Gases and Kinetic Theory
Gases and Kinetic Theory
The exam tests the ideal gas equation, the assumptions of the kinetic model, the conditions under which real gases deviate, and calculations involving molar volume, reacting gas volumes and molar mass determination.
The ideal gas equation
Use pV = nRT with p in Pa, V in m3, n in mol, T in kelvin and R = 8.314 J K-1 mol-1. Convert: 1 dm3 = 1 x 10-3 m3, 1 cm3 = 1 x 10-6 m3, 0 degrees C = 273 K, 1 atm = 1.01 x 105 Pa. Rearranged as n = m/M, it becomes pV = (m/M)RT, so M = mRT/(pV). Avogadro's law follows: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, which allows gas-volume ratios to be read straight from the equation.
Kinetic theory
The model assumes: particles have negligible volume compared with the container; there are no intermolecular forces except during collisions; collisions are elastic; motion is random; and average kinetic energy is proportional to absolute temperature. These assumptions give pV = (1/3)Nm(c_rms)2. Root-mean-square speed rises with temperature and falls with molar mass, which explains why lighter gases effuse faster.
Worked example
A 0.560 g sample of a gas occupies 400 cm3 at 300 K and 1.00 x 105 Pa. Find its molar mass. V = 400 x 10-6 = 4.00 x 10-4 m3. n = pV/RT = (1.00 x 105 x 4.00 x 10-4)/(8.314 x 300) = 40.0/2494 = 1.60 x 10-2 mol. M = 0.560/0.0160 = 35.0 g mol-1, consistent with chlorine, Cl2.
Real gases and traps
The ideal model fails at high pressure (particle volume significant) and low temperature (attractions significant); a real gas then has a smaller volume or lower pressure than predicted. Common errors: using degrees Celsius for T; leaving V in cm3 or dm3; pairing R with the wrong pressure unit; and treating a gas-volume ratio as a mass ratio.
Key ideas
- pV = nRT requires SI units and kelvin.
- M = mRT/(pV) determines molar mass from gas data.
- Average kinetic energy is proportional to absolute temperature only.
- Real gases deviate most at high pressure and low temperature.
- Gas volume ratios equal mole ratios at constant T and p.