Overview
This lecture explains how to convert between atoms and grams (and related units) using Avogadro's number and molar mass, demonstrating the process with progressively complex example problems.
Converting Atoms to Grams (Basic Steps)
- To convert atoms to grams, first convert atoms to moles using Avogadro's number (6.022 × 10²³ atoms = 1 mole).
- Next, convert moles to grams using the substance's molar mass (grams per mole).
- Formula: grams = (atoms ÷ Avogadro's number) × molar mass.
Example Problems
Sodium Example
- 3.7 × 10²⁴ atoms Na ÷ 6.022 × 10²³ × 23 g/mol = 141.3 g Na.
Chromium Example
- 4.8 × 10²³ atoms Cr ÷ 6.022 × 10²³ × 52 g/mol = 41.45 g Cr.
Phosphorus in P₄ Example
- 5.6 × 10²⁵ atoms P ÷ 6 × 10²³ = moles P.
- Convert moles P to moles P₄: 1 mol P₄ = 4 mol P.
- Find molar mass: P₄ = 4 × 30.97 = 123.88 g/mol.
- Calculation: (atoms ÷ Avogadro's number ÷ 4) × 123.88 = 2880 g P₄.
Carbon Tetrachloride (CCl₄) Example
- 7.5 × 10²⁵ atoms Cl ÷ Avogadro's number × (1 mol CCl₄ ÷ 4 mol Cl) × 153.81 g/mol ÷ 1000 = 4.789 kg CCl₄.
Tin(IV) Phosphate Example
- Find chemical formula: Sn₃(PO₄)₄ (3 Sn, 4 P, 16 O).
- Molar mass: 735.98 g/mol.
- 8.7 × 10²² atoms O ÷ Avogadro's number × (1 mol Sn₃(PO₄)₄ ÷ 16 mol O) × 735.98 × 1000 = 6645 mg Sn₃(PO₄)₄.
Key Terms & Definitions
- Avogadro's Number — 6.022 × 10²³ items/mole; converts between atoms/molecules and moles.
- Mole (mol) — SI unit for amount of substance; 1 mol = Avogadro's number of entities.
- Molar Mass — Mass (in grams) of one mole of a substance.
- Formula Unit — The simplest ratio of ions represented in an ionic compound.
- Molecule — Two or more atoms bonded together; e.g., P₄.
Action Items / Next Steps
- Practice by attempting similar conversion problems, starting from atoms and finding grams or kilograms.
- Review periodic table for molar masses of common elements and compounds.
- Ensure you understand how to derive chemical formulas and molar masses for polyatomic compounds.