2.S: Gases (Summary)
- Page ID
- 84447
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
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.