Structure 1.5.4 — Ideal Gas Equation and Combined Gas Law

Ideal Gas Equation

The behavior of an ideal gas can be described using the ideal gas law:

\( PV = nRT \)

Where:

• \( P \) = pressure in pascals (Pa)
• \( V \) = volume in cubic meters (m³)
• \( n \) = amount of substance in moles (mol)
• \( R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1} \) (universal gas constant)
• \( T \) = temperature in kelvin (K)

 Unit Conversions:

• Volume: cm³ → m³: divide by \( 10^6 \)
• Volume: dm³ → m³: divide by \( 1000 \)
• Temperature: °C → K: add 273.15
• Pressure: kPa → Pa: multiply by 1000

 Rearranged Forms of the Ideal Gas Equation:

• \( n = \frac{PV}{RT} \)
• \( V = \frac{nRT}{P} \)
• \( P = \frac{nRT}{V} \)
• \( T = \frac{PV}{nR} \)

 Combined Gas Law

The combined gas law relates pressure, volume, and temperature before and after a change:

\( \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \)

• Use when the number of moles remains constant.
• All temperatures must be converted to kelvin (K).
• All pressures must be in pascals (Pa) and volumes in m³.

 Molar Volume at STP

• Standard Temperature and Pressure (STP):
  • Temperature = 273 K (0°C)
  • Pressure = \( 1.00 \times 10^5 \, \text{Pa} \)
  • Molar volume of an ideal gas = 22.7 dm³ mol⁻¹

So at STP:

\( V = n \times 22.7 \quad \text{(in dm}^3\text{)} \quad \text{or} \quad n = \frac{V}{22.7} \)

Ensure volume is in dm³ when using this shortcut equation.