Formula Mass and Mass Percent Composition

Formula Mass and Mass Percent Composition

This study guide covers the calculation of formula mass and mass percent composition, essential concepts in General Chemistry for understanding the quantitative relationships in chemical compounds.

Counting Atoms in a Chemical Formula

To analyze a chemical formula, first determine the number of each type of atom present. This is the foundation for calculating formula mass and percent composition.

• Step 1: Identify the subscript for each element in the formula. If no subscript is present, it is understood to be 1.

• Example: For N2O:

  • N: 2 atoms

  • O: 1 atom

• Example: For Ca(NO3)2:

  • Ca: 1 atom

  • N: 2 atoms (1 × 2)

  • O: 6 atoms (3 × 2)

Calculating Formula Mass (Molar Mass)

The formula mass (or molar mass) of a compound is the sum of the atomic masses of all atoms in its formula, expressed in g/mol.

• Step 1: Find the number of each element in the formula.

• Step 2: Find the atomic mass of each element (from the periodic table).

• Step 3: Multiply the number of atoms by the atomic mass for each element.

• Step 4: Add all the masses together to get the formula mass.

Formula:

$\text{Formula Mass} = \sum (\text{number of atoms of element}) \times (\text{atomic mass of element})$

• Example: For CCl4:

  • C: 1 × 12.01 = 12.01 g/mol

  • Cl: 4 × 35.45 = 141.8 g/mol

  • Total: 12.01 + 141.8 = 153.81 g/mol

Converting Between Mass, Moles, and Number of Particles

Stoichiometric calculations often require converting between mass, moles, and number of molecules or atoms using Avogadro's number and molar mass.

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

• Key Relationships:

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

  • Moles $\leftrightarrow$ Number of particles: $\text{particles} = \text{moles} \times 6.022 \times 10^{23}$

• Example: To find the mass of $3.55 \times 10^{24}$ molecules of H2O:

  • Step 1: Convert molecules to moles: $\frac{3.55 \times 10^{24}}{6.022 \times 10^{23}} = 5.90$ mol

  • Step 2: Multiply by molar mass of H2O (18.015 g/mol): $5.90 \times 18.015 = 106.3$ g

Calculating Mass Percent Composition

Mass percent composition expresses the percentage by mass of each element in a compound.

• Step 1: Find the total mass of each element in one mole of the compound.

• Step 2: Find the formula mass of the compound.

• Step 3: Calculate mass percent for each element:

$\text{Mass percent of element} = \frac{\text{mass of element in 1 mol compound}}{\text{molar mass of compound}} \times 100$

• Example: For acetic acid (C2H4O2), to find percent composition of oxygen:

  • O: 2 × 15.999 = 31.998 g

  • Molar mass: 60.052 g/mol

  • Percent O: $\frac{31.998}{60.052} \times 100 = 53.28\%$

Sample Table: Mass Percent Composition Calculation

The following table summarizes the steps for calculating mass percent composition:

Step	Description	Formula/Example
1	Find mass of element in 1 mol compound	e.g., O in C2H4O2: 2 × 15.999 = 31.998 g
2	Find molar mass of compound	e.g., C2H4O2: 60.052 g/mol
3	Calculate mass percent	$\frac{31.998}{60.052} \times 100 = 53.28\%$

Using Mass Percent in Practical Calculations

Mass percent can be used to determine the amount of a specific element in a given mass of compound.

• Example: If sodium chloride (NaCl) is 39% sodium by mass, how much sodium is in 22 g NaCl?

  • Calculation: $22 \text{ g NaCl} \times \frac{39 \text{ g Na}}{100 \text{ g NaCl}} = 8.6 \text{ g Na}$

Summary of Key Steps

• Always start by determining the number of each atom in the formula.

• Use atomic masses from the periodic table for calculations.

• Apply the correct formulas for molar mass and mass percent composition.

• Use unit analysis to ensure correct conversions between mass, moles, and number of particles.

Additional info: These notes include step-by-step problem-solving strategies and annotated worked examples, which are essential for mastering stoichiometry and composition calculations in General Chemistry.