Molecular Formulas, Molar Mass, and Mole Calculations in GOB Chemistry

Molecular Formulas and Molar Mass

Understanding Molecular Formulas

The molecular formula of a compound shows the exact number and type of atoms present in a single molecule of that substance. It is essential for determining the composition and properties of chemical compounds.

• Molecular Formula: Indicates the number of each type of atom in a molecule (e.g., C10H8N2O2S2 for dipyrithione).

• Structural Formula: Shows how atoms are connected (not required here, but often depicted in diagrams).

Example: The molecular formula for dipyrithione is C10H8N2O2S2.

Calculating Molar Mass

The molar mass of a compound is the mass of one mole of its molecules, expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in the molecular formula.

• Formula: $\text{Molar mass} = \sum (\text{number of atoms of each element} \times \text{atomic mass of element})$

• Example Calculation for Dipyrithione (C10H8N2O2S2):

  • C: 10 × 12.01 g/mol = 120.10 g/mol

  • H: 8 × 1.008 g/mol = 8.064 g/mol

  • N: 2 × 14.01 g/mol = 28.02 g/mol

  • O: 2 × 16.00 g/mol = 32.00 g/mol

  • S: 2 × 32.07 g/mol = 64.14 g/mol

  Total molar mass: $120.10 + 8.064 + 28.02 + 32.00 + 64.14 = 252.32$ g/mol

Additional info: Atomic masses are based on standard values from the periodic table.

Mole Calculations

Converting Mass to Moles

The number of moles in a given mass of a substance can be calculated using its molar mass.

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

• Example: Number of moles in 10.0 g of a compound with molar mass 252.32 g/mol:

  • $\text{Moles} = \frac{10.0\ \text{g}}{252.32\ \text{g/mol}} = 0.0396$ mol

Calculating Moles of a Specific Element in a Compound

To find the number of moles of a specific element (e.g., carbon) in a given mass of a compound:

• First, calculate the moles of the compound.

• Then, multiply by the number of atoms of the element per molecule.

• Formula: $\text{Moles of element} = \text{moles of compound} \times \text{number of atoms of element per molecule}$

• Example: Moles of C in 25.0 g of dipyrithione:

  • Moles of dipyrithione: $\frac{25.0}{252.32} = 0.0991$ mol

  • Moles of C: $0.0991 \times 10 = 0.991$ mol

Relating Moles to Number of Atoms

To determine how many moles of a compound contain a specific number of atoms of an element:

• Use Avogadro's number ($6.022 \times 10^{23}$ atoms/mol) to convert between atoms and moles.

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

• To find moles of compound: $\text{Moles of compound} = \frac{\text{moles of element}}{\text{number of atoms of element per molecule}}$

• Example: How many moles of dipyrithione contain $8.2 \times 10^{24}$ atoms of N?

  • Moles of N: $\frac{8.2 \times 10^{24}}{6.022 \times 10^{23}} = 13.62$ mol N

  • Each molecule has 2 N atoms, so moles of dipyrithione: $\frac{13.62}{2} = 6.81$ mol

Summary Table: Key Calculations

Calculation	Formula	Example (Dipyrithione)
Molar Mass	$\sum (\text{atoms} \times \text{atomic mass})$	252.32 g/mol
Moles from Mass	$\frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$	$\frac{25.0}{252.32} = 0.0991$ mol
Moles of Element	$\text{moles of compound} \times \text{atoms per molecule}$	$0.0991 \times 10 = 0.991$ mol C
Moles from Atoms	$\frac{\text{atoms}}{6.022 \times 10^{23}}$	$\frac{8.2 \times 10^{24}}{6.022 \times 10^{23}} = 13.62$ mol N
Moles of Compound from Element	$\frac{\text{moles of element}}{\text{atoms per molecule}}$	$\frac{13.62}{2} = 6.81$ mol dipyrithione

Additional info: These calculations are fundamental in GOB Chemistry for understanding chemical composition, stoichiometry, and quantitative relationships in chemical reactions.