Chapter5-Gases

Chapter 5: Gases

• Gases are one of the four phases of matter.

• Key characteristics of gases include:

  • Expand to fill their container.

  • Exert pressure on container surfaces and objects within.

  • Essential for everyday life (e.g., air as a mixture of O2 and N2).

Pressure

• Pressure (P) is defined as the force (F) exerted over a given area (A).

  • Formula: 𝑃 = 𝐹 / 𝐴.

• Forces exerted by gases contribute to pressure, including atmospheric pressure.

• Units:

  • Force is measured in Newtons (N).

  • Pressure is measured in Pascals (Pa).

  • Conversion: 1 Pa = 1 kg/m·s² = 1 N/m².

Example Calculation

• On the moon, with a mass of 68 kg:

  • Weight on the moon due to gravity (1.6 m/s²): (673 N = 68 kg imes 1.6 m/s²).

  • Area standing on: (0.5 m \times 0.5 m = 0.25 m²).

  • Pressure exerted: (P = \frac{670 N}{0.25 m²} = 2700 Pa).

• High pressure under stiletto heels can cause pain due to small surface area.

Atmospheric Pressure

• The most relatable pressure experienced daily is atmospheric pressure.

• Measurement tools:

  • Manometer for measuring gas pressure.

  • Barometer for measuring atmospheric pressure (mm Hg unit).

• Standard atmospheric pressure:

  • 1 atm = 101,325 Pa = 760 mm Hg = 760 torr.

Gas Laws

• Derived by Boyle, Charles, and Avogadro:

  • Boyle’s Law: Pressure is inversely proportional to volume (at constant temperature).

    • Formula: 𝑃𝑉 = 𝑘 or (P_1V_1 = P_2V_2).

  • Charles’s Law: Volume of a gas is directly proportional to its temperature (in Kelvins) at constant pressure.

    • Formula: ( \frac{V}{T} = b ) or ( V = bT ), (V_1/T_1 = V_2/T_2).

  • Avogadro’s Law: Volume is directly proportional to the number of moles of a gas at constant temperature and pressure.

    • Formula: ( V = an ), (V_1/n_1 = V_2/n_2).

Example Calculations (Gas Laws)

• Boyle's Law Example:

  • Given: 1.3 atm, 27 L → What is the volume at 3.9 atm?

  • Prediction: Increasing pressure will decrease volume.

  • Calculation: (1.3 atm (27 L) = 3.9 atm (V_2)) → (V_2 = 9.0 L).

• Charles's Law Example:

  • Given: Volume 0.842 L at 30°C, find volume at 60°C.

  • Conversion to K: T1 = 303 K, T2 = 333 K.

  • Calculation: (V_2 = \frac{0.842 L \cdot 333 K}{303 K} = 0.925 L).

• Avogadro's Law Example:

  • Given: 5.20 L with 0.436 moles, if an additional 1.27 moles is added at the same conditions, find new volume.

  • Total moles = 1.706, predicting volume increase to: (V_2 = 20.3 L).

Ideal Gas Law

• Combines Boyle’s, Charles’s, and Avogadro’s laws.

• Expresses state of a gas: (PV = nRT), where:

  • P = pressure (atm)

  • V = volume (L)

  • n = number of moles

  • R = 0.08206 (L atm)/(K mol)

  • T = temperature (Kelvin).

Example of Ideal Gas Law

• Given: 0.614 moles, 12.0°C, volume 12.9 L; find pressure.

  • Conversion: T = 285 K.

  • Use ideal gas equation: (P = \frac{(n)(R)(T)}{V} = 1.11 atm).

Gas Stoichiometry

• Molar Volume: Volume of 1 mole of gas at STP (0 °C, 1 atm): (22.42 L).

• Use molar volume and gas laws for calculations.

• Molar mass can be determined using density: (MM = \frac{dRT}{P}).

Example of Gas Stoichiometry

• Reaction: 2H2(g) + O(g) → 2H2O(g).

  • 0.500 L H2 reacts with 0.600 L O at STP;

  • Need to determine limiting reactant.

  • Calculate volume of H2O produced: Result = 1.14 L.

Dalton's Law of Partial Pressures

• States total pressure = sum of partial pressures of individual gases: (P_{total} = P_1 + P_2 + ... + P_n).

• Mole fraction: Ratio relating number of moles of component to total moles; (χ_i = \frac{n_i}{n_{total}} = \frac{P_i}{P_{total}}).

Example of Partial Pressures

• Calculating total pressure after adding He to a vessel containing N2:

  • Concluded partial pressures and total pressure both calculated and verified.

Kinetic Molecular Theory of Gases

• Postulates:

  1. Gas particle volume is negligible.

  2. Particles are in constant motion; collisions create pressure.

  3. Particles exert no forces on one another.

  4. Average kinetic energy relates directly to Kelvin temperature.

Kinetic Energy Calculations

• Formula for average KE: (KE_{average} = \frac{3}{2}RT) or (KE = \frac{1}{2}mv^2).

• Root Mean Square Velocity:

  • (u_{rms} = \sqrt{\frac{3RT}{M}}).

Effusion and Diffusion

• Diffusion: Mixing of gases.

• Effusion: Gas passage through an orifice.

• Graham’s Law: Rate of effusion inversely proportional to mass of gas.

Real Gas Law

• Adjusted ideal gas equation: Van der Waals equation includes corrections for pressure and volume.