Chapter 6: Chemical Composition – Moles, Mass, and Counting Atoms

Chapter 6: Chemical Composition

6.1 Counting Atoms: The Mole Concept

In chemistry, atoms are far too small and numerous to count individually. Instead, we use the concept of the mole to count atoms by mass. The mole provides a bridge between the atomic scale and the macroscopic scale, allowing chemists to relate the mass of a substance to the number of particles it contains.

• Mole (mol): The SI unit for amount of substance. One mole contains exactly $6.022 \times 10^{23}$ entities (Avogadro's number).

• Avogadro's Number: $6.022 \times 10^{23}$ particles (atoms, molecules, ions, etc.) per mole.

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

Additional info: The mole is analogous to the term "dozen" (12 items), but much larger, suitable for counting atoms.

6.2 Relating Moles, Mass, and Number of Atoms

The mass of a mole of atoms is called the molar mass, which is numerically equal to the atomic mass in grams per mole (g/mol). This allows conversion between mass, moles, and number of atoms.

• Molar Mass: The mass of 1 mole of a substance, expressed in g/mol. For example, copper has a molar mass of 63.55 g/mol.

• Atomic Mass Unit (amu): The atomic mass of an element in amu is numerically equal to the molar mass in g/mol.

• Conversion Relationships:

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

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

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

• Example: Calculate the number of moles of carbon in a 0.58 g diamond:

  • Molar mass of carbon = 12.01 g/mol

  • $\text{moles} = \frac{0.58\ \text{g}}{12.01\ \text{g/mol}} = 0.048\ \text{mol}$

Additional info: The molar mass varies for different elements (e.g., 32.07 g/mol for sulfur, 6.94 g/mol for lithium).

6.3 Applications: Dietary Sodium and Chemical Formulas

Understanding the relationship between mass, moles, and atoms is essential in real-world applications, such as nutrition and chemical manufacturing.

• Dietary Sodium Example:

  • The recommended daily intake of sodium is 2.3 g.

  • Table salt (sodium chloride, NaCl) contains both sodium and chlorine.

  • To determine how much NaCl can be consumed without exceeding the sodium recommendation, calculate the mass of sodium in a given mass of NaCl using the chemical formula and molar masses.

  • Calculation Steps:

    1. Find the molar mass of NaCl: $\text{Na} = 22.99\ \text{g/mol}$, $\text{Cl} = 35.45\ \text{g/mol}$, $\text{NaCl} = 58.44\ \text{g/mol}$

    2. Calculate the mass of sodium in a given mass of NaCl: $\text{mass of Na} = \text{mass of NaCl} \times \frac{22.99}{58.44}$

  • Example: How many grams of NaCl can you consume and stay below 2.3 g sodium?

• Counting by Mass Analogy: Just as you can count nails by weighing them, chemists count atoms by measuring mass and using molar mass.

Mole Conversion Diagram

The following diagram summarizes the relationships between mass, moles, and number of particles:

• 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.

Practice Problems

• How many moles are in 0.58 g of carbon?

• How many atoms are in a 15.0 g aluminum can? (Molar mass of Al = 26.98 g/mol)

• How many grams of NaCl contain 2.3 g of sodium?

Summary Table: Molar Mass and Conversions

Element	Molar Mass (g/mol)	Atoms in 1 mol
Carbon (C)	12.01	$6.022 \times 10^{23}$
Sulfur (S)	32.07	$6.022 \times 10^{23}$
Lithium (Li)	6.94	$6.022 \times 10^{23}$
Copper (Cu)	63.55	$6.022 \times 10^{23}$

Additional info: The number of atoms in a mole is always Avogadro's number, but the mass of a mole varies by element.