My objective is to find an equation of state (EoS) for density, i.e. density as a function of pressure, temperature and concentration, for aqueous acids, bases and salts.
A StackExchange user suggested that I look into the following paper:
The paper describes the EoS as "the total change in the Helmholtz free energy for forming the electrolyte solution on this path" in which they combine contributions from Peng-Robinson model, Born model, and MSA (Mean Spherical Approximation) model:
$$ A(T,V,\bar n)-A^{IGM}(T,V,\bar n)=\Delta A^{PR}+\Delta A^{Born}+\Delta A^{MSA}, $$
where $T$ is the temperature of the system, $V$ is the system volume, $\bar n$ is the vector of the number of moles of each component of the mixture, and $A^{IGM}$ is the Helmholtz free energy an ideal gas mixture.
In the paper, they included graphs of density vs. molality of aqueous $NaCl, NaBr, CaCl_2$. So it seems like this EoS is what I need, but the paper doesn't explicitly describe how to calculate density from the EoS.
I've seen how taking partial derivatives of Helmholtz free energy results in equations for pressure, entropy, and $\mu$, but not for density. I'm wondering if someone has already figured out how exactly one can calculate density from Helmholtz free energy.
UPDATE: Also, I don't think the Helmholtz free energy I described above (from the paper) is the same as this.
