Mole, Avogadro’s Number and Numerical Calculations
Concept of the Mole
The mole is the SI unit for amount of substance, defined such that one mole contains exactly 6.02214076×1023 elementary entities (atoms, molecules, ions, electrons, etc.). It provides a bridge between the atomic scale and macroscopic measurements.
Avogadro’s Number
Avogadro’s number (NA = 6.02214076×1023) is the fixed numerical value of entities per mole. It allows conversion between number of particles and moles:
Number of moles = (Number of entities) ÷ NA
Mole–Mass Relationship
The molar mass (g/mol) of a substance equals its relative atomic or molecular mass. Conversions:
- Moles = mass (g) ÷ molar mass (g/mol)
- Mass = moles × molar mass
Mole and Gas Volume at STP
At standard temperature and pressure (0 °C, 1 atm), one mole of an ideal gas occupies 22.414 L. Thus:
- V (L) = moles × 22.414
- Moles = V (L) ÷ 22.414
Molarity & Solution Calculations
Molarity (M) is moles of solute per liter of solution:
M = moles of solute ÷ volume of solution (L)
To prepare solutions, calculate required mass:
Mass (g) = M × volume (L) × molar mass (g/mol)
Numerical Calculation Examples
- Calculate moles in 5.0 g of NaCl (M = 58.44 g/mol).
- Determine mass of 0.250 mol H₂O (M = 18.02 g/mol).
- Find volume at STP of 2.00 mol CO₂.
- Prepare 500 mL of 1.00 M glucose solution (C₆H₁₂O₆, M = 180.16 g/mol).
Common Pitfalls & Tips
- Ensure units match (grams vs. liters).
- Watch for significant figures in constants.
- Convert mass to moles before volume in gas calculations.
- Use proper molar mass (sum of atomic masses from periodic table).
Conclusion
Mastering the mole concept and related calculations is fundamental to quantitative chemistry. With practice, converting between mass, moles, and volume becomes intuitive, enabling precise experimental design and analysis.