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# Value of freezing point and Gibbs energy of mixture

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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

(SEE QUESTIONS IN PROPER FORMAT FROM ATTACHED FILE "chem1.pdf")

https://brainmass.com/chemistry/energetics-and-thermodynamics/value-of-freezing-point-and-gibbs-energy-of-mixture-537231

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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.

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## Gases, Temperature, Current and Reactions

1) Calculate w and Delta E for the expansion of 20.0g of nitrogen gas from a volume of 30.0 L to a volume of 40.0 L at a constant 300.0K.

2) The density of ice at its normal freezing temperature is 0.917g/mL while that of liquid water at the same temperature is 0.9998 g/mL . If Delta H(fusion) of ice is 6.009 kJ/mol, what is Delta E(fusion).

3) The heat of fusion of potassium bromide is 20.9 kJ/mol. If the entropy of fusion of this compound is 20.5 J/K-mol, what is the melting point of this compound?

4) Calculate the Gibbs Free Energy of the combustion of acetylene to form carbon monoxide and liquid water at 25 degrees Celsius.

5) Calculate the value of the equilibrium constant at 25 degrees Celsius for the reaction.

2SO2(g) + O2 <==> 2 SO3

6) Write the diagram of a cell which utilizes the following reaction.

2Fe^2+(aq) + Cl2 (g) => 2 Fe^3+(aq) + 2Cl^1-

7) A voltage of 1.09 V at 25 degrees Celsius was obtained from the cell

Sn(s) | Sn^2+ (aq) || Ag^1+ (aq, 0.05 M) | Ag (s)

What was the molar concentration of Sn^2+ in the cell?

8) Calculate the standard molar free energy of formation of liquid water at 25 degrees Celsius. Use the standard reduction potentials for this calculation.

9) A solution of nickel sulfate was electrolyzed for 1.50 hours between inert electrodes. If 35.0 grams of nickel was plated out, what was the average current.

10) Some fragments of bone from an excavation in Egypt were found to have a ^14C radioactivity of 0.629 times that in the bones of living animals. How old are the fragments?

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