Chapter 6: Chemical Composition – Study Notes

Chapter 6: Chemical Composition

Introduction to Chemical Composition

Chemical composition refers to the types and amounts of elements that make up a substance. Understanding chemical composition is essential for quantifying substances in chemical reactions and for relating the mass of a substance to the number of particles it contains.

The Mole Concept

Definition and Importance of the Mole

The mole (mol) is the SI unit for the amount of substance. It allows chemists to count atoms, ions, or molecules by weighing them, since these particles are too small and numerous to count individually. One mole contains Avogadro’s number of particles:

• Avogadro’s Number: $6.022 \times 10^{23}$ particles/mol

• One mole of any element has a mass (in grams) equal to its atomic mass (in amu).

• One mole of any compound has a mass (in grams) equal to its formula mass (in amu).

Counting by Weighing: The Analogy

Just as hardware stores sell nails by the pound rather than individually, chemists use the mole to relate mass to number of particles. The concept of a dozen (12 items) is analogous to the mole, but the mole is much larger due to the small size of atoms.

Conversions Involving Moles

Converting Moles to Number of Atoms

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

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

Converting Number of Atoms to Moles

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

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

Converting Between Grams and Moles

The molar mass of an element or compound is the mass of one mole of that substance, expressed in grams per mole (g/mol). It is numerically equal to the atomic or formula mass in amu.

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

• Formula: $\text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)}$

Converting Between Grams and Number of Atoms

To find the number of atoms in a given mass of an element:

1. Convert grams to moles using the molar mass.

2. Convert moles to atoms using Avogadro’s number.

Molar Mass and Atomic Mass

Definition and Examples

The atomic mass unit (amu) is defined as one-twelfth the mass of a carbon-12 atom. The molar mass of an element is numerically equal to its atomic mass in amu but expressed in grams per mole.

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

Counting Molecules by the Gram

Molar Mass of Compounds

For compounds, the molar mass is the mass of one mole of molecules (for molecular compounds) or formula units (for ionic compounds). The formula mass is the sum of the atomic masses of all atoms in the chemical formula.

• Example: Water (H2O) has a molar mass of 18.02 g/mol.

Converting Between Number of Molecules and Mass

To convert between the number of molecules and the mass of a compound:

1. Convert molecules to moles using Avogadro’s number.

2. Convert moles to grams using the molar mass.

Chemical Formulas as Conversion Factors

Using Chemical Formulas

Chemical formulas provide relationships between the number of atoms of each element in a compound. These relationships can be used as conversion factors between moles of a compound and moles of a constituent element.

• Example: In CO2, there are 2 moles of O atoms per 1 mole of CO2 molecules.

Converting Between Moles of a Compound and Moles of an Element

To find the number of moles of an element in a given amount of compound, use the ratio from the chemical formula.

Converting Between Grams of a Compound and Grams of an Element

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

1. Convert grams of compound to moles of compound.

2. Convert moles of compound to moles of element (using the formula ratio).

3. Convert moles of element to grams of element.

Mass Percent Composition

Definition and Calculation

The mass percent composition of an element in a compound is the percentage of the compound’s total mass contributed by that element.

• Formula: $\text{mass percent of element X} = \frac{\text{mass of X in 1 mol compound}}{\text{mass of 1 mol compound}} \times 100\%$

Using Mass Percent as a Conversion Factor

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

• Example: If NaCl is 39% sodium by mass, then 39 g Na per 100 g NaCl.

Empirical and Molecular Formulas

Empirical Formula

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

Calculating Empirical Formulas from Experimental Data

Steps to determine the empirical formula:

1. Write down the masses of each element in the sample.

2. Convert masses to moles using molar masses.

3. Write a pseudoformula using the mole values as subscripts.

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

5. If necessary, multiply all subscripts by a small integer to obtain whole numbers.

Calculating Molecular Formulas

The molecular formula is determined from the empirical formula and the molar mass:

• Formula: $n = \frac{\text{molar mass of molecular formula}}{\text{molar mass of empirical formula}}$

• Multiply the empirical formula subscripts by n to get the molecular formula.

Summary Table: Key Conversion Factors

Conversion	Factor/Formula
Moles ↔ Number of particles	$1 \text{ mol} = 6.022 \times 10^{23}$ particles
Grams ↔ Moles	$\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$
Moles of compound ↔ Moles of element	From chemical formula (e.g., 2 mol H per 1 mol H2O)
Grams of compound ↔ Grams of element	Use molar mass and formula ratios
Mass percent composition	$\frac{\text{mass of element in 1 mol compound}}{\text{mass of 1 mol compound}} \times 100\%$

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.

• Use mass percent composition as a conversion factor.

• Determine mass percent composition from a chemical formula.

• Determine an empirical formula from experimental data.

• Calculate an empirical formula from reaction data.

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