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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")

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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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