The Mole: Conversions Between Mass, Moles, and Particles in GOB Chemistry

The Mole

Definition and Importance

The mole is a fundamental unit in chemistry that represents a specific number of particles (atoms, ions, molecules, or formula units). It allows chemists to count entities by weighing them, bridging the microscopic and macroscopic worlds.

• Atom: A single element with no charge.

• Ion: A single element with a positive or negative charge.

• Molecule: A compound with two or more nonmetals together.

• Formula Unit: General term for a compound composed of a metal and nonmetal.

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

• a) Na2CO3

• b) CH3COONa

• c) BF3 (Correct: BF3 is a molecule, not a formula unit)

• d) MnCl2

Converting Between Moles and Particles

Avogadro's Number

Avogadro's Number defines the number of particles in one mole of a substance:

• $6.022 \times 10^{23}$ particles per mole

Particles can refer to atoms, ions, molecules, or formula units depending on the substance.

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

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

• a) $7.23 \times 10^{-1}$ mol

• b) $5.02 \times 10^{-1}$ mol

• c) 1.38 mol (Correct: $8.33 \times 10^{23} \div 6.022 \times 10^{23} \approx 1.38$ mol)

• d) $6.65 \times 10^{2}$ mol

Converting Between Mass and Moles

Molar Mass

The molar mass of a substance is the mass of one mole of that substance, typically expressed in grams per mole (g/mol).

• Example: 1 mole of chlorine gas (Cl2) weighs 70.90 grams.

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

• a) 82.85 g

• b) 165.91 g (Correct: $2.34 \text{ mol} \times 70.90 \text{ g/mol} = 165.91 \text{ g}$)

• c) 0.0669 g

• d) 0.033 g

Converting Between Mass and Particles

Using the Mole as a Bridge

The mole serves as a bridge to connect mass, number of particles, and chemical formulas. The conversion process typically involves two steps:

• Mass → Moles → Particles

• Particles → Moles → Mass

Example: How many grams of Cl2 contain $9.25 \times 10^{24}$ molecules of Cl2?

• Step 1: Convert molecules to moles using Avogadro's number.

• Step 2: Convert moles to grams using molar mass.

Formula:

• $\text{Moles} = \frac{\text{Number of particles}}{6.022 \times 10^{23}}$

• $\text{Mass (g)} = \text{Moles} \times \text{Molar mass (g/mol)}$

Practice Problems

Applying Mole Concepts

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

• Practice: Calculate the number of oxygen atoms found in 783.9 g of NaCl · 6 H2O.

• Practice: If the density of water is 1.00 g/mL at 25°C, calculate the number of water molecules found in 1.50 × 103 μL of water.

• Practice: A cylindrical copper wire is used for fences around a house. The copper 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)

• Practice: The density of the sun is 1.41 g/cm3 and its volume is 1.41 × 1027 m3. How many hydrogen molecules are in the sun if we assume all the mass is hydrogen gas?

Summary Table: Mole Relationships

Quantity	Conversion Factor	Example
Mass (g)	Molar Mass (g/mol)	Grams → Moles: $\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}$
Moles	Avogadro's Number ($6.022 \times 10^{23}$)	Moles → Particles: $\text{Particles} = \text{Moles} \times 6.022 \times 10^{23}$
Particles	Avogadro's Number ($6.022 \times 10^{23}$)	Particles → Moles: $\text{Moles} = \frac{\text{Particles}}{6.022 \times 10^{23}}$

Additional info: The notes include practice problems that reinforce the use of the mole as a bridge between mass, moles, and particles, which is a core concept in GOB Chemistry.