Gases: MDCAT Notes and MCQs
Kinetic molecular theory — postulates
- Gases consist of tiny particles in constant, random, straight-line motion.
- Actual volume of molecules is negligible compared with the container volume.
- No attractive/repulsive forces between molecules.
- Collisions are perfectly elastic; pressure is due to collisions with container walls.
- Average kinetic energy ∝ absolute temperature (KE = 3/2 kT).
STP
Standard temperature = 273.15 K (0 °C); standard pressure = 1 atm = 760 mm Hg = 760 torr = 101325 Pa. Molar volume = 22.414 dm3.
Gas laws
- Boyle's law (constant T, n): V ∝ 1/P → PV = k; P1V1 = P2V2. Graph of P vs V is a hyperbola (isotherm).
- Charles's law (constant P, n): V ∝ T → V/T = k. Volume changes by 1/273 of its volume at 0 °C per °C.
- Absolute zero = −273.15 °C (0 K) — theoretical temperature at which gas volume would become zero and molecular motion stops. K = °C + 273.
- Avogadro's law: V ∝ n (equal volumes of gases at same T, P contain equal number of molecules).
Ideal gas equation: PV = nRT
| Value of R | Units |
|---|---|
| 0.0821 | dm3 atm K−1 mol−1 |
| 62.4 | dm3 mm Hg (torr) K−1 mol−1 |
| 8.314 | J K−1 mol−1 (= N m K−1 mol−1) |
| 1.987 ≈ 2 | cal K−1 mol−1 |
R is the work done per mole per kelvin. Also: PM = dRT (density form).
Real vs ideal gases
Ideal gases obey PV = nRT at all conditions; real gases deviate at high pressure and low temperature (molecular volume and attractions become significant). Behave most ideally at low P, high T. Van der Waals equation corrects: (P + an²/V²)(V − nb) = nRT. Compressibility factor Z = PV/nRT (= 1 for ideal gas).
PMDC learning outcomes for this unit
- Kinetic Molecular Theory & Gas Laws: 3.1 List the postulates of Kinetic Molecular Theory
- Kinetic Molecular Theory & Gas Laws: 3.2 Describe the motion of particles of the gas according to kinetic theory.
- Kinetic Molecular Theory & Gas Laws: 3.3 State the values of standard temperature and pressure (STP)
- Kinetic Molecular Theory & Gas Laws: 3.4 Describe the effect of change in pressure on the volume of gas.
- Kinetic Molecular Theory & Gas Laws: 3.5 Describe the effect of change in temperature on the volume of gas.
- Kinetic Molecular Theory & Gas Laws: 3.6 Explain the significance of the absolute zero, giving its value in degree.
- Kinetic Molecular Theory & Gas Laws: 3.7 Derive ideal gas equation using Boyle's law, Charles's law and Avogadro's law.
- Kinetic Molecular Theory & Gas Laws: 3.8 Explain the significance and different units of ideal gas constant.
- Kinetic Molecular Theory & Gas Laws: 3.9 Distinguish between real and ideal gases.