Overview
This lesson covers the formula for calculating moles, volume, and molar volume of gases at standard temperature and pressure (STP), and how to use it along with related formulas involving mass and number of particles.
The Gas Moles Formula
- The formula is ( n = \frac{V}{V_M} ), where ( n ) = moles, ( V ) = volume (dm³), ( V_M ) = molar volume (dm³).
- This formula is only used for gases, not solids or liquids.
- At STP (0°C, 1 atm), the standard molar volume ( V_M ) is 22.4 dm³.
- STP means standard temperature (0°C) and pressure (1 atm, 101.3 kPa, or 101300 Pa).
Using the Formula — Example Calculations
- To find moles of hydrogen gas given 44.8 dm³ at STP: ( n = \frac{44.8}{22.4} = 2 ) mol.
- To find volume from mass (e.g., 88 g CO₂): First use ( n = \frac{m}{M} ) where ( M ) is molar mass (CO₂: 12 + 2×16 = 44 g/mol).
- ( n = \frac{88}{44} = 2 ) mol, then ( V = n \times V_M = 2 \times 22.4 = 44.8 ) dm³.
Connecting Formulas: Grams and Particles to Volume
- For mass to volume: Find moles from mass, then use the gas moles formula.
- For particles to volume: Use ( n = \frac{\text{number of particles}}{\text{Avogadro's number}} ).
- Example: If number of particles gives ( n = 20 ) mol, then ( V = 20 \times 22.4 = 448 ) dm³.
Key Terms & Definitions
- n (moles) — Amount of substance measured in moles.
- V (volume) — Volume of gas, measured in cubic decimeters (dm³).
- V_M (molar volume) — Volume occupied by one mole of gas at STP (22.4 dm³).
- STP (Standard Temperature and Pressure) — 0°C and 1 atm pressure.
- Molar mass (M) — Mass of one mole of a substance (g/mol).
- Avogadro's number — ( 6.02 \times 10^{23} ), the number of particles in one mole.
Action Items / Next Steps
- Practice problems using the formulas for mass, volume, and particles for gases at STP.
- Memorize the standard molar volume (22.4 dm³ at STP).