Chapter 6: Chemical Composition – Study Notes

Chapter 6: Chemical Composition

Introduction

This chapter explores the concept of chemical composition, focusing on how chemists quantify the amount of elements and compounds using the mole, molar mass, and chemical formulas. Understanding these principles is essential for calculating the quantities of substances in chemical reactions and everyday applications.

How Much Sodium?

Sodium in Diet and Health

• Sodium is a vital dietary mineral, commonly consumed as sodium chloride (table salt).

• Sodium helps regulate body fluids, but excessive intake can cause high blood pressure.

How Much Sodium in Sodium Chloride?

Distinguishing Sodium from Sodium Chloride

• The FDA recommends less than 2.3 g (2300 mg) of sodium per day.

• The mass of sodium is not the same as the mass of sodium chloride consumed.

• The chemical composition of sodium chloride is represented by its formula, NaCl.

• There is one sodium ion for every chloride ion in NaCl.

• To determine sodium intake from NaCl, we must calculate the amount of sodium in a given mass of the compound.

Using Chemical Formulas to Calculate Constituent Elements

Applications of Chemical Formulas

• Chemical formulas, combined with atomic or molecular masses, allow calculation of the amount of a specific element in a compound.

• Examples: Determining iron in iron ore or chlorine in a chlorofluorocarbon.

Counting by Weighing

Nails by the Pound – Analogy for Atoms

• Hardware stores sell nails by the pound, which is easier than counting individual nails.

• This is analogous to counting atoms in a given mass of an element.

Example Calculation

• A customer buys 2.60 lb of nails; a dozen nails weigh 0.150 lb.

• Conversion steps:

  • Step 1: Convert pounds to dozens using weight per dozen.

  • Step 2: Convert dozens to number of nails (1 dozen = 12 nails).

• Calculation:

  • $2.60 \text{ lb nails} \times \frac{1 \text{ dozen nails}}{0.150 \text{ lb nails}} \times \frac{12 \text{ nails}}{1 \text{ dozen nails}} = 208 \text{ nails}$

Counting by Weighing: Atoms by the Gram

Why Use the Mole?

• Atoms are extremely small and numerous, making direct counting impractical.

• A dozen is too small for atoms; chemists use the mole (mol) as a counting unit.

• 1 mole = $6.022 \times 10^{23}$ units (Avogadro's number).

Avogadro’s Number

Definition and Application

• Avogadro's number ($6.022 \times 10^{23}$) is the number of units in one mole of any substance.

• Examples: 1 mole of marbles = $6.022 \times 10^{23}$ marbles; 1 mole of sand grains = $6.022 \times 10^{23}$ sand grains.

One Mole of Atoms, Ions, or Molecules

Practical Examples

• 22 copper pennies contain about 1 mole of copper atoms.

• 2 large helium balloons contain about 1 mole of helium atoms.

The Size of the Mole

Measured Quantity

• The mole is defined as the number of atoms in exactly 12 g of pure carbon-12.

• This links mass (grams) and number of atoms (Avogadro's number), allowing counting by weighing.

Conversions: Moles, Grams, and Atoms

Converting Moles to Number of Atoms

• Example: Convert 3.5 mol He to atoms.

  • Relationship: $1 \text{ mol He} = 6.022 \times 10^{23}$ He atoms

  • Calculation: $3.5 \text{ mol He} \times \frac{6.022 \times 10^{23} \text{ He atoms}}{1 \text{ mol He}} = 2.1 \times 10^{24}$ He atoms

Converting Number of Atoms to Moles

• Example: Convert $1.1 \times 10^{22}$ Ag atoms to moles.

  • Relationship: $1 \text{ mol Ag} = 6.022 \times 10^{23}$ Ag atoms

  • Calculation: $1.1 \times 10^{22} \text{ Ag atoms} \times \frac{1 \text{ mol Ag}}{6.022 \times 10^{23} \text{ Ag atoms}} = 1.8 \times 10^{-2}$ mol Ag

Converting Between Grams and Moles

• Example: Calculate moles of carbon in 0.58 g diamond.

  • Relationship: $12.01 \text{ g C} = 1 \text{ mol C}$

  • Calculation: $0.58 \text{ g C} \times \frac{1 \text{ mol C}}{12.01 \text{ g C}} = 4.8 \times 10^{-2}$ mol C

Converting Between Grams and Number of Atoms

• Example: Number of Al atoms in 16.2 g Al.

