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Chapter 7 Lecture Notes - CHEM 1113 Broering

Chapter 7: Gases

Properties of Gases

  • Matter exists in three states: solid, liquid, and gas.

  • Gases:

    • No definite volume; expands to fill the entire volume of its container.

    • Gas particles are far apart, resulting in much lower densities compared to solids and liquids.

    • Gas particles move constantly and collide with each other and surfaces.

      • Collisions exert tiny forces against surfaces of the container.

  • Pressure: Defined as force per unit area.

    • It is the sum of all forces from gas molecules impacting surface area.

Atmospheric Pressure

  • Pressure Formula:

    • Pressure (P) = Force (F) / Surface Area (A)

    • Atmospheric pressure varies by location and weather.

  • Barometer: Instrument to measure atmospheric pressure.

    • Standard Atmospheric Pressure:

      • 1 atm = 760 mm Hg = 760 torr

      • 1 atm = 1.01325 x 10^5 Pa = 101.324 kPa

Kinetic Molecular Theory (KMT)

  • Assumptions of KMT:

    1. Gas particles are in constant, random motion.

    2. Volume of gas particles is negligible (considered as point masses).

    3. Collisions between gas particles are perfectly elastic (no energy loss).

    4. Negligible forces exist between gas particles, except during collisions.

    5. All gases at the same temperature have the same average kinetic energy, irrespective of mass.

    • Kinetic Energy (KE) formula:

      • KE = 1/2 * mass * speed²

Distribution of Gas Particles’ Velocity: Boltzmann Plots

  • Molecules of a gas have a range of speeds at a constant temperature and exhibit broader distributions at higher temperatures.

  • Kinetic Energy Relation: Changes in temperature affect speed and kinetic energy of gas particles.

Root Mean Square Speed of Gases

  • Particle Speed Relation:

    • Speed inversely related to particle mass.

  • Root-Mean-Square Speed (vrms):

    • Defined as the square root of the average of the squared speed of all particles.

  • formula: vrms = √(3RT / M)

    • R = Ideal Gas Constant,

    • T = absolute temperature,

    • M = molar mass of the gas.

  • Higher temperatures increase speed, while higher molar mass decreases speed.

Gas Diffusion and Effusion

  • Diffusion: Process of spreading one substance through another.

    • Example: Odors spreading in a room.

  • Effusion: Movement of gas molecules through a small opening into an empty container.

  • Mean Free Path: Average distance a particle travels before colliding with another particle.

Graham’s Law of Effusion

  • Rate of effusion of a gas is inversely proportional to the square root of its molar mass.

  • Formula: effusion rate₁ / effusion rate₂ = √(M₂ / M₁)

  • Gases with lower molar masses effuse faster.

Gas Laws Overview

Boyle’s Law

  • States that volume (V) of gas is inversely proportional to its pressure (P) at constant temperature.

  • Formula: P₁V₁ = P₂V₂

Charles’s Law

  • States that volume of a gas is directly proportional to its absolute temperature (T) at constant pressure.

  • Formula: V₁/T₁ = V₂/T₂

Avogadro’s Law

  • Volume of a gas is proportional to the number of moles of the gas (n) at constant temperature and pressure.

  • Formula: V₁/n₁ = V₂/n₂

Amontons’s Law (Guy–Lussac’s Law)

  • Pressure of a gas is proportional to its absolute temperature if volume does not change.

  • Formula: P₁/T₁ = P₂/T₂

The Combined Gas Law

  • Combines Boyle’s, Charles’s, and Avogadro’s laws to express the relationship of pressure, volume, and temperature.

  • Formula: (P₁V₁)/T₁ = (P₂V₂)/T₂

Ideal Gas Law

  • States relationship between pressure, volume, temperature, and number of moles:

  • Formula: PV = nRT

  • Where R is the ideal gas constant (0.08206 L·atm/(K·mol)).

Real Gases and Deviations

  • Under high pressure and low temperatures, real gas behavior deviates from KMT assumptions.

  • Real gas particles:

    • Have volume.

    • Experience intermolecular forces, affecting collisions and pressure.

Chapter 7: Gases

Properties of Gases

  • Matter exists as solid, liquid, and gas.

  • Gases have no definite volume and expand to fill their container.

  • Gas particles are far apart, resulting in low density and constant motion.

  • Pressure: Force per unit area from gas molecules colliding with surfaces.

Atmospheric Pressure

  • Varies by location and weather; measured with a barometer.

  • Standard Atmospheric Pressure: 1 atm = 760 mm Hg = 101.324 kPa.

Kinetic Molecular Theory (KMT)

  • Assumes gas particles are in constant motion with negligible volume and elastic collisions.

  • All gases at the same temperature have the same average kinetic energy: KE = 1/2 * mass * speed².

Gas Particle Velocity

  • Molecules exhibit a range of speeds; temperature affects speed and kinetic energy.

  • Root-Mean-Square Speed (vrms): vrms = √(3RT / M).

Diffusion and Effusion

  • Diffusion: Spreading substances; Effusion: Gas movement through a small opening.

  • Graham’s Law: Rate of effusion inversely relates to the square root of molar mass.

Gas Laws

  • Boyle’s Law: P₁V₁ = P₂V₂ (volume inversely proportional to pressure).

  • Charles’s Law: V₁/T₁ = V₂/T₂ (volume directly proportional to temperature).

  • Avogadro’s Law: V₁/n₁ = V₂/n₂ (volume proportional to number of moles).

  • Ideal Gas Law: PV = nRT, linking pressure, volume, temperature, and moles.

Real Gases

  • Deviate from KMT at high pressure and low temperature due to volume and intermolecular forces.