[allyson10500]

Hi all, this (attached) problem is from my first semester physical chemistry class's exam 2 review sheet. The professor refuses to post the answer key because it "takes away the fun." If you know how to do even 1 part I would be exceptionally grateful to see the steps.  I know Raoult's Law of Standard State is
 μ = μ* + RTln(x₁), and that the Gibb's-Duhem Equation is Σ(x₁)dμ_i) = 0, but I have no idea how to move forward with the problem. I also tried to take the derivative of μ, but I don't think that I am doing it correctly.

 μ = μ* + RTln(x₁)
dμ/dx₁ = 0 + RT/x₁