It is shown that the hydration correction for the free energy of cluster formation in the classical binary nucleation theory is not applicable for the thermodynamic data of the water-surface acid system commonly used in nucleation calculations. A new form of the hydration correction is presented. For the commonly used thermodynamic data the nucleation rates of the new hydration correction are in the temperature range of 248-323 K, and at a relative humidity greater than 40%, 10(3)-10(6) times lower, respectively, than the nucleation rates of the former theory. The predictions of acid-water nucleation rates of the thermodynamically consistent version of the classical binary homogeneous theory [G. J. Wilemski, Chem. Phys. 80, 1370 (1984)] with the new hydration correction are in accordance with experimental results [B. E. Wyslouzil, J. H. Seinfeld, R. C. Flagan, and K. J. Okuyama, Chem. Phys. 94, 6842 (1991)] obtained at 298 K and with experimental results CD. Boulaud, G. Madelaine, D. Vigla, and J. Bricard, J. Chem. Phys. 66, 4854 (1977)] obtained at 293 K, but at a given number concentration of acid and relative humidity, they predicted nucleation rates are rather more stronger functions of temperature than the experimental rates. The theoretical nucleation rate of water-sulfuric acid vapor is due to the hydration correction sensitive to the thermodynamic properties of dimers and timers.