2.S: Gases (Summary)

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Learning Objectives

After mastering the material covered in this chapter, one will be able to:

Understand the relationships demonstrated by and perform calculations using the empirical gas laws (Boyle’s Law, Charles’ Law, Gay-Lussac’s Law, and Avogadro’s Law, as well as the combined gas law.)
Understand and be able to utilize the ideal gas law in applications important in chemistry.
State the postulates of the Kinetic Molecular theory of gases.
Utilize the Maxwell and Maxwell-Boltzmann distributions to describe the relationship between temperature and the distribution of molecular speeds.
Derive an expression for pressure based on the predictions of the kinetic molecular theory for the collisions of gas molecules with the walls of a container.
Derive and utilize an expression for the frequency with which molecules in a gas sample collide with other molecules.
Derive and utilize an expression for the mean-free-path of molecules based on temperature, pressure, and collisional cross section.
Explain how the van der Waals (and other) model(s) allow for deviations from ideal behavior of gas samples.
Derive an expression for the Boyle temperature and interpret the results based on how a gas’s behavior approaches that of an ideal gas.
Explain and utilize the Principle of Corresponding States.

Vocabulary and Concepts

average
Boyle temperature
collisional cross section
compression factor
critical point
critical temperature
diffusion
effusion
empirical
empirical gas laws
frequency of collisions
frequency of collisions with the wall
gas law constant
ideal gas law
intermolecular potential
isotherm
Kinetic Molecular Theory
Knudsen cell
Leonard-Jones potential
maximum probability
Maxwell’s distribution
Maxwell-Boltzmann distribution
mean free path
normalization constant
number density
principle of corresponding states
reduced variables
root-mean-square
Second Virial Coefficient
Taylor Series Expansion
van der Waals’ equation
Virial Equation

References

Avogadro, A. (1811). Essay on a Manner of Determining the Relative Masses of the Elementary Molecules of Bodies, and the Proportions in Which They Enter into These Compounds. Journal de Physique, 73, 58-76.
Bernoulli, D. (1738). Hydronamica.
Clausius, R. (1857). Ueber die Art der Bewegung, welche wir Wärme nennen. Annalen der Physik, 176(3), 353–379. doi:10.1002/andp.18571760302
Dieterici, C. (1899). Ann. Phys. Chem., 69, 685.
Einstein, A. (1905). Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik, 17(8), 549-560. doi:10.1002/andp.19053220806
Encycolopedia, N. W. (2016). Amedeao Avogadro. Retrieved April 13, 2016, from New World Encycolpedia: http://www.newworldencyclopedia.org/...medeo_Avogadro
Fazio, F. (1992). Using Robert Boyle's Original Data in the Physics and Chemistry Classrooms. Journal of College Science Teaching, 363-365.
Guggenheim, E. A. (1945). Corresponding State for Perfect Liquids. Journal of Chemical Physics, 13, 253-261.
Hunter, M. (2004). Robert Boyle (1627 - 91). Retrieved March 10, 2016, from The Robert Boyle Project: http://www.bbk.ac.uk/boyle/
Johannes Diderik van der Waals - Biographical. (2014). Retrieved March 12, 2016, from Nobelprize.org: http://www.nobelprize.org/nobel_priz...waals-bio.html
Maxwell, J. C. (1860). Illustrations of the dynamical theory of gases. Part 1. On the motions and collisions of perfectly elastic spheres. Phil. Mag., XIX, 19-32.
Maxwell, J. C. (1873). Molecules. Nature, 417, 903-915. doi:10.1038/417903a
Redlich, O., & Kwong, J. N. (1949). On the Thermodynamics of Solutions. V. An Equation of State. Fugacities of Gaseous Solutions. Chemical Reviews, 44(1), 233-244.
van der Waals, J. D. (1913). The law of corresponding states for different substances. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, (pp. 971-981).
van der Waals, J. D. (1967). The equation of state for gases and liquids. Nobel Lectures in Physics 1901 - 1921, 254-265.