chapter5 with added slides MB dist

5.1 Pressure

Why Study Gases?

  • Understanding real-world phenomena related to gases.

  • Insight into how scientific principles operate.

Characteristics of Gases

  • Uniform Filling: Gases fill any container uniformly.

  • Compression: Gases can be easily compressed.

  • Mixing: Gases mix completely with other gases.

  • Exerting Pressure: Gases apply pressure on surroundings.

Units of Pressure

  • SI Units: Newton/meter² = 1 Pascal (Pa)

  • Standard Atmosphere: 1 atm = 101,325 Pa

  • Other conversions:

    • 1 atm = 760 mm Hg

    • 1 atm = 760 torr

Barometer

  • Function: Measures atmospheric pressure.

  • Mechanism: Mercury flows until its column's pressure equals the atmospheric pressure acting on the mercury in the dish.

Manometer

  • Use: Measures the pressure of a gas in a container.

Pressure Conversion Example

  • Example of converting pressure: 2.5 atm into torr and pascals needed for calculations.

Atmospheric Mass Calculation

  • Atmospheric mass:

    • Patm = Matmg / (4πR²)

    • g = 9.81 m/s²

    • R = 6400 km

    • Matm = 5.2 x 10¹⁸ kg, approximately 10⁻⁶ x MEarth.

Collapsing Can Demonstration

  • Used to illustrate the concept of atmospheric pressure.

5.2 The Gas Laws of Boyle, Charles, and Avogadro

Observations with Gas Laws

  • Example: Decrease in temperature corresponds with a decrease in pressure and volume in a balloon with liquid nitrogen.

  • These are factual observations and serve as a basis for establishing gas laws.

Boyle's Law

  • Definition: Pressure and volume are inversely related when temperature and number of moles are constant.

  • Equation: PV = k (k is a constant).

  • Example Calculation: A helium gas occupying 12.4 L at 23°C and 0.956 atm will occupy 9.88 L at 1.20 atm (temperature constant).

Charles's Law

  • Definition: Volume and temperature in Kelvin are directly related when pressure and number of moles are constant.

  • Equation: V = bT (b is the proportionality constant).

  • Absolute zero (0 K) is the starting point for temperature scale.

  • Example Problem: A balloon containing 1.30 L of air at 24.7°C shrinks to 0.849 L when placed in dry ice at -78.5°C.

Avogadro's Law

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

  • Equation: V = an (a is a proportionality constant).

  • Example: 2.45 mol of argon occupies a volume of 89.0 L; 2.10 mol occupies 76.3 L under the same conditions.

Ideal Gas Law

  • Unification of previous laws into: PV = nRT (R = 0.08206 L·atm/mol·K).

  • Examples of Application:

    • Determining moles in an automobile tire: 3.27 mol in a 25 L tire at 3.18 atm.

    • Finding pressure in a tank with helium, calculating temperature for CO2 expansion conditions.

5.4 Gas Stoichiometry

Molar Volume of Ideal Gas

  • STP: Standard Temperature and Pressure (0°C and 1 atm) results in the molar volume of 22.42 L for 1 mole of an ideal gas.

Molar Mass of a Gas

  • Density Equation: d = P / RT - Density of gas at specific conditions.

Exercises Related to Stoichiometry

  • Calculating grams of O2 in given volumes at STP (resulting in 3.57 g).

5.5 Dalton’s Law of Partial Pressures

General Principle

  • For gas mixtures, total pressure = P1 + P2 + P3 + ... (sum of individual pressures).

Applications of Dalton's Law

  • Example Problem: Calculate new partial pressures and total pressure in a tank when combining helium and oxygen under specific conditions.

5.6 Kinetic Molecular Theory of Gases

Basics of the Theory

  1. Particle Size: Gas particle size is negligible compared to the distances between them.

  2. Motion: Particles are in constant motion, with collisions causing gas pressure.

  3. No Interactions: It is assumed gas particles do not attract or repel each other.

  4. Kinetic Energy: The average kinetic energy is directly proportional to the Kelvin temperature of the gas.

Practical Implications of the Kinetic Molecular Theory

  • Explains observed gas behavior and leads to conclusions made about gas properties.

  • Provides a basis for understanding pressure, temperature, and volume relationships.

5.7 Effusion and Diffusion

Definitions

  • Diffusion: Mixing of gases.

  • Effusion: Movement of gas through a tiny opening.

Graham’s Law of Effusion

  • Relates effusion rates of two gases to their molar masses.

5.8 Real Gases

Distinction from Ideal Gases

  • Real gases are affected by intermolecular forces and do not perfectly conform to ideal gas laws under high pressure or low temperature.

  • Conditions determine the need for corrections in gas behavior models.

5.9 Characteristics of Several Real Gases

Maxwell-Boltzmann Distribution

  • Illustrates the distribution of molecular speeds in gases, highlighting the concept of most probable speed, mean speed, and root mean square speed.

Application of the Distribution in Real Gases

  • Important for understanding behavior differences between gases based on molar mass and conditions.