Chemical Composition: Conversions Between Mass, Moles, and Molecules

Chemical Composition

Objectives

This section focuses on quantitative relationships in chemical compounds, specifically how to convert between grams, moles, and molecules, and how to relate the mass of a compound to its constituent elements. These skills are foundational for understanding chemical reactions and stoichiometry.

• 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

Molecules by the Gram

Molar Mass and Formula Mass

The molar mass of a substance is the mass of one mole of its particles (atoms, molecules, or formula units). For elements, it is the mass of 1 mole of atoms; for compounds, it is the mass of 1 mole of molecules or formula units.

• Molar mass (g/mol) = formula mass of compound

• Formula mass = sum of atomic masses of all atoms in the chemical formula

For example, the molar mass of water (H2O) is calculated as:

• 2 × atomic mass of H + 1 × atomic mass of O

• 2 × 1.01 + 16.00 = 18.02 g/mol

Conversions Between Grams and Moles of a Compound

Example: Water (H2O)

To find the mass in grams of 1.75 mol of water:

• Moles of H2O: 1.75 mol

• Molar mass of H2O: 18.02 g/mol

Set up the conversion:

• $1.75~\text{mol}~H_2O \times \frac{18.02~\text{g}~H_2O}{1~\text{mol}~H_2O} = 31.5~\text{g}~H_2O$

Key Point: Use molar mass as a conversion factor between moles and grams.

Conversions Between Number of Molecules and Mass

Example: Nitrogen Dioxide (NO2)

To find the mass of 4.78 × 1024 molecules of NO2:

• Number of molecules: 4.78 × 1024

• Avogadro's number: $6.022 \times 10^{23}$ molecules/mol

• Molar mass of NO2: 14.01 + 2 × 16.00 = 46.01 g/mol

Set up the conversion:

• $4.78 \times 10^{24}~\text{molecules}~NO_2 \times \frac{1~\text{mol}~NO_2}{6.022 \times 10^{23}~\text{molecules}~NO_2} \times \frac{46.01~\text{g}~NO_2}{1~\text{mol}~NO_2}$

Key Point: Use Avogadro's number to convert between molecules and moles, then molar mass to convert to grams.

Formulas as Conversion Factors

Understanding Ratios in Chemical Formulas

Chemical formulas provide ratios of atoms and molecules in a compound, which can be used as conversion factors in calculations. This is analogous to using everyday ratios, such as the number of leaves per clover.

• Example: How many leaves are on 14 clovers?

• Each clover has 3 leaves: $14~\text{clovers} \times \frac{3~\text{leaves}}{1~\text{clover}} = 42~\text{leaves}$

Similarly, in chemistry:

• 1 molecule of CO2 contains 1 atom of C and 2 atoms of O

• 1 mole of CO2 contains 1 mole of C and 2 moles of O

Conversions Between Moles of a Compound and Moles of a Constituent Element

Example: Calcium Carbonate (CaCO3)

To find the number of moles of O in 1.7 mol CaCO3:

• Each mole of CaCO3 contains 3 moles of O

• $1.7~\text{mol}~CaCO_3 \times \frac{3~\text{mol}~O}{1~\text{mol}~CaCO_3} = 5.1~\text{mol}~O$

Conversions Between Grams of a Compound and Grams of a Constituent Element

Example: Sodium Chloride (NaCl)

To find the mass of sodium in 15 g of NaCl:

• Molar mass of NaCl: 58.44 g/mol

• Each mole of NaCl contains 1 mole of Na (atomic mass: 22.99 g/mol)

Set up the conversion:

• $15~\text{g}~NaCl \times \frac{1~\text{mol}~NaCl}{58.44~\text{g}~NaCl} \times \frac{1~\text{mol}~Na}{1~\text{mol}~NaCl} \times \frac{22.99~\text{g}~Na}{1~\text{mol}~Na}$

Key Point: Use the chemical formula to determine the ratio of elements, and molar masses to convert between grams and moles.

Summary Table: Key Conversion Factors

Conversion	Factor	Example
Grams → Moles	$\frac{1~\text{mol}}{\text{molar mass (g)}}$	Water: $\frac{1~\text{mol}~H_2O}{18.02~\text{g}~H_2O}$
Moles → Molecules	$6.022 \times 10^{23}~\text{molecules}/1~\text{mol}$	NO2: $6.022 \times 10^{23}~\text{NO}_2~\text{molecules}/1~\text{mol}~NO_2$
Moles of Compound → Moles of Element	From chemical formula	CaCO3: $3~\text{mol}~O/1~\text{mol}~CaCO_3$
Grams of Compound → Grams of Element	Use molar masses and formula ratios	NaCl: $\frac{22.99~\text{g}~Na}{58.44~\text{g}~NaCl}$

Additional info: These conversion techniques are essential for quantitative chemical analysis and are foundational for stoichiometry and chemical reaction calculations.