  The binary additive hard-sphere mixtures have been studied by the
Ornstein-Zernike integral equation coupled with the Martynov-Sarkisov (MS)
closure approximation. Virial equation of state is computed in the MS
approximation. The excess chemical potential for the mixture is evaluated with
a closed-form expression based on correlation functions. The excess Helmholtz
free energy is obtained using the Euler relation of thermodynamics. Moreover,
these thermodynamic quantities are obtained by the
Boubl\'{i}k-Mansoori-Carnahan-Starling-Leland (BMCSL) formulas. Our findings
for pressure and excess chemical potential for a number of binary sets of the
mixtures from the MS approximation show good agreements with those obtained by
the BMCSL formulas and available data in literature, having a maximum deviation
of $5\%$ for a packing fraction up to 0.5. The maximum deviation of the excess
free energy obtained for the mixtures is shown to be $\sim 16\%$ for a packing
fraction of 0.5. To our knowledge, this work presents an initial calculation of
an excess chemical potential of the system in the MS approximation.
