Capturing carbon dioxide from the atmosphere ("air capture") in an industrial process has been proposed as an option for stabilizing global CO(2) concentrations. Published analyses suggest these air capture systems may cost a few hundred dollars per tonne of CO(2), making it cost competitive with mainstream CO(2) mitigation options like renewable energy, nuclear power, and carbon dioxide capture and storage from large CO(2) emitting point sources. We investigate the thermodynamic efficiencies of commercial separation systems as well as trace gas removal systems to better understand and constrain the energy requirements and costs of these air capture systems. Our empirical analyses of operating commercial processes suggest that the energetic and financial costs of capturing CO(2) from the air are likely to have been underestimated. Specifically, our analysis of existing gas separation systems suggests that, unless air capture significantly outperforms these systems, it is likely to require more than 400 kJ of work per mole of CO(2), requiring it to be powered by CO(2)-neutral power sources in order to be CO(2) negative. We estimate that total system costs of an air capture system will be on the order of $1,000 per tonne of CO(2), based on experience with as-built large-scale trace gas removal systems.