Due date: Wednesday, October 10th
Do all of the following problems. Show your work.
“I knew chemistry would be worse because I’d seen a chart of the ninety-odd elements hung up in the chemistry lab, and all the perfectly good words like gold and silver and cobalt and aluminum were shortened to ugly abbreviations with different decimal numbers after them. If I had to strain my brain with any more of that stuff I would go mad.”
- Sylvia Plath
1) For each of the following systems that are at equilibrium find F, the number of degrees of freedom, using the Gibbs phase rule.
a) Solid water and a liquid solution of methyl alcohol and water.
b) A mixture of water and phenol containing an aqueous layer (water with a trace of phenol), an organic layer (phenol with a trace of water), and a vapor phase.
c) An aqueous solution of sodium chloride in equilibrium with a vapor phase containing water.
2) The volume of an aqueous solution of NaCl at T = 25.0 (C was measured at a series of molalities b, and it was found that its volume fit the expression
V = 1003. + 16.62 x + 1.77 x3/2 + 0.12 x2 (2.1)
where V is the volume of a solution formed from 1.000 kg of water and added sodium chloride, and x = b/b( where b( ( standard molality (1 mole solute/kg solvent). Find the partial molar volume of water (M = 18.01 g/mol) and sodium chloride (M = 58.44 g/mol) for a solution where b = 0.100 mol/kg. HINT:
Vm,NaCl = ((V/(nNaCl)p,T,nH2O = ((V/(x)p,T,nH2O ((x/(nNaCl)p,T,nH2O (2.2)
where x = b/b(, as defined above.
3) In class we derived the following expression for the free energy of mixing of two ideal gases initially at the same temperature and pressure
(Gmix = nRT [ XA lnXA + XB lnXB ](3.1)
The same procedure can be used to find (Gmix when the two gases are originally at different pressures.
Consider the system below. 1.000 mol of argon (Ar) is initially confined to the left side of the container, which has a volume 3V0. 1.00 mol of helium (He) is initially confined to the right side of the container, which has a volume V0. The barrier between the two sides of the container is removed and the gases are allowed to mix until equilibrium is reached. Temperature remains constant at T = 300.0 K throughout the process. Find (Gmix. You may assume that argon and helium behave ideally. HINT: You cannot simply use equn 3.1 to answer this question since it was derived assuming the initial pressures of the two gases were equal to each other. However, the method used in class to derive equn 3.1 can be used to solve this problem.
4) The vapor pressure of pure methyl alcohol (Me, M = 32.04 g/mol) and ethyl alcohol (E, M = 46.07 g/mol) at T = 20.0 (C are pMe* = 88.73 torr, pE* = 44.48 torr.
A solution is formed by mixing 50.0 g methyl alcohol and 50.0 g ethyl alcohol. Assuming that methyl alcohol and ethyl alcohol form an ideal liquid solution, find XMe (mole fraction of methyl alcohol in the liquid phase) and YMe (mole fraction of methyl alcohol in the gas phase) for the above solution.
5) A solution of ethyl alcohol (E, M = 46.07 g/mol) and chloroform (C, M = 119.38 g/mol) is formed by mixing 0.400 mol of ethyl alcohol and 0.600 mol of chloroform at T = 35. (C. The vapor pressure of the pure liquids at this temperature are pE* = 0.13703 bar and pC* = 0.39345 bar.
a) Assuming ethyl alcohol and chloroform form an ideal liquid solution, find (Gmix and YE, the mole fraction of ethyl alcohol in the vapor above the solution.
b) Ethyl alcohol and chloroform do not in fact form an ideal solution. Experimentally, it is found that YE = 0.1864, ptotal = 0.38690 bar. Find aE and aC (the activities of ethyl alcohol and chloroform), (Gmix for the real solution that forms, and GE, the “excess” free energy for solution formation. You may assume the vapor behaves ideally, but not the liquid solution.
6) As discussed in class, we can write...