The Mole Concept: Chemical Composition and Quantities in Chemical Reactions

Concept: Mole Concept

The Mole

The mole is a fundamental unit in chemistry that represents a specific number of particles, atoms, ions, or molecules. It allows chemists to count entities at the atomic scale using macroscopic measurements.

• Definition: One mole of a substance contains the same number of units as atoms in 12.00 g of Carbon-12.

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

• Atoms: A single element with no charge.

• Ions: An atom or molecule with a charge.

• Molecules: A compound with two or more atoms bonded together.

• Formula Units: The lowest ratio of ions in an ionic compound.

Example: Which of the following compounds would not be associated with the term "formula unit"?

• NaCO3

• CH3COOH (Answer)

Additional info: Formula units refer to ionic compounds, while molecules refer to covalent compounds.

Converting Between Moles and Particles

To relate the number of moles to the number of particles (atoms, molecules, ions), Avogadro's number is used as a conversion factor.

• Formula: $1 \text{ mole} = 6.022 \times 10^{23}$ particles

• Example: 1 mole of chlorine gas contains $6.022 \times 10^{23}$ molecules of Cl2.

Example: How many moles of chlorine gas are there in $3.01 \times 10^{23}$ molecules?

• Calculation: $\frac{3.01 \times 10^{23}}{6.022 \times 10^{23}} = 0.500$ moles

Converting Between Mass and Moles

The mass of a substance can be converted to moles using its molar mass, which is the mass of one mole of that substance.

• Formula: $\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}$

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

• Calculation: $2.34 \text{ mol} \times 70.90 \text{ g/mol} = 166.91 \text{ g}$

Connecting Mass, Moles, and Particles

The mole serves as a bridge between mass, number of particles, and chemical formulas. This allows chemists to convert between grams, moles, and number of atoms/molecules/formula units.

• Conversion Pathways: Atoms, Ions, Molecules, Formula Units → Mole → Grams

• Example: How many grams of O2 contain $9.25 \times 10^{25}$ molecules?

• Calculation: $9.25 \times 10^{25} \text{ molecules} \times \frac{1 \text{ mol}}{6.022 \times 10^{23} \text{ molecules}} \times \frac{32.00 \text{ g}}{1 \text{ mol}} = 4916 \text{ g}$

Practice Problems

• Practice 1: If a sample of sodium chloride (NaCl) contains 71.1 kg, what is its number of formula units? $6.12 \times 10^{25}$ formula units

• Practice 2: Calculate the number of oxygen atoms found in 71.1 g NO2 + H2O. $2.14 \times 10^{24}$ O atoms

• Practice 3: If the density of water is 1.00 g/mL at 25°C, calculate the number of water molecules found in 1.50 × 104 μL of water. $5.01 \times 10^{23}$ molecules

• Practice 4: A cylindrical copper wire is used for the furnace around a house. The copper wire has a diameter of 0.750 in. How many copper atoms are found in its 160 m length? The density of copper is 8.96 g/cm3 ($V = \pi r^2 h$). $6.56 \times 10^{25}$ Cu atoms

• Practice 5: 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? $8.13 \times 10^{57}$ H2 molecules