Chapter Review

Gases

Gas Laws and Kinetic Molecular Theory · Ideal Gas Equation and Real Gases

Kinetic Molecular Theory

A microscopic model explaining macroscopic gas behaviour through the random motion and elastic collisions of molecules. Eight postulates define an ideal gas: tiny molecules in haphazard motion, no intermolecular forces, negligible molecular volume, and average kinetic energy proportional to absolute temperature.

Key Points

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    Gas molecules are in continuous, random motion and collide elastically with each other and container walls
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    No intermolecular forces of attraction or repulsion exist between ideal gas molecules
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    Actual molecular volume is negligible compared to the total gas volume
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    Gravity's effect on molecular motion is negligible compared to the effect of collisions
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    Average kinetic energy of molecules varies directly with absolute temperature
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    Molecular velocities follow Maxwell's distribution — not all molecules move at the same speed

Kinetic Equation and RMS Velocity

The kinetic equation connects macroscopic pressure-volume to microscopic molecular mass and speed. From it, RMS velocity quantifies how fast molecules move, linking speed to temperature and molar mass.

Key Points

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    Kinetic equation: where = mass of one molecule, = total molecules
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    is the mean square velocity (average of squared velocities of all molecules)
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    RMS velocity: — lighter molecules move faster at the same temperature
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    in the RMS formula must be in kg/mol
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    Average translational KE per molecule:
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    Pressure originates from billions of molecular collisions per second with the container walls
Formula

Boyle's Law

At constant temperature and fixed moles, gas pressure and volume are inversely proportional. Compressing a gas increases pressure because molecules travel shorter distances and hit walls more frequently per unit area.

Key Points

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    — holds only when temperature and amount of gas are constant
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    V vs P graph is a hyperbola (isotherm); higher temperatures shift the curve away from axes
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    P vs 1/V gives a straight line through the origin
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    PV vs P gives a horizontal line, confirming PV = constant
  • •
    Derived from kinetic equation: at constant T, is constant, so PV = constant
Formula

Charles's Law and Absolute Zero

At constant pressure, gas volume is directly proportional to absolute temperature. Extrapolating the V-T line to zero volume defines absolute zero (−273 °C = 0 K).

Key Points

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    — only valid with temperature in Kelvin
  • •
    Volume changes by 1/273 of its value at 0 °C for every 1 °C change at constant pressure
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    Absolute zero (0 K = −273.16 °C) is theoretical — real gases liquefy before reaching it
  • •
    Volume-temperature equation:
  • •
    Always convert °C to K before using gas laws:
Formula

STP and Temperature Scales

Standard Temperature and Pressure provides a universal reference: 0 °C (273 K) and 1 atm. One mole of any ideal gas occupies 22.4 dm³ at STP. The Kelvin scale is mandatory for all gas law calculations.

Key Points

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    STP: 0 °C (273 K), 1 atm (101.325 kPa, 760 mmHg)
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    Molar volume at STP = 22.4 dm³/mol for any ideal gas
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    K = °C + 273.16; °C = 5/9(°F − 32); °F = 9/5(°C) + 32
  • •
    The Kelvin scale starts from absolute zero and has the same increment size as Celsius

Ideal Gas Equation

Combines Boyle's, Charles's, and Avogadro's laws into one equation relating pressure, volume, moles, temperature, and the universal gas constant. It is the master equation for all gas calculations.

Key Points

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    where R = 0.0821 dm³ atm K⁻¹ mol⁻¹ (most common) or 8.314 J K⁻¹ mol⁻¹ (SI)
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    Ratio form for fixed moles:
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    Density form: — density increases with molar mass and pressure
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    Mass form:
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    R value must match the units of P and V — the unit of R itself tells you which units to use
Formula

Ideal vs Real Gases

Real gases deviate from ideal behaviour when intermolecular forces and molecular volume become significant — at high pressure and low temperature. The compressibility factor measures deviation: Z = 1 for ideal gases.

Key Points

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    Ideal: no intermolecular forces, zero molecular volume; Real: both are non-negligible
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    Gases behave most ideally at LOW pressure and HIGH temperature
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    : attractive forces dominate (gas more compressible); : repulsive forces dominate
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    CO₂ deviates most (strongest intermolecular forces); H₂ and He deviate least
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    At low P, molecules are far apart so forces and volume become negligible → ideal behaviour

van der Waals Equation

Corrects the ideal gas equation for real gas behaviour by adding a pressure correction () for intermolecular attraction and subtracting an excluded volume () for molecular size.

Key Points

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    One mole:
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    n moles:
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    Pressure correction is ADDED (observed P is less than ideal), volume correction is SUBTRACTED
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    = intermolecular attraction strength — larger for gases with stronger forces (SO₂, Cl₂ have highest)
  • •
    = excluded volume ≈ 4 × actual molecular volume
  • •
    When and , the equation reduces to ideal gas law
Formula

Formulas

Kinetic Equation

Relates macroscopic PV to molecular mass, number, and mean square velocity

RMS Velocity

Molecular speed in terms of temperature and molar mass (M in kg/mol)

Boyle's Law

Constant T and n: P and V are inversely proportional

Charles's Law

Constant P and n: V and T (Kelvin) are directly proportional

Ideal Gas Equation

Master equation: R = 0.0821 dm³ atm K⁻¹ mol⁻¹ or 8.314 J K⁻¹ mol⁻¹

Combined Gas Equation

Fixed moles changing between two states — no R or n needed

Gas Density

Density from molar mass, pressure, and temperature

van der Waals (1 mole)

Real gas correction: a = attraction, b = excluded volume