Rucete ✏ AP Chemistry In a Nutshell
6. Gases
This chapter explains the physical behavior of gases, described by the ideal gas law and the kinetic molecular theory. It covers the relationships among pressure, volume, temperature, and moles, and how to apply these relationships in calculations and experiments.
Gas Laws Overview
• Gases are described by four variables: pressure (P), volume (V), temperature (T), and amount in moles (n).
• Each individual gas law keeps two variables constant and explores how the other two are related.
• The ideal gas law combines all relationships into one equation.
Boyle’s Law
• Describes inverse relationship between pressure and volume at constant temperature and moles: P₁V₁ = P₂V₂.
• As volume decreases, pressure increases due to more frequent particle collisions.
Charles’s Law
• Describes direct relationship between temperature and volume at constant pressure and moles: V₁/T₁ = V₂/T₂.
• Absolute zero is the temperature where volume theoretically reaches zero (−273.15°C or 0 K).
Gay-Lussac’s Law
• Describes direct relationship between temperature and pressure at constant volume and moles: P₁/T₁ = P₂/T₂.
• Higher temperatures increase kinetic energy, causing stronger and more frequent collisions.
Avogadro’s Principle
• Equal volumes of gases contain equal numbers of moles at constant temperature and pressure: V₁/n₁ = V₂/n₂.
• Volume is directly proportional to moles of gas.
Ideal Gas Law
• Combines all four gas variables: PV = nRT.
• R is the universal gas constant; its value depends on units used (e.g., 0.0821 L·atm/mol·K).
• All calculations require Kelvin temperature and consistent units for volume, pressure, and moles.
Using the Ideal Gas Law
• Solve for any one variable when the other three are given.
• Alternatively, compare two conditions using: (P₁V₁)/(n₁T₁) = (P₂V₂)/(n₂T₂).
• By canceling variables held constant, this form reduces to Boyle’s, Charles’s, Gay-Lussac’s, or Avogadro’s law.
Standard Temperature and Pressure (STP)
• STP is defined as 1.00 atm and 273 K (0 °C).
• At STP, 1 mole of any ideal gas occupies 22.4 L.
Molar Mass, Density, and Molar Volume
• Molar mass = (grams × RT) / (PV)
• Density = (molar mass × P) / (RT)
• These equations come from manipulating PV = nRT and are used to identify gases and calculate densities.
Kinetic Molecular Theory (KMT)
• Gases consist of particles in constant, random motion.
• Collisions between particles are elastic (no energy loss).
• Particle volume is negligible compared to container volume.
• There are no intermolecular forces between gas particles.
• Average kinetic energy is proportional to temperature in Kelvin.
Graham’s Law of Effusion
• Describes how gas particles move through a tiny hole into a vacuum without collisions.
• Lighter gases effuse faster than heavier gases.
• Rate of effusion is inversely proportional to the square root of molar mass:
• rate₁ / rate₂ = √(M₂ / M₁)
Diffusion vs. Effusion
• Diffusion is the movement of gas through other gases; effusion is through a small hole into a vacuum.
• Diffusion is slower because of particle collisions, even though the theory assumes ideal behavior.
Partial Pressure and Dalton’s Law
• The total pressure of a gas mixture is the sum of the partial pressures of each individual gas.
• P(total) = P₁ + P₂ + ... + Pn
• Each gas exerts pressure independently as if it were alone in the container.
• Partial pressure = mole fraction × total pressure
Collecting Gases Over Water
• When collecting gas over water, water vapor contributes to the total pressure.
• P(dry gas) = P(total) − P(water vapor)
• Water vapor pressure depends on temperature and must be subtracted to find the pressure of the collected gas.
Real Gases and Deviations from Ideal Behavior
• Gases deviate from ideal behavior at high pressures and low temperatures.
• Real gases have intermolecular forces and occupy volume.
• Most gases behave ideally at low pressure and high temperature.
Van der Waals Equation
• A modified ideal gas equation that corrects for volume and intermolecular forces:
• [P + a(n/V)²] × [V − nb] = nRT
• The “a” term accounts for attraction between particles, and “b” corrects for particle volume.
In a Nutshell
Gases follow predictable relationships described by the ideal gas law and related formulas. Their behavior is governed by kinetic molecular theory, and real gases deviate from ideality under extreme conditions. Understanding gas laws, pressure, volume, temperature, and mole relationships allows chemists to calculate and predict gas behavior in laboratory and real-world scenarios.