Chapter 6: Chemical Composition – Study Guide

Chemical Composition

Introduction to Chemical Composition

Chemical composition refers to the types and amounts of elements that make up a compound. Understanding chemical composition is essential for quantifying substances, predicting reactions, and analyzing materials in chemistry.

The Mole Concept

Definition and Importance

The mole is a fundamental unit in chemistry used to count atoms, molecules, or ions. One mole contains 6.022 × 1023 entities, known as Avogadro’s number. This allows chemists to relate microscopic particles to macroscopic quantities.

• 1 mole = 6.022 × 1023 units (atoms, molecules, ions, etc.)

• The mole bridges the gap between atomic scale and laboratory scale measurements.

• Example: 1 mole of copper atoms is approximately the number of atoms in 22 pennies.

Counting by Weighing: Analogy

Counting atoms is analogous to counting objects by weight, such as nails sold by the pound. Conversion factors are used to relate mass to number of items.

• For nails: Use weight per dozen and number per dozen as conversion factors.

• For atoms: Use molar mass and Avogadro’s number as conversion factors.

Atomic Mass and Molar Mass

Definitions

The atomic mass unit (amu) is defined as one-twelfth the mass of a carbon-12 atom. The molar mass of an element is the mass of 1 mole of its atoms, expressed in grams per mole (g/mol).

• Atomic mass (amu) is used for individual atoms.

• Molar mass (g/mol) is used for bulk quantities.

• Example: Copper has an atomic mass of 63.55 amu and a molar mass of 63.55 g/mol.

Conversions: Moles, Grams, and Atoms

Converting Moles to Number of Atoms

To convert moles to number of atoms, multiply by Avogadro’s number:

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

• Example: 3.5 mol He × 6.022 × 1023 = 2.1 × 1024 He atoms

Converting Number of Atoms to Moles

To convert number of atoms to moles, divide by Avogadro’s number:

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

• Example: $1.1 \times 10^{22}$ Ag atoms ÷ $6.022 \times 10^{23}$ = $1.8 \times 10^{-2}$ mol Ag

Converting Grams to Moles

To convert grams to moles, use the molar mass as a conversion factor:

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

• Example: 0.58 g C ÷ 12.01 g/mol = 0.048 mol C

Converting Grams to Moles to Atoms

To find the number of atoms in a given mass:

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

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

Converting Grams to Atoms: Example with Aluminum

For a 16.2 g aluminum can:

• Step 1: $\text{Moles Al} = \frac{16.2\text{ g}}{26.98\text{ g/mol}}$

• Step 2: $\text{Atoms Al} = \text{Moles Al} \times 6.022 \times 10^{23}$

• Result: $3.62 \times 10^{23}$ Al atoms

Molar Mass of Compounds

Definition and Calculation

The molar mass of a compound is the mass of 1 mole of its molecules or formula units. It is calculated by summing the atomic masses of all atoms in the chemical formula.

• For water: $\text{Molar mass H}_2\text{O} = 2 \times 1.01 + 16.00 = 18.02 \text{ g/mol}$

• For NO2: $\text{Molar mass NO}_2 = 14.01 + 2 \times 16.00 = 46.01 \text{ g/mol}$

Converting Between Grams and Moles of a Compound

To convert moles to grams, multiply by the molar mass:

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

• Example: 1.75 mol H2O × 18.02 g/mol = 31.5 g H2O

Converting Number of Molecules to Mass

To convert molecules to mass:

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

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

• Example: 4.78 × 1024 NO2 molecules = 365 g NO2

Chemical Formulas as Conversion Factors

Using Chemical Formulas

Chemical formulas indicate the ratio of elements in a compound. These ratios can be used as conversion factors between moles of compound and moles of constituent elements.

• Example: CO2 has 2 O atoms per 1 CO2 molecule.

• Conversion factor: 2 mol O : 1 mol CO2

Converting Between Moles of Compound and Moles of Element

To find moles of an element in a compound:

• Use the ratio from the chemical formula.

• Example: 1.7 mol CaCO3 × (3 mol O / 1 mol CaCO3) = 5.1 mol O

Converting Between Grams of Compound and Grams of Element

To find the mass of an element in a given mass of compound:

• Step 1: Convert grams of compound to moles.

• Step 2: Convert moles of compound to moles of element.

• Step 3: Convert moles of element to grams.

• Example: 15 g NaCl contains 5.9 g Na.

Mass Percent Composition

Definition and Calculation

Mass percent composition is the percentage by mass of each element in a compound. It is calculated as:

• $\text{Mass percent of element X} = \frac{\text{mass of X in sample}}{\text{mass of sample}} \times 100\%$

• Example: Chromium in a metal oxide sample: $\frac{0.358\text{ g}}{0.523\text{ g}} \times 100\% = 68.5\%$

Using Mass Percent Composition as a Conversion Factor

Mass percent can be used to convert between grams of an element and grams of compound.

• Example: Sodium chloride is 39% sodium by mass.

• Conversion factor: 39 g Na : 100 g NaCl

Application: Dietary Sodium

To stay within FDA guidelines for sodium intake, calculate the maximum grams of sodium chloride that can be consumed:

• Given: 2.4 g Na, NaCl is 39% Na by mass.

• $2.4\text{ g Na} \times \frac{100\text{ g NaCl}}{39\text{ g Na}} = 6.2\text{ g NaCl}$

Mass Percent from Chemical Formula

Mass percent can also be calculated from a chemical formula using molar masses:

• $\text{Mass percent Cl} = \frac{4 \times \text{molar mass Cl}}{\text{molar mass C}_2\text{Cl}_4\text{F}_2} \times 100\%$

• Example: For C2Cl4F2, Cl mass percent = 69.58%

Empirical and Molecular Formulas

Empirical Formula

The empirical formula shows the simplest whole-number ratio of atoms in a compound. The molecular formula is a whole-number multiple of the empirical formula.

• Example: Hydrogen peroxide (H2O2) has empirical formula HO.

• Molecular formula = Empirical formula × n

Calculating Empirical Formula from Experimental Data

Steps to determine empirical formula:

1. Write down masses of each element.

2. Convert masses to moles using molar mass.

3. Write a pseudo-formula using mole values as subscripts.

4. Divide all subscripts by the smallest value to get whole numbers.

5. If subscripts are not whole numbers, multiply by a small integer (see table below).

Calculating Molecular Formula from Empirical Formula and Molar Mass

The molecular formula is determined by multiplying the empirical formula by n, where:

• $n = \frac{\text{molar mass}}{\text{empirical formula molar mass}}$

• Example: For fructose, empirical formula CH2O, molar mass 180.2 g/mol, empirical formula molar mass 30.03 g/mol, n = 6.

• Molecular formula = CH2O × 6 = C6H12O6

Summary and Learning Objectives

Key Concepts

• The mole allows chemists to count atoms and molecules by weighing.

• Molar mass relates mass to moles for elements and compounds.

• Chemical formulas provide conversion factors for calculations.

• Mass percent composition quantifies the proportion of elements in compounds.

• Empirical and molecular formulas are determined from experimental data and molar mass.

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 moles of a compound and moles of a constituent element.

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

• Use mass percent composition as a conversion factor.

• Determine mass percent composition from a chemical formula.

• Determine an empirical formula from experimental data.

• Calculate a molecular formula from an empirical formula and molar mass.