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Unformatted text preview: Chemistry 120B SP11 Problem Set 11 Solutions 1. (i) The transition state theory rate constant is k TST A B = k B T h Q vib Q A vib e- E The total vibrational partition function is the product of the q vib s of all the modes. Ignoring quantum mechanical effects, q vib = 1 / ~ . So, Q vib = 1 ~ n 1 1 2 n ! and Q A vib = 1 ~ n +1 1 1 2 n The ratio of these partition functions is Q vib Q A vib = ~ 1 2 n 1 2 n and the rate constant is k TST A B = 1 2 1 2 n 1 2 n ! e- E = 2 Y j j j e- E (ii) Assume the isotopic substitution affects only fluctuations along , so all the j s and j s cancel except j = . Since E is the same for both isotopes, k H k D = H D = r D H = s m D m C m D + m C m H + m C m...
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