Gas Laws Comprehensive Notes

Gas Laws

Objectives

• Define the pressure of a gas
• Express pressure in different units
• State the laws governing gas behavior
• Present gas laws in equation form
• Utilize gas laws for determining pressure, volume, and temperature under varying conditions
• Apply the ideal gas equation for calculations involving pressure, volume, temperature, or number of moles

Properties of Gases

• Pressure: The force exerted by a gas against the walls of its container.
• Volume: The space occupied by gas, typically measured in cubic meters (m³) or liters (L).
• Amount (Moles): Amount measured in moles (mol) based on the molecular or formula weight.
• Temperature: A measure of how hot or cold a substance is, related to the average kinetic energy of its particles.

Pressure of Gases

• SI Unit: Pascal (Pa) where $1 ext{ Pa} = 1 ext{ N/m}^2$.
• Common Units:
  • 1 psi = 6894.76 Pa
  • 1 bar = 100000 Pa or 100 kPa
  • 1 torr = 133.322 Pa
  • 1 atm = 101325 Pa or 101.325 kPa

Volume of Gases

• The SI unit for volume is the cubic meter (m³), but liters (L) are more commonly used in practice.

Amount of Substance (Moles)

• 1 mole of substance contains approximately $6.022 imes 10^{23}$ particles.

Temperature of Gases

• Represents the average kinetic energy of gas particles, expressed in Kelvin (K).

Boyle’s Law

• Describes the relationship between pressure and volume at constant temperature.
• Equation: $P<em>1V</em>1 = P<em>2V</em>2$
• As pressure increases, volume decreases, and vice versa.

Application of Boyle’s Law

1. If a gas sample exerts a pressure of 3.0 kPa in a 12.0 L vessel at 20 °C, and is transferred to a 9.0 L vessel, calculation shows pressure increases to 4.00 kPa.

Charles’ Law

• States that the volume of a gas is directly proportional to its absolute temperature at constant pressure.
• Equation: $\frac{V<em>1}{T</em>1} = \frac{V<em>2}{T</em>2}$
• Application: Heating a gas will increase its volume.

Example Problems for Charles’ Law

1. A gas occupying 12.0 L at 27 °C will have a volume of 13.2 L if heated to 57 °C at the same pressure.

Gay-Lussac’s Law

• Defines the direct relationship between pressure and absolute temperature at constant volume.
• Equation: $\frac{P<em>1}{T</em>1} = \frac{P<em>2}{T</em>2}$

Sample Problems for Gay-Lussac’s Law

1. A gas at 3.00 atm and 127 °C has a pressure of 3.75 atm at 227 °C with constant volume.

Avogadro’s Law

• States that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.
• Equation: $\frac{V<em>1}{n</em>1} = \frac{V<em>2}{n</em>2}$

Practical Application of Avogadro’s Law

1. Additional helium added to an already filled balloon increases its volume when pressure and temperature are constant.

Kinetic Molecular Theory

1. Gases consist of tiny particles in mostly empty space.
2. No attractive forces between molecules.
3. Constant, random straight-line motion of the molecules.
4. Elastic collisions with container walls result in gas pressure.
5. Average kinetic energy is proportional to the temperature in Kelvin.

Ideal Gas Law

• Equation: $PV = nRT$ where
  • P = pressure (atm)
  • V = volume (L)
  • n = number of moles
  • T = temperature (K)
  • R = universal gas constant (0.08205 L·atm/mol·K)

Example Problem for Ideal Gas Law

1. For 1.28 moles of sulfur hexafluoride in a 4.50 L vessel at 79.5 °C, the pressure is calculated to be 8.23 atm.

Dalton's Law of Partial Pressures

• The total pressure of a gas mixture is the sum of the partial pressures of each component:
  $P<em>{total} = P</em>a + P_b + …$

Sample Problem Using Dalton's Law

1. Given a mixture of gases in a tank, the partial pressures of Ar, O₂, and N₂ can be calculated based on their moles in a total pressure of 1000 torr, resulting in individual partial pressures of 200 torr, 300 torr, and 500 torr respectively.

Diffusion and Effusion

• Diffusion: Spread of gas molecules from high to low concentration.
• Effusion: Escape of gas through a small hole.