States of Matter Based on Kinetic Theory

Ideal Gases

Definition

  • A gas is a state of matter where atoms are in motion and fill their container.
  • Ideal gases are based on simplifying assumptions:
    • Particles are dimensionless points in random motion.
    • The identity of the gas is irrelevant.
    • Particles don't interact except for elastic collisions.

Variables

  • Four variables are used to describe ideal gases:
    • Pressure (P): The force exerted by the gas on its container.
    • Temperature (T): The heat energy available for kinetic energy of motion.
    • Volume (V): The size of the container.
    • Moles (n): The number of particles in the container.

Boyle's Law

  • States that pressure and volume are inversely proportional when moles and temperature are constant.
  • Equation: P1V1 = P2V2
  • If volume decreases, pressure increases, and vice versa.
  • Example: Compressing a gas (decreasing volume) increases the pressure if the number of particles and their speed remain constant.

Charles's Law

  • States that volume and temperature are directly proportional when pressure and moles are constant.
  • If one doubles the other must double based on the formula.

Kelvin Scale

  • An absolute temperature scale is used in gas law calculations.
  • One degree Kelvin is the same magnitude as one degree Celsius.
  • Zero Kelvin is absolute zero (the lowest temperature possible).
  • Conversion:
    • K = C + 273
    • C = K - 273

Combined Gas Law

  • A combination of Boyle's and Charles's laws.

Avogadro's Law

  • Equal volumes of gases at the same temperature and pressure contain the same number of molecules.
  • One mole of ideal gas occupies 22.4 liters at standard temperature and pressure (STP), regardless of the gas's identity.

Ideal Gas Law

  • Relates all four variables (P, V, n, T) in one equation:
    • PV = nRT
    • Where R is the ideal gas constant.
  • Value of R depends on the units used:
    • R = 0.0821 \frac{L \cdot atm}{mol \cdot K} (predominantly used)
  • Use: To find the value of one variable when the other three are known at a specific state.

Applications

  • If you know three of the four variables (P, V, n, T) for a gas sample, you can solve for the fourth using the ideal gas law.
  • If given initial and final conditions, use Boyle's, Charles's, or the combined gas law to find unknown information.