Problem Set #19 Assigned: February 19, 2024 Due: Feb. 21, 2024 at 2:30 pm 1. Trouton’s Rule states that vaporization entropies, vapS, are typically 85 J/K regardless of the vapH values. This holds true for many organic molecules. Nevertheless, the value for water is 109.1 K. (a) Provide an explanation for why this value is higher than expected. (b) vapS = 45.1 for formic acid. Explain why this value is lower than expected. 2. Consider a liquid that obeys Trouton’s rule. The normal boiling point is 127.5 °C. What is the vaporization enthalpy of this molecule? 3. At 4.2 K the heat capacity of a silver sample is 0.0145 J/K. Assuming that the Debye extrapolation holds, Cv = aT3, determine the entropy difference between the value at 4.2 K and 0 K. 4. Transferring energy in the form of heat to a substance in order to melt it is usually associated with a smaller phase transition entropy than transferring heat in order to boil the same substance. This occurs despite the fact that dStrans = dqtrans/Ttrans, whereby Ttrans is a lower value for melting than boiling (i.e. Tmelt < Tboil). Using the definition of the entropy change at the phase transition, dStrans, explain this apparent paradox. (Note, in class we partially justified this idea in terms of the volume expansion. Here, I’m asking you to justify it on the basis of the equation.) 1. (a) The value is higher than expected because once water reaches the stage of being a gaseous vapor it becomes more disordered which creates a higher value of entropy since the de nition of entropy is the amount of disorder in a system. (b) The dimerization of formic acid causes the entropy of vaporization to be so much lower than the other values. 2 127.5 C 273 Draph 88 88 400.5K monk Tb 400.5 35244 1m01 3 ΔS of at f F at If αT AT α 0 514.2k S OK α 0.0145 mol.is 3 ΔS 0.00483 mol 4. The de nition of entropy is the increase of disorder and in the solid stage there is little disorder and as the system moves more towards the gaseous phase there is an increase in the entropy hence why the entropy associated with melting is lower than the one associated with boiling.