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A detailed comparison between the Boubl\'ik-Mansoori-Carnahan-Starling-Leland(BMCSL)equation of state of hard-sphere mixtures is made with MolecularDynamics (MD) simulations of the same compositions. The Lab\'ik and Smithsimulation technique [S. Lab\'ik and W. R. Smith, Mol. Simul. \textbf{12},23-31 (1994)] was used to implement the Widom particle insertion method tocalculate the excess chemical potential, $\beta \mu_0^\text{ex}$, of a testparticle of variable diameter, $\sigma_0$, immersed in a hard-sphere fluidmixture with different compositions and values of the packing fraction, $\eta$.Use is made of the fact that the only polynomial representation of $\beta\mu_0^\text{ex}$ which is consistent with the limits $\sigma_0\to 0$ and$\sigma_0\to\infty$ has to be of the cubic form, i.e.,$c_0(\eta)+\overline{c}_1(\eta)\sigma_0/M_{1}+\overline{c}_2(\eta)(\sigma_0/M_{1})^2+\overline{c}_3(\eta)(\sigma_0/M_{1})^3$,where $M_{1}$ is the first moment of the distribution. The first twocoefficients, $c_0(\eta)$ and $\overline{c}_1(\eta)$, are known analytically,while $\overline{c}_2(\eta)$ and $\overline{c}_3(\eta)$ were obtained byfitting the MD data to this expression. This in turn provides a method todetermine the excess free energy per particle, $\beta a^\text{ex}$, in terms of$\overline{c}_2$, $\overline{c}_3$, and the compressibility factor, $Z$. Verygood agreement between the BMCSL formulas and the MD data is found for $\beta\mu^\text{ex}_0$, $Z$, and $\beta a^\text{ex}$ for binary mixtures andcontinuous particle size distributions with the top-hat analytic form. However,the BMCSL theory typically slightly underestimates the simulation values,especially for $Z$, differences which the Boubl\'ik-Carnahan-Starling-Kolafaformulas and an interpolation between two Percus-Yevick routes capture well indifferent ranges of the system parameter space.

Chemical potential of a test hard sphere of variable size in hard-sphere fluid mixtures