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Chemistry 4595 Problem Set #5 Fall 1998 Due: Thursday, October 8 1. The figure below was scanned from an article by Burton and Brant (Biopolymers, 22, 1769-92 (1983)). It represents a computer simulation of a polysaccharide. The scales are marked in Angstroms. Assuming this particular conformation to be “average,” estimate the persistence length of the chain being simulated. 2. Use a calculator or computer to plot the percent error in Stirling’s approximation for numbers N, beginning with N = 0 and going as high as you can. Plot the percent error against N. Remember, Boltzmann’s idea that entropy is klnW rests on the this relation, so the problem bears upon the burning question: how big must a molecular system be to be “thermodynamic”? When would you be satisfied that a system was big enough? Give an answer both in terms of N and qualitative descriptors of what it means to be a thermodynamic system. 3. For a general polymer solution, we can write 1-1o = -RTV1oc(M2-1 + A2c) where c is the concentration as g/mL, M2 is the molecular weight of solute, A2 is the second virial coefficient and V1o is the solvent molar volume and RT is the molar thermal energy, as usual. Write an expression for 2-2o and discuss the meaning of the standard state for component 2 (solute). Hint: we proved 3 general equations in our study of partial molar quantities and the method of intercepts. Use one of these, adapted for free energy. 4. A solution is made by weight: g1 = 6.5937 grams of solvent; g2 = 0.35897 grams of solute. Compute the weight fraction. Later, in order to compare some light scattering results to the usual theoretical expressions, it is decided to convert the weight fraction to c2 (the weight/volume concentration in g/mL) and also to (the volume fraction of solute). Accordingly, the partial specific volumes are measured for solute and solvent, using the method of intercepts described in lecture. In the concentration range of interest, they are found to be: v 2 = 0.815 mL/g and v 1 = 1.182 mL/g. From these data, compute c2 and 2 exactly. Also, estimate the density of the solute and solvent. 5. Give a recipe for preparing a polyethylene/trichlorobenzene solution in its 1 molal standard state. Assume a molecular weight of 8,500,000 for the PE, and indicate exactly how much mass of the solute, PE, and solvent, trichlorobenzene, will be required. 6. Consider a regular solution in which the enthalpy of mixing is given by: Hmix = (0.5 kJ/mol)xb + (2.5 kJ/mol)exp[-(xb - 0.5)2]. Does this system undergo phase separation at any temperature? 7. In class, we did not carefully evaluate the integral after converting it from a sum (the step) in the Flory derivation of Smix . I told you to leave some space in your notes for the proof. Show me what you wrote in your notes (you can just photocopy from your notes paste to this page). 8. Write an experimental procedure for determining the partial specific volume of toluene in polystyrene at 15% by weight polystyrene and 25oC. Assume you have only access to volumetric glassware, a good analytical balance and a temperature regulation bath.