Value of freezing point and Gibbs energy of mixture

1. If the vapor pressures of the two components in a binary solution are grven by
P1 = x1*P1*e^(u(x2^2))/RT and P2 = x2*P2*e^(u(x1^2))/RT
Show that,
Del(mix)*G/u = Del(mix)*G/(n1+n2)u = (RT/u) * (x1 ln(x1) * x2ln(x2))*x1x2
Del(mix)*S/R = Del(mix)*S/(n1+n2)R= -(x1 ln(x1) * x2ln(x2))
Del(mix)*H/u = Del(mix)*H/(n1+n2) = x1x2

A solution that satisfies these equations is called a regular solution. A statistical thermodynamic model of binary solutions shows that u is proportional to 2E12 - E11 -E22 ,where, Eij is the interaction energy between molecules of components i and j. Note-that u = 0 if E12 = (E11+ E22)/2, which means that energetically, moiecules of components 1 and 2 *like" the opposite molecules as well as their own.

2. Calculate the value of the freezing point depression constant for nitro-benzene, whose freezing point is 57 degree centigrade and whose enthalpy of fusion is 11.59 kJ/mol

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Solution Summary

Step-by-step solutions of both problems is explained. The first problem is statement proven for Gibbs energy of mixture(binary solution) using A statistical thermodynamic model. The second problem is calculation of Value of freezing point for nitro-benzene.

How many grams of naphthalene, C10H8, would you add to 49.5 g of benzene, C6H6 (l), to produce a solution that has the same freezingpoint as pure water? (Use the data from the table as needed.)
Molal FreezingPoint Depression and Molal Boiling Point Elevation Constants:
Solvent Normal Freezing K(fr) Normal

Delta S (standard conditions) for the following reaction is favorable even though delta H (standard conditions) is not:
C2H5OH (l) <-> C2H5OH (g)
Assume that ethanol boils at the temperature where delta G (standard conditions) for this reaction becomes zero. Use the values of delta H and delta S for this reaction to estimate

The standard Gibbs free energy of formation of NH3(g) is given by ∆Gfo=-16.5 kj/mol-1 at T=298K.
What is the Gibbs free energy (∆G) for the reaction: N2(g) + 3H2 ↔ 2NH3(g) when the partial pressures are: PN2=3.0 bar; PH2=1.0 bar; and PNH3=4.0 bar?

Suppose your thermometer read consistently 1.0 o C lowered throughout both parts in the colligative properties lab. What effect would that have on your experimental value for the molar mass of your unknown solute?
-no effect
-higher molar mass
-lower molar mass
If the freezingpoint of the mixture had been incorrectly

A 0.573g sample of a nonvolatile solute is added to 15.6g of napthalene and the mixture warmed until melted. The freezingpoint of the solution was determined and found equal to 78.1C. The freezingpoint of naphthalene is 80.2C. How do you find out if the boiling pt and the vapor pressure increases or decreases?
How do you

Salt lowers the freezingpoint of water. So will sugar. If one tablespoon of solid (salt or sugar) is dissolved in ¼ cup of water, which material, salt or sugar will lower the freezingpoint of the water by the greater amount? Why?

The change in G and the change in H are equal:
a. At O degrees Cesius
b. At O degrees K
c. When concentrations equal 1M and partal pressure equal 1 atm
d. When all reactants and products are in the same phase
e. When the reaction is exothermic

When 8.900 g of a mixture of an alkali metal chloride (XCl) and an alkaline earth chloride (YCl2) was dissolved in 150.0g of water, the freezingpoint of the resultant solution was -4.42C. Addition of an excess of aqueous AGNO3 to the solution yielded a white precipitate with a mass of 27.575 g (This white precipitate would be

Urea (NH2CONH2), an important nitrogen fertilizer, is produced industrially by the reaction
2 NH3(g) + CO2(g) → NH2CONH2(aq) + H2O(l)
Given that delta G^o = -13.6 kJ, calculate delta G at 25 oC for the following sets of conditions.
(a) 10 atm NH3, 10 atm CO2, 1.0 M NH2CONH2
(b) 0.1 atm NH3, 0.1 atm CO2, 1.0 M NH2CON