Gases

Gas Laws

Characteristics of Gases

  • Gases assume the volume and shape of the container.

  • Gases are the most compressible state of matter.

  • Gases mix evenly and completely when confined to the same container.

  • Gases have much lower densities than liquids and solids.

Kinetic Molecular Theory (KMT)

1. Motion of Gas Molecules

  • Gas molecules are in constant random motion, frequently colliding with one another.

  • Collisions are perfectly elastic, allowing energy to be transferred between molecules.

2. Intermolecular Forces

  • Gas molecules do not attract or repel each other; they do not interact.

3. Particle Separation

  • Gas is composed of molecules separated by distances far greater than their dimensions.

  • Gas particles have negligible mass.

4. Average Kinetic Energy

  • The average kinetic energy of gas molecules is proportional to the temperature in Kelvin.

  • Any two gases at the same temperature will have the same average kinetic energy.

Factors Affecting Gases

  • Pressure (P)

  • Volume (V)

  • Temperature (T)

  • Amount of Gas (measured by the number of moles)

Pressure (P)

  • Force exerted by gas molecules when they hit a surface; measured as force per unit area.

  • SI unit: Pascal (Pa).

Volume (V)

  • The amount of space an object occupies; expressed in cubic decimeters (dm3) or liters (L).

Temperature (T)

  • SI unit: Kelvin (K).

  • Conversion formula: Kelvin (K) = °C + 273.15.

Amount of Matter

  • Amount of matter present in a sample measured in moles (mol).

Gas Laws Overview

  • Gas laws show relationships between pressure, volume, temperature, and moles.

Boyle’s Law

  • Discovered by Robert Boyle: Doubling the pressure of an enclosed gas at constant temperature and moles reduces the volume by half.

  • Volume is inversely proportional to pressure at constant temperature.

Charles’ Law

  • Studied by Jacques Charles: Volume of a gas is directly proportional to its temperature at constant pressure.

  • The temperature must be measured in Kelvin.

Gay-Lussac’s Law

  • Named after Joseph Louis Gay-Lussac: Pressure of a gas is directly proportional to its temperature at constant volume.

Avogadro’s Law

  • Equal volumes of any gas at the same temperature and pressure contain the same number of molecules.

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

Relationship Summary of Gas Laws

  • Boyle’s Law: Volume inversely proportional to pressure (constant T).

  • Charles’ Law: Volume directly proportional to temperature (constant P).

  • Gay-Lussac’s Law: Pressure directly proportional to temperature (constant V).

  • Avogadro’s Law: Volume directly proportional to moles (constant T and P).

Practice Problems

Problem 1

  • A sample of oxygen gas has a volume of 425 mL at a pressure of 387 kPa. Calculate the new pressure when it expands to 1.75 L.

Problem 2

  • A balloon filled with 1.90 L of helium gas contains 0.0920 mol. Additional 0.0210 mol is added. Calculate the new volume (at constant T and P).

Problem 3

  • A balloon is filled to 2.20 L at 22°C and heated to 71°C. Find the new volume.

Ideal Gas Law

  • The ideal gas law is a single equation relating pressure, volume, temperature, and number of moles of an ideal gas: PV = nRT.

  • Ideal gases do not attract or repel and have negligible volume compared to their container.

  • Ideal gas constant R is required for calculations.

Standard Temperature and Pressure (STP)

  • Under conditions of 0°C (273 K) and 1 atm, 1 mole of an ideal gas occupies 22.4 L.

Stoichiometry in Gases

  • Mole relationships in reactions involving gases:

    • Amount of reactant (volume or weight) ➔ Moles of reactant ➔ Moles of product ➔ Amount of product (volume or weight).

Dalton’s Law of Partial Pressures

  • Total pressure of a mixture of gases equals the sum of the pressures each gas would exert alone.

  • Partial pressure (P) is the pressure of an individual gas component in a mixture.

Dalton's Law Formulas

  • Ptotal = P1 + P2 + ...

  • Partial pressure calculations: P1 = n1RT/V, P2 = n2RT/V.

Mole Fraction

  • Mole fraction (Xi) expresses the ratio of moles of one component to the total moles in a mixture: Xi = ni / ntotal.

  • The sum of mole fractions for all gases must equal 1 in a system.

Gas Diffusion and Effusion

Diffusion

  • Gradual mixing of gases from high concentration to lower concentration due to kinetic properties.

Effusion

  • Process of gas escaping from a compartment through a small opening.

  • Example: Helium-filled balloons deflate faster due to lighter helium atoms.

Example Problems

  • Example 1: Mixture of 4.46 moles of Ne, 0.74 moles of Ar, and 2.15 moles of Xe; calculate partial pressures at 2.00 atm.

  • Example 2: Reaction of 9.0 L of NO with excess O2; calculate the volume of NO produced.

  • Example 3: Combustion of 15.0 moles of CH4; find volume of CO2 produced at 23.0°C and 0.985 atm.