Ideal+Gases 2

Gases

• State of Matter Characteristics

  • Low interaction energy between individual particles compared to kinetic energy.

  • Exhibits elastic collisions at room temperature.

  • Wide separation of particles results in low density and high compressibility.

  • Shape: Expands to fill the container and exerts pressure on the walls.

Pressure

• Definition

  • Pressure = Force / Area

  • Directly proportional to force (doubling force doubles pressure).

  • Inversely proportional to area (doubling area reduces pressure by half).

• Examples

  • Elephants: Large feet distribute weight over a larger area, reducing pressure.

  • Breaking ice: Laying down distributes weight, reducing pressure on the ice.

  • Solids (rigid shapes) exert no lateral pressure.

Gas Pressure

• Particle Behavior

  • Particles do not stick to one another and move freely, escaping gravity's pull at ambient temperatures.

  • Collisions among particles and with container walls exert force, contributing to gas pressure.

Pressure Units

• S.I. Unit

  • Pascal (Pa)

    • Pa = N/m², where N is Newton.

• Common Units in Chemistry

  • Atmosphere (atm), Torr/mm Hg, Bar.

• Conversions

  • 1 atm = 101,325 Pa

  • 1 bar = 100,000 Pa

  • 1 atm = 760 torr/mm Hg

Pressure of a Liquid

• Force Exerted by Liquids

  • Even in a vacuum, a liquid exerts a downward force due to weight.

  • Formula: P = mg/A, P = gpv/A, P = gph for a liquid.

  • Utilize height rather than mass for pressure measurement if container is open to atmosphere.

Vacuum and Atmospheric Pressure

• Vacuum Effects

  • Air pressure combined with gravitational force holds liquid down.

  • Mercury in barometers is used due to its high density.

  • Standard mercury height at sea level is 760 mm.

Empirical Gas Laws

• Scientific Method

  • Observations lead to controlled conditions that summarize large bodies of data.

• Boyle's Law

  • At constant temperature and amount of gas, pressure increases as volume decreases (P1V1 = P2V2).

Charles's Law

• Temperature-Volume Relationship

  • At constant pressure, increasing temperature increases volume (V ∝ T).

  • Zero degrees Celsius corresponds to 273.15 K.

Avogadro's Law

• Volume-Molecule Relationship

  • Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

  • Volume is directly proportional to amount of gas n (V = nRT).

Ideal Gas Law

• Formulated as PV = nRT, relating pressure, volume, temperature, and moles of gas.

• Constants:

  • R (ideal gas constant) = 0.0821 L·atm/(K·mol) or 8.314 J/(K·mol).

Calculating Gas Density

• Ideal Gas Law

  • PV = nRT can be rearranged for density calculations using molecular weight (M.W.).

  • PV = (mass/M.W.)RT; can lead to understanding of gas density in g/L.

Gases in Chemical Reactions

• Number of gas particles influences pressure, volume, and temperature (n = PV/RT).

• Gas stoichiometry relates volumes and amounts in reactions.

Mole Fraction and Partial Pressure

• Mole fraction (X) = moles of component / total moles.

• Partial pressure (Pi) can be calculated using X and total pressure (P).

Kinetic-Molecular Theory of Gases

• Explains gas behavior based on particle motion and interactions.

• Assumes particles are in constant random motion with negligible volume.

Real Gases

• Deviate from ideal behavior due to particle interactions and volume effects.

• Utilizing van der Waals equation for real gas behavior helps account for these deviations.