Conceptual Problems
1 a) If I add KH2PO4 crystals
to water, how many independent components are in the final solution? Explain.
Note that predominantly KH2PO4
ionizes to form K+ and H2PO4-.
b) If I then add KOH solid (which ionizes to form K+ and OH- ions), converting half of the H2PO4- to HPO42- (H2PO4- + OH- ---> H2O + HPO42-), how many independent components are there? Explain.
2) Explain why there are no degrees of freedom (F=0) at the triple point of a pure substance.
3) Explain why the freezing point of a pure liquid decreases when solute is added to it. Your explaination should include the effects that solutes have on the chemical potential of a solvent.
4) The free energy of mixing of ideal liquids is always negative and therefore mixing of ideal liquids is always spontaneous. What is it about real liquids that results in some liquids being immiscible (not spontaneously mixing, such as oil and water)?
5) How does an ideal solution (Raoult’s Law solution) of two components differ from a ideal dilute solution (a Henry’s Law solution)? Explain this in terms of the interactions between molecules.
6) Explain in words why solids with higher melting points tend to be less soluble.
7) Often in biochemical preparations, one uses dialysis membranes (membranes with pores in them that allow water and small molecules to pass through but not big molecules such as protein or DNA) to remove unwanted small molecules from a solution of, for example, protein. This is done by placing the protein solution in a tube of dialysis membrane and then putting the tube in a large quantity of water-based dilute solution. Usually the water based solution on the outside has no protein in it. After the dialysis has occured, the bag swells and there is more water inside it than originally. Also it actually bursts when you open it (the pressure inside is larger than the atmospheric pressure outside). Explain these observations.
8) If I consider solute concentrations and activities in terms of molalities, what will be the limiting value of the activity coefficient as I make my solute more and more dilute?
9) Describe the standard state of a gas. Be sure to differenciate between real and ideal gases.
10) Describe the standard state of a solvent.
11) Describe the standard state of a solute in terms of molality.
12) A small amount of sugar is dissolved in water. For the liquid and vapor phases of this material, state whether you would expect the chemical potential to increase, decrease or stay the same. Explain.
13) It used to be a common practice to put salt on roads in the winter time to help melt the ice. Why does this work?
Numerical Problems
14) Dissolving a small organic molecule in benzene caused its boiling point to change by 2 degrees. How much was the chemical potential of liquid benzene at 25 C changed by dissolving the solute in it (assume an ideal solution)? Make sure you say whether the change is an increase or a decrease. For benzene, the boiling point is 353.2 K, the melting point is 278.61, the enthalpy of vaporization is 30.8 kJ/mole, the enthalpy of fusion is 10.59 kJ/mole and the molecular weight is 78.11 g/mole.
15) What is the free energy of mixing, the entropy of mixing and the
enthalpy of mixing that results from combining:
a) 0.5 liter each of two ideal gases at 1 atm and 298 K
b) 0.5 moles each of two liquids that form an ideal solution at 298K
16) What is the entropy change for mixing 1 liter of a monoatomic ideal gas (call it A) at 2 atm and 100 C with 2 liters of a different monoatomic ideal gas (call it B) at 0.5 atm and 0 C (the total volume is confined to 3 liters)? Assume CV is 1.5R for both gases.
17) Consider two beakers at 298K each initially containing 1 liter of water connected at the bottom by a tube. Each beaker is a cylinder 15 cm in diameter. In the tube conecting the beakers is a semipermeable membrane which only lets water through and not sugar. Sugar is dissolved in the beaker on the right-hand side. The beaker on the left-hand side is left with pure water in it. If the concentration of the sugar in the beaker on the right is 0.1 M, what are the final volumes of liquid in the two beakers?
18) The osmotic pressure of 1 liter of a two component aqueous solution at 298 K is 100 kPa (note that 100 kPa = 1 Bar). Calculate the concentration of the solute and the boiling point of the solution.
19) Two components, A and B, were mixed forming a nonideal solution and their liquid and vapor phases were allowed to equilibrate at 298 K and a pressure of 1 atm. The mole fraction of A in the liquid phase was found to be 0.380. The mole fraction of A in the vapor phase was 0.490. Calculate the activities and activity coefficients of both A and B in the solution on the basis of Raoult’s law. The vapor pressures of the pure liquids were p*(A) = 790 Torr and p*(B) = 600 Torr (remember that 760 Torr is 1 Atm).
20) Let’s say I have two vessels that are connected by a tube, but are otherwise enclosed (the total volume is constant). In one vessle there is 500 mls of a 0.1 molal solution of sodium chloride. In the other vessle is 500 mls of a 0.2 molal solution of sodium chloride. Note that water is volitile and will have a vapor pressure above the solutions while sodium chloride will not. Thus water molecules can pass through the air between the two solutions, but not the salt. When the system comes to equilibrium (which could easily take weeks, depending on the temperature), what will be volumes and of liquid in the two vessels and the concentrations of sodium chloride?
Applied Problems
21) One can make the following observations with red blood cells. When these cells are put into pure water, they burst. When they are put into a saline solution (a solution with a salt concentration similar to that of the liquid that surrounds the blood cells in your circulatory system) they retain their normal shape and size. When they are put into a saturated salt solution they shrivel up. Explain these observations. Include expressions for the chemical potentials inside and outside the cell in each case. (You can think of a red blood cell as a cell surrounded by a structurally weak, semipermeable membrane that lets water go through but not much else. Note that inside a red blood cell there are a variety of salts, small organic molecules, proteins and other chemicals which are in an aqueous solution.)
22) I like to backpack in the high country of the Sierra. One of my favorite areas is Evolution Valley, the floor of which is about 11,000 feet. However, a drawback of being at such high elevations is that it takes longer to cook rice in boiling water than it does at sea level (note that at higher elevations, the atmospheric pressure decreases compared to sea level). It turns out that the time it takes to cook rice is quite dependent on the temperature of the water you cook it in. The warmer the water the faster it cooks. Explain why my rice cooks more slowly at the higher elevation and suggest what might I do to speed the cooking time up. Use chemical potentials and appropriate equations in your argument. Be as explicit as possible.
23) You can think of a yeast cell as a bunch of salts and organic molecules enclosed in a membrane vesicle which only lets certain molecules go in and out. One thing that the yeast does is to bring in glucose to feed on. Generally, the concentration of glucose in the cell is greater than that outside the cell which means that the cell must expend energy to bring in the food. If the concentration of glucose outside the cell is 1 mM and the concentration inside is 2 mM, what is the free energy per mole for yeast cells to transport glucose inside? Note that for aqueous solutions, molality and molarity are approximately the same.
24) You have been put in charge of designing a desalination plant (a plant for converting sea water into pure water). You are considering the following three desalination processes. a) Evaporating the sea water and then condensing the vapor to liquid water (distillation). b) Pushing the sea water through a membrane that only allows water and not salt to pass (reverse osmosis). c) Freezing a fraction of the sea water and collecting the ice for remelting into water. Assuming that the average ambient temperature (the temperature of the enviroment) is 25 C, discuss the energy efficiencies of each process. Explain your reasoning comparing equations as appropriate.