06 / CHAPTER 02
The ideal gas model
Relate pressure, volume, temperature, and amount of gas.
ANCHOR EQUATION
Ideal gas law
In symbols: pV = nRT
Pressure, volume, amount, and absolute temperature define an ideal gas state.
The ideal gas law counts microscopic state
Pressure comes from molecular impacts, volume sets the available space, temperature sets the energy scale, and n counts amount of gas. The ideal model neglects molecular volume and intermolecular attraction.
Combine the empirical proportionalities
For fixed n and T, experiments give p ∝ 1/V; for fixed V and n, p ∝ T; for fixed p and T, V ∝ n. Combining gives pV ∝ nT. Define the constant as R = 8.314 J/(mol·K): pV = nRT. Variables are pressure p, volume V, amount n, and absolute temperature T.
One mole of gas at T = 300 K and p = 101 kPa occupies V = nRT/p = 8.314(300)/101000 = 0.0247 m³, or 24.7 L.
The ideal model has a regime
At high pressure or near condensation, molecular size and attraction matter, so pV = nRT becomes inaccurate. Always use kelvin and consistent pressure-volume units; 1 Pa·m³ = 1 J.
Work it: A sealed 2.0 L vessel contains 0.080 mol at 300 K. Calculate pressure. Then predict the pressure at 360 K if volume and amount stay fixed.