Gas Laws: Volume, Moles, and Molar Volume

Key Concepts

• n: Number of moles
• V: Volume of gas (measured in decimeters cubed, dm³)
• Vm: Molar volume (measured in dm³ or dm³/mol)
  • Commonly used value: 22.4 dm³/mol at STP

STP (Standard Temperature and Pressure)

• Temperature: 0°C (273.15 K)
• Pressure:
  • 1 atmosphere (atm)
  • 101.3 kilopascals (kPa)
  • 101,300 pascals (Pa)

Formula Usage

• Formula: n = V / Vm
  • Used exclusively for gases
  • Vm is used as 22.4 dm³/mol at STP

Example Problems

Example 1

• Given: 44.8 dm³ of hydrogen gas at STP
• Find: Number of moles (n)
• Solution:
  • Use n = V / Vm
  • Calculate n = 44.8 / 22.4 = 2 moles

Example 2

• Given: 88 grams of CO₂
• Find: Volume at STP
• Solution:
  1. Calculate moles using n = m / M
     • CO₂: Molar mass (M) = 12 (C) + 2 * 16 (O) = 44 g/mol
     • n = 88 g / 44 g/mol = 2 moles
  2. Calculate volume using V = n * Vm
     • V = 2 moles * 22.4 dm³/mol = 44.8 dm³*

Example 3

• Given: Number of particles = 1.204 * 10²⁵
• Find: Volume at STP
• Solution:
  1. Calculate moles using n = number of particles / Avogadro's number
     • Avogadro's number = 6.02 * 10²³
     • n = 1.204 * 10²⁵ / 6.02 * 10²³ = 20 moles
  2. Calculate volume using V = n * Vm
     • V = 20 moles * 22.4 dm³/mol = 448 dm³

Tips

• Vm of 22.4 dm³/mol is a constant value at STP.
• Ensure you are working with consistent units (e.g., convert grams to moles before applying gas formulas).
• Use outlined formulas for specific gas scenarios.