[Tautomer]

The goal of a part of a given question is to solve for

dp_vm/dx,

where p_vm is partial molar volume of substance A and x is the mole fraction of substance A (in a two component system). We know x is 0.5 (equimolar), and knowing the Gibbs-Duhem equation as

Σ n_jdμ_j = 0,

I set

n_adμ_a = -n_bdμ_b

I've tried several ways to change this equation around, but I can't find a way to start. The only known value is the mole fraction, so any quantitative number will have to involve only this.

EDIT: I also have access to a list of partial molar volumes for each component and certain mole fractions. But considering that I'm trying to find the change in molar volume with respect to the mole fraction, I don't think these will be used in the final equation. I already used the slope formula to find the slope of the tangent line, so I'm trying to compare the high school method to the college method (dp_vm/dx).