AP Chemistry - Chapter 5: Gases

Measurement of Gas Pressure

• Barometer: Invented by Evangelista Torricelli in 1643, uses mercury column height to measure atmospheric pressure.
• Manometer: Device to measure gas pressure in a container; pressure given by height difference (h) in torr (1 mm Hg = 1 torr).
  • Gas pressure = atmospheric pressure ± h

Pressure Units

• 1 atm = 760.00 mm Hg = 760.00 torr = 101.325 kPa
• SI unit of pressure: Pascal (Pa)

Gas Laws

Boyle's Law

• First quantitative study of gases (1600s); pressure and volume are inversely related.
• Formula: ( P_1V_1 = P_2V_2 )

Charles' Law

• Volume of a gas is directly proportional to Kelvin temperature.
• Formula: ( \frac{V_1}{T_1} = \frac{V_2}{T_2} ) (Temperature in Kelvin)

Avogadro's Law

• Equal volumes of gases at the same temperature and pressure contain the same number of particles.
• Volume is directly proportional to moles of gas.

Gay-Lussac's Law

• Pressure of a gas is directly proportional to Kelvin temperature.
• Formula: ( \frac{P_1}{T_1} = \frac{P_2}{T_2} )

Combined Gas Law

• ( \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} )

Ideal Gas Law

• Combining Boyle's, Charles', and Avogadro's laws: ( PV = nRT )
  • R = 0.08206 (L atm)/(K mol)
• Applies to gases behaving ideally (most gases at pressures < 1 atm).

Applications and Examples

• Calculate changes in pressure, volume, and temperature using the ideal gas law.
• Molar volume at STP (0°C and 1 atm): 22.42 L for an ideal gas

Molecular Weight and Density

• Formula: ( P = \frac{mRT}{MW} )
• Relating density: ( P = \frac{dRT}{MW} )

Dalton's Law of Partial Pressures

• Total pressure is the sum of partial pressures: ( P_{tot} = P_1 + P_2 + P_3 + ... )_

Kinetic Molecular Theory of Gases

• Assumes negligible particle volume, constant motion, no intermolecular forces, kinetic energy proportional to Kelvin temperature.
• Real gases deviate due to interactions and significant particle volume.

Effusion and Diffusion

• Diffusion: Mixing of gases.
• Effusion: Passage of gas through tiny orifice.
• Graham's Law: Rate of effusion inversely proportional to square root of molecular mass.

Real Gases

• Deviate from ideal behavior; best approximated under low pressure and high temperature.
• Van der Waals equation adjusts for real gas behavior: (P_{obs} + a(n/V)^2 = nRT)_