  • Relationships: $26.98 \text{ g Al} = 1 \text{ mol Al}$; $1 \text{ mol Al} = 6.022 \times 10^{23}$ Al atoms

  • Calculation: $16.2 \text{ g Al} \times \frac{1 \text{ mol Al}}{26.98 \text{ g Al}} \times \frac{6.022 \times 10^{23} \text{ Al atoms}}{1 \text{ mol Al}} = 3.62 \times 10^{23}$ Al atoms

Molar Mass and Atomic Mass

Definitions

• Atomic mass unit (amu): One-twelfth the mass of a carbon-12 atom.

• Molar mass: Mass of 1 mol of atoms of an element, numerically equal to atomic mass in grams.

• Example: Copper

  • Atomic mass: 63.55 amu

  • Molar mass: 63.55 g/mol

Molar Mass for Different Elements

• 32.07 g sulfur = 1 mol S = $6.022 \times 10^{23}$ S atoms

• 12.01 g carbon = 1 mol C = $6.022 \times 10^{23}$ C atoms

• 6.94 g lithium = 1 mol Li = $6.022 \times 10^{23}$ Li atoms

• Lighter atoms have less mass per mole.

Counting Molecules by the Gram

Molar Mass of Compounds

• For elements: Molar mass = mass of 1 mol of atoms.

• For compounds: Molar mass = mass of 1 mol of molecules or formula units.

• Ionic compounds use formula units instead of molecules.

• Convert mass of compound to moles, then moles to number of molecules or formula units.

Converting Between Grams and Moles of a Compound

Formula Mass and Molar Mass

• Formula mass: Sum of atomic masses in a chemical formula.

• Molar mass: Formula mass expressed in grams per mole.

Example: Water

• Calculate mass of 1.75 mol H2O:

  • H2O molar mass = 2(1.01) + 1(16.00) = 18.02 g/mol

  • Calculation: $1.75 \text{ mol H}_2\text{O} \times \frac{18.02 \text{ g H}_2\text{O}}{1 \text{ mol H}_2\text{O}} = 31.5 \text{ g H}_2\text{O}$

Converting Between Number of Molecules and Mass of a Compound

Example: NO2

• Calculate mass of $4.78 \times 10^{24}$ molecules of NO2:

  • NO2 molar mass = 14.01 + 2(16.00) = 46.01 g/mol

  • Calculation: $4.78 \times 10^{24} \text{ molecules} \times \frac{1 \text{ mol NO}_2}{6.022 \times 10^{23} \text{ molecules}} \times \frac{46.01 \text{ g NO}_2}{1 \text{ mol NO}_2} = 365 \text{ g NO}_2$

Chemical Formulas as Conversion Factors

Using Formulas for Calculations

• Chemical formulas allow conversion between moles of a compound and moles of constituent elements.

• Example: 1 mol CCl4 contains 4 mol Cl.

• CO2 formula: 2 O atoms per 1 CO2 molecule; 2 mol O per 1 mol CO2.

Summary Table: Key Conversion Relationships

Conversion	Relationship	Example Equation
Moles to Atoms	$1 \text{ mol} = 6.022 \times 10^{23}$ atoms	$\text{mol} \times \frac{6.022 \times 10^{23} \text{ atoms}}{1 \text{ mol}}$
Atoms to Moles	$6.022 \times 10^{23}$ atoms = 1 mol	$\text{atoms} \times \frac{1 \text{ mol}}{6.022 \times 10^{23} \text{ atoms}}$
Grams to Moles	Molar mass (g/mol)	$\text{g} \times \frac{1 \text{ mol}}{\text{molar mass}}$
Moles to Grams	Molar mass (g/mol)	$\text{mol} \times \text{molar mass}$
Moles of Compound to Moles of Element	From chemical formula	$\text{mol compound} \times \frac{\text{mol element}}{\text{mol compound}}$

Review and Learning Objectives

• Convert between moles and number of atoms.

• Convert between grams and moles.

• Convert between grams and number of atoms or molecules.

• Convert between grams and moles of a compound.

• Convert between mass of a compound and number of molecules.

• Convert between moles of a compound and moles of a constituent element.

• Convert between grams of a compound and grams of a constituent element.