For the first time absolute photon mass energy-absorption coefficients of air in the energy range 3 keV to 10 keV have been measured with relative standard uncertainties less than 1%, significantly smaller than those of up to 5% assumed hitherto for calculated data. Monochromatized synchrotron radiation was used to measure both the total radiant energy by means of silicon photodiodes calibrated against a cryogenic radiometer and the fraction of radiant energy that is deposited in dry air by means of a free air ionization chamber. The measured ionization charge was converted into energy absorbed in air by calculated effective W values of photons as a function of their energy based on new measurements of the W values in dry air for electron kinetic energies between 1 keV and 7 keV, also presented in this work. The measured absorption coefficients were compared with state-of-the art calculations and found to agree within 0.7% with data calculated earlier by Hubbell at energies above 4 keV but were found to differ by values up to 2.1% at 10 keV from more recent calculations of Seltzer.