Gas Laws Notes

Gas Laws

Describing a Gas

• Four things are used to describe a gas:
  • Pressure (P): Measured in kilopascals (kPa). Pressure is force per area. Gas particles exert pressure when they collide with the walls of a container.
  • Volume (V): Measured in liters (L). As the volume of gas decreases (compression), the pressure increases.
  • Temperature (T): Measured in Kelvin (K). As the temperature of gas increases, the pressure increases.
  • Number of moles (n): Measured in moles (mol). As the amount of gas increases, the pressure increases.

Kinetic Molecular Theory (KMT) - Major Assumptions

• Particles are very small with lots of space between them, making gases easily compressed.
• In a gas sample, all particles have the same mass but not the same velocity, resulting in different kinetic energies. KE = \frac{1}{2}mv^2 where KE is kinetic energy, m is mass, and v is velocity.
• Particles are in constant motion.
• Particles move in straight paths.
• Collisions are elastic (no energy is lost).

More KMT Information

• Constant motion of particles means gases expand to fill containers.
• Gases have low density because of the empty space between particles.
• Gases are compressible due to the empty space.
• Diffusion is possible because there are no attractive or repulsive forces between gas particles (e.g., the smell of bread traveling).

Gas Unit Conversions

• SI unit of Pressure: Pascal (Pa), commonly expressed as kPa.
• Conversions:
  • 1 \text{ atm} = 101.3 \text{ kPa} = 760 \text{ mmHg} = 760 \text{ torr} = 14.7 \text{ psi}

Boyle's Law

• If the temperature of a gas is constant, as the pressure increases, the volume decreases (inversely proportional).
• P1 \times V1 = P2 \times V2

Charles' Law

• At constant pressure, the volume of a given mass of gas is directly proportional to its Kelvin temperature.
• \frac{V1}{T1} = \frac{V2}{T2}

Gay-Lussac's Law

• At constant volume, the pressure of a gas is directly proportional to its Kelvin temperature.
• \frac{P1}{T1} = \frac{P2}{T2}

Combined Gas Law

• Combines Boyle's, Charles's, and Gay-Lussac's laws.
• The amount of gas is constant.
• \frac{P1V1}{T1} = \frac{P2V2}{T2}

Standard Temperature and Pressure (STP)

• Standard Temperature and Pressure for gases is 1 atm and 273 K.
• All motion stops at absolute zero, which is 0 K.

Ideal Gas Law

• Combines all three laws and the amount of gas.
• PV = nRT
  • P = pressure (atm)
  • V = volume (liters)
  • n = number of moles
  • R = ideal gas constant (0.0821 L ● atm / moles ● K)
  • T = temperature (Kelvin)

Ideal Gas Law & Density

• PV = nRT
• n = \frac{\text{mass of sample (m)}}{\text{Molar Mass (M)}}
• PV = \frac{m}{M}RT
• \frac{m}{V} = \frac{PM}{RT}
• Density = \frac{m}{V}

Graham's Law of Diffusion

• Depends mainly on the mass of the particles.
• Lighter particles diffuse more quickly.
• To compare one gas to another, temperature must remain constant.

Dalton's Law of Partial Pressures

• Each gas in a mixture will exert its own pressure, referred to as a partial pressure.
• The identity of the gas does not matter; only its pressure is of interest.

Gas Collection Over Water

• Gas collected over water contains both the gas and water vapor.
• The vapor pressure of water (P{H2O}) is constant at a given temperature.
• The pressure inside the vessel equals the atmospheric pressure.
• P{H2O} + P{\text{gas}} = P{\text{atm}}
• Atmospheric pressure can change throughout the day but is usually around 1 atm at sea level.

Avogadro's Principle

• Gases that have the same volume, temperature, and pressure will have the same number of particles.
• The volume and the moles of gas are directly proportional if temperature and pressure remain constant.
• Molar Volume: volume that 1 mole of a gas occupies at STP (1.00 atm & 273 K).
  • 1 mol gas = 22.4 L
  • 1 \text{ mol} = 6.02 \times 10^{23} \text{ particles}

Avogadro’s Law

• \frac{V1}{N1} = \frac{V2}{N2}
• Where V2 is 22.4 L and n2 is 1 mol
• Is used to compare experimental data of an ideal gas that is at STP.