Calculations with Chemical Formulas and Equations (Chapter 3 Study Notes)

Calculations with Chemical Formulas and Equations

Molecular Mass

The molecular mass is the sum of the atomic masses of all the atoms in a molecule of a substance. It is a fundamental property used to characterize molecules and is essential for quantitative chemical calculations.

• Definition: The total mass of all atoms in a single molecule, expressed in atomic mass units (amu).

• Example: For water (H2O): $2 \times 1.008 + 16.00 = 18.016$ amu

Formula Mass

The formula mass is the sum of the atomic masses of all atoms in a formula unit of a compound, whether the compound is molecular or ionic.

• Definition: The total mass of all atoms in a formula unit (used for ionic compounds).

• Example: For sodium chloride (NaCl): $22.99 + 35.45 = 58.44$ amu

Calculating Formula Weights

To calculate the formula weight, sum the atomic masses of each atom in the chemical formula, multiplying by the number of times each atom appears.

• Calcium hydroxide, Ca(OH)2: Ca: $1 \times 40.08 = 40.08$ O: $2 \times 16.00 = 32.00$ H: $2 \times 1.008 = 2.016$ Total: $40.08 + 32.00 + 2.016 = 74.096$ amu (rounded to three significant figures: 74.1 amu)

• Methylamine, CH3NH2: C: $1 \times 12.01 = 12.01$ H: $5 \times 1.008 = 5.04$ N: $1 \times 14.01 = 14.01$ Total: $12.01 + 5.04 + 14.01 = 31.06$ amu (rounded to three significant figures: 31.1 amu)

Mole and Avogadro's Number

The mole (mol) is a quantity that represents 6.022 × 1023 particles (atoms, molecules, or formula units). This number is known as Avogadro's Number (NA).

• Definition: 1 mole contains as many entities as there are atoms in exactly 12 g of carbon-12.

• Avogadro's Number: $N_A = 6.022 \times 10^{23}$

Molar Mass

The molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol).

• Example: Carbon-12 has a molar mass of 12 g/mol.

• Formula: $\text{Molar mass} = \frac{\text{mass of sample (g)}}{\text{number of moles}}$

Conversions Using Molar Mass

To convert between grams and moles, use the molar mass as a conversion factor.

• Example: A sample of nitric acid (HNO3) contains 0.253 mol. The molar mass of HNO3 is $1.008 + 14.01 + 3 \times 16.00 = 63.018$ g/mol. $0.253 \text{ mol} \times 63.018 \text{ g/mol} = 15.94 \text{ g}$

Calculating Moles from Mass

To find the number of moles in a given mass of a compound, divide the mass by the molar mass.

• Example: For 23.6 g of CaCO3 (molar mass = 100.09 g/mol): $\frac{23.6 \text{ g}}{100.09 \text{ g/mol}} = 0.236 \text{ mol}$

Daily Requirements and Moles

Chemical quantities in nutrition and medicine are often expressed in moles for precise measurement.

• Leucine (C6H14O2N): If the daily requirement is 2.25 g, and the molar mass is 132.18 g/mol: $\frac{2.25 \text{ g}}{132.18 \text{ g/mol}} = 0.017 \text{ mol}$

• Chromium: For 1.0 × 10-6 g, and atomic mass 51.996 g/mol: $\frac{1.0 \times 10^{-6} \text{ g}}{51.996 \text{ g/mol}} \times 6.022 \times 10^{23} = 1.158 \times 10^{16}$ atoms

Percentage Composition

The percentage composition of a compound is the mass percentage of each element present in the compound.

• Definition: $\text{Percent composition} = \frac{\text{mass of element in 1 mol of compound}}{\text{molar mass of compound}} \times 100\%$

• Example (PbCrO4):

Element	Mass in 1 mol (g)	Percent Composition (%)
Pb	207.2	64.11
Cr	51.996	16.09
O	64.00	19.80

• Example (Sucrose, C12H22O11): Molar mass = 342.30 g/mol C: $\frac{144.12}{342.30} \times 100 = 42.10\%$ H: $\frac{22.176}{342.30} \times 100 = 6.48\%$ O: $\frac{176.00}{342.30} \times 100 = 51.44\%$ To find grams of C in 3.1 g sucrose: $3.1 \text{ g} \times \frac{42.10}{100} = 1.30 \text{ g}$

Experimental Determination of Composition

Percentage composition can be determined by burning a compound and measuring the masses of the resulting oxides (e.g., CO2 and H2O).

• Strategy:

  1. Use mass of CO2 to find mass of carbon.

  2. Use mass of H2O to find mass of hydrogen.

  3. Calculate percent composition from these masses.

*Additional info: These notes cover the first half of Chapter 3, focusing on chemical formulas, molar mass, mole concept, and percentage composition. Later sections (not shown in images) likely cover empirical/molecular formulas and stoichiometry, as indicated in the text transcript.*