Chemistry: The Central Science - Chapter 10

Chemistry: The Central Science - Chapter 10 Notes

Outline

• What are ideal gases?

• 10.1 Characteristics of Gases

• 10.2 The Gas Laws

• 10.3 The Ideal Gas Equation

• 10.4 Gas Mixtures and Partial Pressures

• What is the explanation for ideal gas behavior?

• 10.5 The Kinetic Molecular Theory of Gases

• 10.6 Molecular Speeds, Effusion and Diffusion (Brief Discussion in class)

• How do real gases deviate from ideal behavior?

• 10.7 Deviations from Ideal Behavior (Brief Discussion in class)

What are ideal gases?

• Definition: An ideal gas is a theoretical gas composed of many randomly moving point particles that do not interact except when they collide elastically.

• Characteristics:

  • No fixed shape or volume; expands to fill container.

  • Highly compressible.

  • Extremely low density due to large spaces between molecules.

10.1 Characteristics of Gases

• Physical Properties:

  • Composed mainly of nonmetallic elements with simple formulas and low molar masses.

  • Many molecular compounds exist in the gaseous state.

  • Very few elements are gases at normal temperature and pressure (N2, O2).

  • All gases form a homogeneous mixture when combined.

• Common Gases at Room Temperature:

  • Elements: He, Ne, Ar, Kr, H₂, N₂, O₂, F₂, Cl₂

  • Compounds: HF, HCl, HBr, HI, HCN, H₂S, NH₃, CH₄, C₂H₆, CO, CO₂, NO, N₂O, SO₂, etc.

• Distinction Between Gas and Vapor:

  • Gas: Refers to nitrogen and oxygen.

  • Vapor: Refers to gaseous state of a substance (like water vapor) that is liquid or solid at normal conditions (25°C, 1 atm).

10.2 The Gas Laws

• Key Variables:

  1. Pressure (P)

  2. Volume (V)

  3. Temperature (T)

  4. Amount of gas particles (n, moles)

• The relationships between these variables are defined by the gas laws.

Gas Law 1: Pressure and Volume (Boyle’s Law)

• Definition: The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

• Mathematical Representation: PV = ext{constant}

  • Plotting V vs. P creates a curve.

  • Inverse relationship: As pressure increases, volume decreases.

Gas Law 2: Temperature and Volume (Charles’s Law)

• Definition: The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature (K).

• Mathematical Representation: V ext{ = Constant} imes T

  • Direct relationship: As temperature increases, volume increases.

Gas Law 3: Moles and Volume (Avogadro’s Law)

• Definition: The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.

• Mathematical Representation: V/n = ext{constant}

  • Also expressed as V1/V2 = n1/n2.

  • Avogadro’s Hypothesis: Equal volumes of gases at the same temperature and pressure contain the same number of molecules.

Additional Gas Law: Gay-Lussac’s Law

• Definition: At constant volume, the pressure of a gas is directly proportional to its absolute temperature.

• Relationship: P/T = ext{constant}

  • Demonstrates the relationship between temperature and pressure.

Summary of Gas Laws

• Gas laws allow for determining one variable when others are known by holding two variables constant.

10.3 The Ideal Gas Equation

• Combination of Gas Laws:
  PV = nRT

  • Here, R is the gas constant.

  • Gas constant (R) values include:

  • 0.08206 L·atm/(mol·K)

  • 8.314 J/(mol·K)

  • 62.36 L·torr/(mol·K)

• Standard Temperature and Pressure (STP):

  • T = 273.15 K

  • P = 1.00 atm

  • Molar Volume at STP:
    rac{V}{n} = 22.414 L/mol

• Example Calculation:

  • Use ideal gas law to calculate volumes or moles based on pressure and temperature.

10.4 Gas Mixtures and Partial Pressures

• Dalton’s Law: Total pressure of a mixture of gases equals the sum of the partial pressures of individual gases.
  P{ ext{total}} = P1 + P2 + P3 + …

• Partial Pressure: Pressure exerted by a specific gas in a mixture.

  • Example: For a mixture containing O2, He, and N2, with respective partial pressures of 0.450 atm, 0.780 atm, and 1.675 atm, the total pressure is:
    P_{ ext{total}} = 0.450 + 0.780 + 1.675 = 2.905 atm

• Mole Fraction:
  ext{mole fraction} ( ext{χ}) = rac{n{ ext{component}}}{n{ ext{total}}}

10.5 Kinetic-Molecular Theory of Gases

• Principles of KMT:

  1. Gas particles are in continuous, random straight-line motion.

  2. Collisions between particles are perfectly elastic.

  3. The volume of gas molecules is negligible compared to the volume of the container.

  4. No intermolecular forces.

  5. Average kinetic energy is proportional to absolute temperature:
     KE_{ ext{avg}} = rac{3}{2} kT, where k is Boltzmann constant.

• Distributions of Molecular Speed:

  • Different molecules at the same temperature will have different speeds.

  • Relationships between average kinetic energy and speed are established.

• Application:

  • Increasing volume at constant temperature decreases pressure due to more distance between collisions.

  • Increasing temperature raises pressure as collisions become more frequent and forceful.

10.6 Molecular Speeds, Effusion, and Diffusion

• Effusion: Escape of gas through a tiny hole into a vacuum.

• Diffusion: Spread of one substance throughout space.

• Graham's Law: Relates molar mass to rate of effusion and diffusion:
  rac{r1}{r2} = rac{ ext{MM}2}{ ext{MM}1}

10.7 Real Gases: Deviations from Ideal Behavior

• Conditions for Deviations: Gases behave more ideally at high temperatures and low pressures.

• Corrections for Nonideal Behavior:

  • Van der Waals equation accounts for intermolecular forces and molecular volume.

  • Adjusts the ideal gas equation:
    (P + rac{a n^2}{V^2})(V - nb) = nRT

  • Provides constants (a and b) for different gas molecules, indicating their nonideal behavior.

• Example Calculations:

  • Analyze deviations using specific examples provided in the chapter.