The potential of mean force (PMF) of sodium chloride in water has been calculated by using the ab initio classical free-energy perturbation method at five state points: at 973 K with densities of 0.2796, 0.0935, and 0.0101 g/cm(3) and at 723 K with densities of 0.0897 and 0.0098 g/cm(3). The method is based on a QM-MM model in which Na-H2O, Cl-H2O, and Na-Cl interactions are calculated by ab initio methods. The water-water interactions are from the polarizable TIP4P-FQ model. The logarithm of the dissociation constant (log K-c) has been calculated from the PMF. These predictions, together with experimental measurements, were used to derive ail equation for log K-c at densities from 0 to 0.9 g/cm(3) and temperatures from 723 to 1073 K, as well as from 600 to 1073 K for densities from 0.29 g/cm(3) to 0.9 g/cm(3). Extrapolation of the present equation below 723 K for densities less than 0.29 g/cm(3) does not fit the experimental results. This is attributed to long-range changes in the local dielectric constant due to the high compressibility. Comparisons with previous predictions and simulations are presented.