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Unformatted text preview: Problem Set 10 Chem 3900: Physical Chemistry II
Spring 2011 Due: Class, Friday, April 29th Please make sure to write your name and the recitation you’ll attend. When you print out your work, try to minimize the number of pages. You can do this by printing multiple pages per sheet and/or by using a duplex printer. Problem 1.
Iodine molecules dissociate in the gas phase according to: Ig
2I g i) Use data from Table 18.2 to obtain an expression for Kp(T) for this reaction. As noted in Table 18.1 and on p. 734, halogen atoms have an electronic ground state that is fourfold degenerate. The I2 molecule electronic ground state is nondegenerate. ii) Make a Table of Kp(T) values over the range 500 K ≤ T ≤ 2000 K, using T increments of 100 K. Evaluate and Plot ln[Kp(T)] as a function of 1/T over the temperature range 500 K ≤ T ≤ 2000 K. Fit your plot to a linear function of 1/T and determine the slope. What is this quantity? Problem 2.
Consider the following isotope exchange reaction in the gas phase: DCl g
HCl g HOg Use data given below to obtain an expression for Kp(T) for temperatures near room temperature. That is, assume T to be several hundreds, but not thousands, of degrees Kelvin. To simplify your analysis, split up the equilibrium constant into contributions from the different molecular DOF: i) ii) iii) and evaluate each factor separately. By evaluate each factor separately and Simplify, there will be lots of cancellation. Give the expression for each factor. Evaluate each of the factors of the equilibrium constant and plot Kp(T) over the temperature range 300K ≤ T ≤ 1200 K. Does equilibrium favor reactants or products over this temperature range? Give a molecular explanation of this result. What is the expected value of Kp as T ∞? Make a plot and calculate rHo and rSo for this reaction for 300 ≤ T ≤ 1200 K. Are reactants or products favored by enthalpy? Are reactants or products favored by entropy? Data: • HCl: vib = 4305 K; rot = 15.24 K • DCl: vib = 3087 K; rot = 7.843 K • HDO: vib = 3925 K, 2018 K, 5337 K; rot = 33.65 K, 13.10 K, 9.237 K • H2O: vib = 5263 K, 2296 K, 5406 K; rot = 40.13 K, 20.89 K, 13.37 K 1 Note: (i) Within the Born‐Oppenheimer approximation (Sec. 9.1), the energy of the electronic ground state of a molecule is unchanged by isotopic substitution. (ii) All of these molecules have nondegenerate electronic ground states. (iii) H2O and HDO are asymmetric top molecules. That is, they have 3 unequal moments of inertia. The rotational partition function of an asymmetric top is given in Eq. (18.56). Don’t forget the rotational symmetry number . (iv) H2O and HDO each have 3 normal modes of vibration. The vibrational partition function for a polyatomic molecule is given in Eq. (18.46). 2 ...
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