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(x_{1}), and that the Gibb's-Duhem Equation is Σ(x_{1})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(x_{1})

dμ/dx_{1} = 0 + RT/x_{1}