In the comparison in air of mass standards having different volumes, the major source of uncertainty arises from the determination of the density of moist air (buoyancy correction). The method being commonly used is the application of a recommended equation of state (CIPM 81/91 formula); a second method developed and used by only a few laboratories is based on two special artefacts having the same mass and surface area but very different volumes. Comparisons carried out by weighing the artefacts in air and in vacuum revealed a relative discrepancy of 6.4 × 10⁻⁵ between air density as measured by the artefacts and by the CIPM formula. Additional measurements were carried out at the BIPM in dry nitrogen. The comparison of the gas density obtained by the two methods confirmed the discrepancy already obtained for moist air but showed a much smaller discrepancy for dry nitrogen. These results reinforce the hypothesis that the accuracy of the air density using the CIPM formula is limited by the estimation of its composition, in particular the mole fraction of argon which may be underestimated. To test this hypothesis, an alternative value for the mole fraction of argon in air, arising from a recent redetermination, has been considered for use in the CIPM 81/91 formula. Modification of the CIPM 81/91 formula to include the recent argon determination would remove the discrepancy between the two methods of determining the density of moist air.