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Unformatted text preview: Chemistry 350 Midterm Solutions November 1, 2004 1. (20 marks) Briefly answer each of the following: (a) Sketch, on one set of axes, the compressibility Z if a gas vs. pressure P for an ideal gas, for a slightly non-ideal gas, and for a very non-ideal gas. Assume the temperature is the same for all gases. Answer: If we look at a series of gases in terms of increasing non-ideality, they would be, in that order, Ideal, He, N 2 and CH 4 , which are depicted below (b) When are Boltzmann statistics valid (give a mathematical expression)? When are they invalid? Please provide at least three examples or two conditions under which they may be invalid. Answer: Boltzmann statistics are valid when the inequality, N V h 2 8 mkT 3 / 2 1 , is satisfied. This inequality is most commonly unsatisfied for free electrons in a metal, or for molecular hydrogen or atomic helium at close to their boiling points. In each of these cases, the conditions of very low mass, as well as low temperature, lead to non-Boltzmann statistics. This basically means there are insufficient translational states available for statistical approximations to hold true, and the quantum natures of these systems are still manifested. (c) What is the difference in Q as expressed in terms of the molecular partition function q for a system of distinguishable vs. indistinguishable particles? When are particles distinguishable? When are they indistinguishable?distinguishable?...
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