The Ideal Gas Law: Applications and Exceptions

Chapter 10: 4-8 Homework

• Reading Preparation
• WebLecture
• Study Activity
• Preparation work for chat
• Online Quiz
• Lab Instructions

Reading Preparation

Textbook assignment: Read Kotz and Triechel, Chemistry and Chemical Reactivity Chapter 10: Sections 4 to 8

Study Notes

• 10.4: We can use gas laws to predict the outcome of chemical reactions, for example, the volume of gas released if known amounts of reactances are combined in a gas-producing reaction.
• 10.5: In an ideal world, individual gas samples each contribute to the pressure of mixture without affecting each other. We can figure out partial pressures (the pressure exerting by one gas) by assigning to each gas a fraction of pressure based on the fraction of its molecules to the total sample. If we have 2 moles of hydrogen gas mixed with 1 mole of oxygen gas, hydrogen will be responsible for 2/3 of the pressure exerted by the gas sample.
• 10.6: We can relate the temperature of a gas to the average kinetic energy of the molecules of gas using the average velocity of all of the molecules. The value û is the average velocity (this is usually u with a bar over it; a circumflex is as close as I can get in unicode). Average Kinetic Energy then is 1/2 the average mass (for a gas, this will be the exact mass for all molecules) times the square of the average velocity. The quantity û² is the mean square speed (we use speed rather than the vector quantity velocity to emphasize that we are not concerned with direction). The root-mean-square of the average velocity (now independent of direction) is directly related to the temperature of the gas. While all gases have the same KE at the same temperature, because the molar mass of the gas M varies, the average velocity will vary. The heavier the gas, the lower the average velocity at the same temperature.
• 10.7: Diffusion is the dispersal of gases over time to uniformly fill a volume. Effusion is the dispersal of a gas from one container through a narrow opening into another. Since diffusion rates depend on root mean square speed, which in turn is dependent on the mass of the molecules, differences in rates of effusion for two different gases at the same temperature and pressure depends only on the molar mass, a relationship known as Graham's Law.
• 10.8: We have to compensate the "ideal" situation described by PV = nRT for real gases. We recognize that pressure will be affected by intermolecular forces -- the fact that mass attracts mass and electrical fields can attract or repel, depending on charges. This means that collisions are not perfectly elastic, so our observed pressure will be somewhat less than the predicted ideal temperature. We also realize that gas particles do occupy volume in reality, so the space available to a gas has to be slightly diminished by the space occupied by the individual molecules. We compensate for deviations from the ideal gas law by using the van der Waals equation.

  Key Formula

  Concept	Formula	Notes
  Kinetic energy-Temperature Dependency	$$\mathrm{KE}=\text{½}m{v}^2=\frac{3}{2}\mathrm{RT}$$	KE: Kinetic Energy m: mass of individual particles v: velocity R: Gas constant T: absolute temperature (K)
  Velocity-Temperature Dependency	$$\sqrt{{\overline{u}}^2}=\sqrt{\frac{3\mathrm{RT}}{M}}$$	ū: average velocity (eliminate direction)
  Graham's Law	$$\frac{\mathrm{Rate}\mathrm{of}\mathrm{effusion}\mathrm{of}\mathrm{gas}1}{\mathrm{Rate}\mathrm{of}\mathrm{effusion}\mathrm{of}\mathrm{gas}2}=\frac{\sqrt{\overline{{u_1}^2}}}{\sqrt{\overline{{u_2}^2}}}=\frac{\sqrt{\frac{3\mathrm{RT}}{M_1}}}{\sqrt{\frac{3\mathrm{RT}}{M_2}}}$$	M1,M2: masses of individual molecules
  Van der Waals Equation	: $$(P+a{[\frac{n}{V}]}^2)(V-\mathrm{bn})=\mathrm{nRT}$$	a: intermolecular force correction (per substance) b: molecular volume correction (per substance)

  So in general, we need to increase observed pressure slightly and decrease observed volume slightly to match the values predicted by the ideal gas law.

Read the following weblecture before chat: Gases in Chemical Reactions

Study Activity