Due in class on Thursday Sept. 8 th

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1 Problem Set #1 Chem 391 Due in class on Thursday Sept. 8 th ame Solutions A note: To help me read quickly, I structure the problem set like an exam. I have made small spaces for answers where I d like short answers. You won t win friends by waxing eloquent. Pithy answers that get to the point quickly are hugely preferred. As is legible handwriting. 1. For the following processes, identify whether G, and S are positive (+), negative (-) or about zero (~0) at the standard state and 298 K. ffer brief explanations. Reaction G S Explanation 2 does not spont. decompose to atoms. 2 (g) 2 (g) Breaking bonds is enthalpically unfavorable, but two atoms from one molecule is favorable entropically. 2 3 (aq) 3 3 (aq)* o enthalpic value to -bond since it s just replacing -bonds with water. But 3 loses entropy (2 free molecules to 1 complex) C 6 12 (aq) C 6 12 (l) Pretty much as above. It happens, even though hexane makes better IMFs with water than itself. Why? ydrophobic effect! * The formation of an -bonded dimer of ammonia in water 2. Ethanol (C 2 5 ) is highly soluble in water but propane (C 3 8 ) is fairly insoluble, even though the molecules are about the same size. Why? Compare: Δ ΔS (cal/molk) G C 2 5 (l) C 2 5 (aq) C 3 8 (l) C 3 8 (aq) a. Does ethanol dissolve spontaneously in water (at the standard state)? ow do you know? Explain the values of and S associated with dissolution. You bet it dissolves spontaneously ( G <0). Entropy is positive due to mixing (both ethanol and water will occupy a larger volume) and enthalpy is negative presumably because ethanol makes stronger -bonds with water than itself and the water forms stronger vdw with the ethyl group than ethanol does. b. Does propane dissolve spontaneously in water (at the standard state)? Why? Explain the values of and S associated with dissolution. o propane does not, as evidenced by positive G. is still favorable (stronger IMFs betw. water and propane than betw. propane & propane), but S is now negative due to the hydrophobic effect and formation of clathrates around propane surfaces.

2 3. Calculate K and G at 25 C for the following, make-believe equilibrium conditions in a reaction where A(aq) + B(aq) C(aq). See if you can avoid using a calculator. [A] [B] [C] K G 0.5 mm 2 mm 1 mm 1 x M µm 1 nm 1 mm 1 x M mm 1 µm 1 pm 1 x 10-3 M Consider molecules A & B below. A. B. a. Identify heteroatoms ( & ) that can act as -bond donors by circling them. If they can act as acceptors, draw a square around them. If they can both donate and accept, draw a diamond. b. Redraw A & B and orient them so that each molecule is both donating an - bond to and accepting an -bond from the other. Be careful! Make sure that the -bond has a roughly 180 angle about the hydrogen atom. ote that there are multiple ways to achieve this. c. Sketch a scheme in which molecule B accepts two hydrogen bonds from A. Explain why it is a bad -bonding scheme. ote steric clash on hydrogen in red. Also, maybe less important, lone pairs on ring s point way from where s are. 5. Draw the structure of the peptide WISPER, in the dominant ionization state for p 8.0.

3 6. Fatty acids are amphiphilic molecules possessing a polar head group and a non-polar tail. Most are sparingly soluble in water as individual molecules and above a particular concentration (the cmc, critical micelle concentration) they aggregate to form micelles spherical aggregates of a few dozen to a few hundred molecules where the tails are buried from solution and the heads are exposed (see picture). a. The cmc s of several fatty acids are given above. Given the values of cmc listed above, how does the free energy of micelle formation change with increasing number of carbons in the tail? Explain briefly. G of micelle formation is more negative as tail length grows. A lower concentration of free amphiphile is needed to form micelle. If less reactant present at equilibrium, K is larger and therefore G is more negative. b. Consider the enthalpic issues attached to aggregation and briefly state whether you expect them to be favorable or unfavorable: i. for transfer of tail from water to micelle interior: Slightly positive. Tail gives up dipole/induced dipole interaction for induced dipole/induced dipole interaction. ii. for transfer of head group from water to micelle surface. Positive. egative charges packed on surface repel each other, which is enthalpically unfavorable. c. What entropic considerations are responsible for that trend? Briefly discuss each of the following concerns and ID the one that i. Conformational entropy of the chain: egative loss of free rotations in C-C bonds is unfavorable. ii. Entropy of aggregation egative many free molecules aggregate to form one object. Loss of translational freedom. iii. Solvent entropy Positive clathrates disrupted by tails being segregated from water. d. Given you analysis of enthalpic and entropic contributions to micelle formation, briefly identify the contribution that you think dominates the trend in free energy of micelle formation. nly solvent entropy contributes to greater spontaneity of micelle formation as tail length grows.

4 7. Rebecca performed her senior thesis on a molecule that would use a hydrogen bond between carbon and oxygen (that is C- ; carbon is the donor, oxygen the acceptor). I used to argue with Alan about this a lot. The following plots show the geometry of - vs. C- interactions. a. Why might C- typically be considered a poor -bond donor (no reference to above plots necessary)? The C- bond is not polar, and therefore wouldn t expect to participate in strong dipole-dipole interactions. b. Assume a simple vdw contact between a - group and a carbonyl oxygen (see handout from lecture 1). What would the predicted to distance be? Compare to the plots above. Is anything unusual happening? The - bond is 1 Å and the vdw radius of is 1.1 Å. The vdw radius of is 1.4 Å. Thus we expect the to distance to be Å = 3.5 Å. In fact, the average -bond has a distance of about 2.8 Å. Much shorter than predicted by vdw concerns. c. Assume a simple vdw contact between a C- group and a carbonyl oxygen. What would the predicted C to distance be? Compare to the plots above. Is anything unusual happening? The C- bond is 1.1 Å and the vdw radius of is 1.1 Å. The vdw radius of is 1.4 Å. Thus we expect the to distance to be Å = 3.6 Å. In fact, the average -bond from carbon has a distance of about 3.6 Å. This seems like a standard vdw interaction. d. As I stressed in lecture, -bonds between / donors/acceptors impose significant stereochemical restraints on the geometry of intermolecular interactions. ow is that made visible in the =C plot? Would that be true for C- =C bonds? o there seems to be no strong angular preference, indicating that the position of the C and can be sort of random.

5 8. Suggest how each of the following scenarios might affect the pk a of the specified amino acid side chain. a. Cysteine in a 50:50 mixture of water and ethanol (a reduced polarity environment). pk a will increase because anionic conjugate base becomes destabilized in non-polar environment. b. Lysine adjacent to an aspartate side chain. pk a will increase because cationic conjugate acid is stabilized by association with anionic Asp. c. Tyrosine -bonded to an ammonium ion. pk a will decrease because ammonium ion stabilizes anionic conjugate base of tyrosine. 9. Draw the side chains of the following amino acids with the appropriate protonation states for the p s identified below. Amino acid p 3 p 7 p 11 Gln Glu 50:50 mixture of the stuff at p 3 and the stuff at p 11. is* Lys *is has two resonance forms at p 3 and two tautomers at p 11. Please draw both at each p