A review of requirements for equations to calculate the conductivity of a mixture of ions in low dielectric constant solvents (i.e., water at high temperatures) shows that there are conceptual difficulties with all current equations. To explore whether these difficulties limit our ability to predict mixtures, four models for the activity coefficients, two models for the conductivity of a single strong electrolyte, and an equation for the change in equivalent conductivity on mixing single strong electrolytes were chosen. These equations were then tested on the theoretical equation of Turq et al. (J. Phys. Chem. 1995, 99, 822−827) for three ion mixtures. Next the equations were tested on a single 1−1 electrolyte, NaCl (aq) at 652.6 K and 22.75 MPa measured by Gruskiewicz and Wood (J. Phys. Chem. B 1997, 101, 61549−6559) and new measurements at 623.9 K and 19.79 MPa. Then it was tested with new measurements on Na2SO4 (aq) from 300 to 574 K because, in water at high temperatures, this salt produces a solution containing six different ions (Na+, SO4 2-, NaSO4 -, HSO4 -, H+, OH-). The equations were able to reproduce the experimental data. Values of equilibrium constants, K, for the dissociation of NaCl and NaSO4 - and equivalent conductances Λo derived by a least-squares fit agreed with reported data determined by other methods, showing that conductivity measurements can yield accurate equilibrium constants in complex mixtures of ions. The values of K and Λo were not very sensitive to changes in (1) the single electrolyte conductance equation, (2) assumed values of Λo for minor species, or (3) equilibrium constants for minor reactions. Uncertainty in the activity coefficient model was the largest contributor to uncertainty in K and Λo. This method should allow rapid and accurate measurements of the equilibrium constant for any reaction, which changes the number of ions in solution. The equilibrium constants for many reactions of this type are unknown in water at high temperatures.