Chemical Composition: Moles, Mass, and Counting Atoms (Ch. 6.1–6.3)

Chemical Composition: Moles, Mass, and Counting Atoms

Objectives

Understanding chemical composition is essential for quantifying substances in chemistry. This section introduces the mole concept, relationships between mass and number of atoms, and how to use chemical formulas for calculations.

• Why use mass to count atoms? Atoms are extremely small and numerous, making direct counting impractical. Chemists use mass as a proxy for counting atoms.

• Relationship between moles and number of atoms: The mole is a counting unit that relates the number of atoms to a measurable quantity.

• Relationship between grams and moles: Mass in grams can be converted to moles using the molar mass of an element or compound.

• Relationship between grams and number of atoms: By combining molar mass and Avogadro's number, grams can be related directly to the number of atoms.

Counting Atoms: The Mole Concept

Definition and Importance

The mole (mol) is the SI unit for amount of substance, allowing chemists to count atoms, molecules, or ions by weighing them.

• Avogadro's Number: One mole contains $6.022 \times 10^{23}$ entities (atoms, molecules, etc.).

• Analogy: Just as a "dozen" means 12 items, a "mole" means $6.022 \times 10^{23}$ items.

• Example: 1 mol of helium atoms = $6.022 \times 10^{23}$ He atoms.

Relating Mass, Moles, and Number of Atoms

Molar Mass

The molar mass of an element is the mass of one mole of its atoms, expressed in grams per mole (g/mol). It is numerically equal to the atomic mass in atomic mass units (amu).

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

• General Formula:

  • For any element: $\text{Molar mass (g/mol)} = \text{Atomic mass (amu)}$

Conversions Between Grams, Moles, and Atoms

Conversions are essential for solving chemical problems. The following relationships are used:

• Grams to Moles:

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

  • Example: Number of moles of carbon in a 0.58 g diamond: $\text{Moles of C} = \frac{0.58\ \text{g}}{12.01\ \text{g/mol}} = 0.048\ \text{mol}$

• Moles to Number of Atoms:

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

  • Example: Number of helium atoms in 2 mol He: $2\ \text{mol} \times 6.022 \times 10^{23}\ \text{atoms/mol} = 1.2044 \times 10^{24}\ \text{atoms}$

• Grams to Number of Atoms:

  • Step 1: Convert grams to moles using molar mass.

  • Step 2: Convert moles to atoms using Avogadro's number.

  • Example: Number of aluminum atoms in a 3.62 g can: Step 1: $\text{Moles of Al} = \frac{3.62\ \text{g}}{26.98\ \text{g/mol}} = 0.134\ \text{mol}$ Step 2: $0.134\ \text{mol} \times 6.022 \times 10^{23}\ \text{atoms/mol} = 8.08 \times 10^{22}\ \text{atoms}$

Mole Conversion Diagram

The following diagram summarizes the relationships:

• Grams → Moles → Number of Atoms

• Use molar mass to convert between grams and moles.

• Use Avogadro's number to convert between moles and number of atoms.

Application: Sodium in Diet

Calculating Sodium Intake

Dietary recommendations often specify the amount of sodium to consume. However, sodium is usually ingested as sodium chloride (NaCl), so calculations must account for the mass of sodium in NaCl.

• Recommended sodium intake: 2.3 g per day.

• Key question: How many grams of sodium chloride can you consume and still stay below the sodium recommendation?

• Calculation steps:

  1. Find the mass of sodium in NaCl.

  2. Find the mass of chlorine in NaCl.

  3. Relate the mass of sodium to the total mass of NaCl.

  4. Calculate the amount of NaCl that provides 2.3 g sodium.

• Example:

  • Molar mass of Na = 22.99 g/mol

  • Molar mass of Cl = 35.45 g/mol

  • Molar mass of NaCl = 22.99 + 35.45 = 58.44 g/mol

  • Fraction of Na in NaCl: $\frac{22.99}{58.44} = 0.393$

  • To get 2.3 g Na: $\frac{2.3\ \text{g Na}}{0.393} = 5.85\ \text{g NaCl}$

Worked Example: Counting Nails Analogy

Using Mass to Count Items

Just as chemists use mass to count atoms, you can use mass to count everyday items like nails.

• Example: You buy 2.60 lb of nails, and a dozen nails weigh 0.150 lb. How many nails did you buy?

  • Step 1: $\frac{2.60\ \text{lb}}{0.150\ \text{lb/dozen}} = 17.33\ \text{dozen nails}$

  • Step 2: $17.33\ \text{dozen} \times 12 = 208\ \text{nails}$

Additional info: This analogy helps students understand why mass is used to count atoms in chemistry.

Summary Table: Key Relationships

Conversion	Formula	Example
Grams to Moles	$\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}}$	0.58 g C → $\frac{0.58}{12.01} = 0.048$ mol
Moles to Atoms	$\text{Atoms} = \text{Moles} \times 6.022 \times 10^{23}$	0.048 mol C → $0.048 \times 6.022 \times 10^{23} = 2.89 \times 10^{22}$ atoms
Grams to Atoms	Grams → Moles → Atoms	3.62 g Al → $\frac{3.62}{26.98} = 0.134$ mol → $0.134 \times 6.022 \times 10^{23} = 8.08 \times 10^{22}$ atoms