23} \frac{\text{molecules}}{\text{mol}} = 1.51 \times 10^{24}$ molecules

Moles of Elements in a Formula

Determining Moles of Each Element

In a compound, the number of moles of each element is determined by the chemical formula.

• Example: In 1 mole of Na2SO4:

• Na: 2 moles

• S: 1 mole

• O: 4 moles

Calculating Moles of an Element in a Compound

Stepwise Guide

• Step 1: Identify the number of atoms of the element in the formula.

• Step 2: Multiply the number of moles of the compound by the number of atoms of the element per formula unit.

• Step 3: Result is the moles of the element.

Molar Mass

Definition and Use

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol).

• For elements: Molar mass equals the atomic mass from the periodic table.

• For compounds: Molar mass is the sum of the atomic masses of all atoms in the formula.

• Example: Molar mass of H2O = 2(1.01 g/mol) + 16.00 g/mol = 18.02 g/mol

Calculating Molar Mass of a Compound

Stepwise Guide

• Step 1: List the number of each type of atom in the formula.

• Step 2: Multiply the number of atoms by their atomic masses.

• Step 3: Add the masses to obtain the total molar mass.

Converting Mass to Moles

Using Molar Mass as a Conversion Factor

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

• Example: How many moles are in 58.5 g of NaCl? $\frac{58.5 \text{ g}}{58.44 \text{ g/mol}} = 1.00 \text{ mol}$

Map: Mass–Moles–Particles

Relationships Between Mass, Moles, and Particles

Quantity	Conversion Factor
Mass (g) to Moles	Divide by molar mass (g/mol)
Moles to Particles	Multiply by $6.022 \times 10^{23}$
Particles to Moles	Divide by $6.022 \times 10^{23}$
Moles to Mass (g)	Multiply by molar mass (g/mol)

Mole Relationships in Chemical Equations

Stoichiometry and Balanced Equations

Balanced chemical equations show the mole ratios of reactants and products.

• Example: $2H_2 + O_2 \rightarrow 2H_2O$

• 2 moles H2 react with 1 mole O2 to produce 2 moles H2O

Law of Conservation of Mass

Fundamental Principle in Chemistry

The law of conservation of mass states that mass is neither created nor destroyed in a chemical reaction.

• Application: The total mass of reactants equals the total mass of products.

• Example: Burning magnesium: mass of Mg + mass of O2 = mass of MgO formed.

Stoichiometric Calculations

Using Mole Ratios to Calculate Quantities

• Step 1: Write the balanced chemical equation.

• Step 2: Identify the known and unknown quantities.

• Step 3: Use mole ratios from the equation to set up conversion factors.

• Step 4: Convert between mass, moles, and particles as needed.

Equations: Mass of A to Mass of B

General Approach

• Step 1: Convert mass of A to moles of A using molar mass.

• Step 2: Use mole ratio from balanced equation to find moles of B.

• Step 3: Convert moles of B to mass of B using molar mass.

• Formula: $\text{mass of B} = \text{mass of A} \times \frac{1 \text{ mol A}}{\text{molar mass of A}} \times \frac{\text{mol B}}{\text{mol A}} \times \text{molar mass of B}$

Summary Table: Key Conversion Factors

Conversion	Factor
Mass (g) to Moles	$\frac{1 \text{ mol}}{\text{molar mass (g)}}$
Moles to Mass (g)	$\text{molar mass (g)}$
Moles to Particles	$6.022 \times 10^{23}$
Particles to Moles	$\frac{1 \text{ mol}}{6.022 \times 10^{23}}$
Mole Ratio (from equation)	$\frac{\text{mol B}}{\text{mol A}}$

Practice Problems and Solutions

Worked Examples

• Example 1: How many molecules are in 3.0 moles of H2O?

• Solution: $3.0 \text{ mol} \times 6.022 \times 10^{23} = 1.81 \times 10^{24}$ molecules

• Example 2: What is the mass of 2.5 moles of NaCl?

• Solution: $2.5 \text{ mol} \times 58.44 \text{ g/mol} = 146.1 \text{ g}$

Additional info: These notes expand on the original slides by providing full definitions, stepwise guides, and example calculations for all major concepts related to moles, molar mass, and stoichiometry in chemical equations.