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).
• $P<em>1 \times V</em>1 = P<em>2 \times V</em>2$

Charles' Law

• At constant pressure, the volume of a given mass of gas is directly proportional to its Kelvin temperature.
• $\frac{V<em>1}{T</em>1} = \frac{V<em>2}{T</em>2}$

Gay-Lussac's Law

• At constant volume, the pressure of a gas is directly proportional to its Kelvin temperature.
• $\frac{P<em>1}{T</em>1} = \frac{P<em>2}{T</em>2}$

Combined Gas Law

• Combines Boyle's, Charles's, and Gay-Lussac's laws.
• The amount of gas is constant.
• $\frac{P<em>1V</em>1}{T<em>1} = \frac{P</em>2V<em>2}{T</em>2}$

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 $(P<em>{H</em>2O})$ is constant at a given temperature.
• The pressure inside the vessel equals the atmospheric pressure.
• $P<em>{H</em>2O} + P<em>{\text{gas}} = P</em>{\text{atm}}$
• 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

• $\frac{V<em>1}{N</em>1} = \frac{V<em>2}{N</em>2}$
• Where $V<em>2$ is 22.4 L and $n</em>2$ is 1 mol
• Is used to compare experimental data of an ideal gas that is at STP.