Homework

# The Ideal Gas Law: Applications and Exceptions

## Chapter 10: 4-8 Homework

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

ConceptFormulaNotes
Kinetic energy-Temperature Dependency KE: Kinetic Energy
m: mass of individual particles
v: velocity
R: Gas constant
T: absolute temperature (K)
Velocity-Temperature Dependency ū: average velocity (eliminate direction)
Graham's Law M1,M2: masses of individual molecules
Van der Waals Equation: 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

#### Videos for Chapter 10: Gases and their Properties

Review the Videos at Thinkwell Video Lessons.

• Under "Gases: The Ideal Gas Law and Kinetic-Molecular Theory of Gases"
• The Ideal Gas Law
• Partial Pressure and Dalton's Law
• Applications of the Gas Laws
• The Kinetic-Molecular Theory of Gases
• Under "Gases: Molecular Motion of Gases
• Molecular Speeds
• Effusion and Diffusion
• Under "Gases: Behavior of Real Gases
• Comparing Real and Ideal Gases

#### Interactive Simulations

Use the simulation below to explore the energy window to explore energy and motion of gas particles.

• Use the pump to inject gas particles in the chamber.
• Use the heat source to change temperature.
• Observe the changes to the speed distribution of molecules of different masses, the average speed of the molecules, and the kinetic energy of the gases.
• Use the diffusion window to explore how changing the number of particles, mass, radius, and temperature affect rates of diffusion.

#### Chat Preparation Activities

• Essay question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
• Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

#### Chapter Quiz

• Required: Complete the Mastery exercise with a passing score of 85% or better.
• Go to the Moodle and take the quiz for this chapter.

#### (Aligns to) AP #8 GUIDED INQUIRY — Measuring the deviation of real gases from the ideal gas law — Phase II

Carry out your procedure to collect data and formulate a prediction for gas behavior, including behavior near absolute zero. Identify test cases to use for validating your predictions.

References:

• IGHCE Lab 14.1 OR HSCKM VIII-1: Volume-Pressure relationships (Boyle's Law)
• IGHCE Lab 14.2 OR HSCKM VIII-2: Volume-Temperature relationships (Charles' Law)
• IGHCE Lab 14.3 Pressure-Temperature relationship (Gay-Lussac's Law)
• Alternate Labs (two): Gas Volumes and Gas Generation