Chapter 10 - Gases

• Characteristics of gases
• No definite shape or volume
• vapors - co-exist w/l or s
• mixtures always homogeneous
• Pressure
• force per unit area (psi)
• atmospheric pressure - due to gases in the atmosphere
• standard atmospheric pressure - 1atm
• give values for psi, torr, in Hg, kPa, Pa
• explain barometer
• show conversions among units
• manometer

• Gas laws
• Boyle's Law
• Charles' Law
• P/T relationship
• Combined gas law
• Avogadro's Law
• Ideal Gas Law
• combines all variables (P, V, T, n) to PV = nRT
• R - Ideal Gas Constant
• 0.08206 L atm mol-1 K-1
• 8.314 L torr mol-1 K-1
• 62.36 L kPa mol-1 K-1
• STP
• molar volume - 22.41 L @ STP
• some variation for some 'real' gases

• Molar Mass - Densities
• Molar Mass (MW) = grams/mole
• rearrange n=g/MW
• substitute into ideal gas law - PV = (g/MW)RT
• Rearrange - M``W ~ = ~ {g``R``T} OVER {P``V}
• Density = g/L for a gas
• substitute n = g/MW into ideal gas equation
• rearranging - {g} OVER {V} ~=~ {P``(M`W`)} OVER {R``T}

• Partial Pressures
• PT = Pi
• mole fractions ()
• PT * i = Pi

• Volumes of gases in Chemical Reactions
• Collection over water (Appendix B - partial pressures of water)

• Kinetic - Molecular Theory
• 5 postulates
• Large # of molecules in continuous, random motion.
• gas molecule volume >>> volume contained in.
• Intermolecular forces negligible.
• Energy transferred in collisions, but the average kinetic energy constant with constant temp. (perfectly elastic collisions.)
• Average kinetic energy proportional to absolute T.
• Explain gas laws
• Boyle's - lower volume & increase frequency of same energy collisions.
• P/T - increase T and increase energy & frequency of collisions
• Charles' - for P to remain constant must decrease frequency of higher energy collisions.
• Graham's Law

• {r SUB 1} OVER {r SUB 2} ~=~ SQRT {{(M``W) SUB 2} over {(M``W) SUB 1}}

• mean free path (100 nm @ typical pressures)

• Deviations from ideal behavior
• Molecular volume d/n 0
• molecular interaction 0
• van der Walls
• (P``+`` {n SUP{ 2} ``a} over {V SUP {2}})~(V``-``nb) ~=~ n``R``T

• a - correct for IM forces
• b - correct for molecular volume
• a & b determined experimentally

Learning goals:

1. Describe the general characteristics of gases as compared to other states of matter, and list the ways in which gases are distinct.

2. Define atmosphere, torr, and pascal (the most important units in which pressure is expressed) and describe how a barometer and manometer work.

3. Describe how a gas responds to changes in pressure, volume, temperature, and quantity of gas.

4. Use the ideal gas equation to solve for one variable given the other three, or information from which the other variables can be calculated.

5. Use the gas laws, including the combined gas law, to calculate how one variable of a gas responds to changes in one or more of the other variables.

6. Calculate the molar mass of a gas, given the mass or density under specified conditions of temperature and pressure.

7. Calculate the partial pressure of any gas in a mixture, given the composition of that mixture.

8. Calculate the mole fraction in a mixture, given its partial pressure and the total pressure of the system.

9. Describe how the distribution of speeds and the average speeds for gas molecules changes with changes in temperature.

10. Describe how the relative rates of effusion and diffusion of two gases depend on their molar masses.

11. Cite the conditions of P and T under which real gases most closely approximate ideal-gas behavior.

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