In a binary mixture, why do the partial molar properties of species 1 and 2 have opposite slopes (when plotting the partial molar properties as a function of x1)? Justify your answer.

I need answer

The differential form of the Helmholtz free energy, for a closed, one-component system, is  dA = -PdV - SdT Starting from A=U-TS,  derive the above expression. Show that  ΔA=ΔU-TΔS.   The Helmholtz energy can be used to determine the spontaneity of a process in the same way as the Gibbs energy:                             dA = -PdV - SdT + ∑µi dNi           which at equilibrium dA = 0            Under what conditions and/or for what types of systems would                    it be easier to use the Helmholtz free energy, as opposed to                          the Gibbs free energy?

Which of the following D 4h Muliken symbols represent the five 3d orbitals in Jahn-Teller distorted [Cu(H 20) 6] O a. A 1g, B 1g, B 2g, Eg O b. A 1g, B 2g, A 2u, Eu Ⓒc. A 1g, A 2g, B 1g, B 2g, Eg O d. A 1g, Eg, Eu 2+