For the first time the absolute photon mass energy-absorption coefficient of air in the energy range of 10 to 60 keV has been measured with relative standard uncertainties below 1%, considerably smaller than those of up to 2% assumed for calculated data. For monochromatized synchrotron radiation from the electron storage ring BESSY II both the radiant power and the fraction of power deposited in dry air were measured using a cryogenic electrical substitution radiometer and a free air ionization chamber, respectively. The measured absorption coefficients were compared with state-of-the art calculations and showed an average deviation of 2% from calculations by Seltzer. However, they agree within 1% with data calculated earlier by Hubbell. In the course of this work, an improvement of the data analysis of a previous experimental determination of the mass energy-absorption coefficient of air in the range of 3 to 10 keV was found to be possible and corrected values of this preceding study are given.