Metal-air batteries are among the most promising next-generation energy storage devices. Relying on abundant materials and offering high energy densities, potential applications lie in the fields of electro-mobility, portable electronics, and stationary grid applications. Now, research on secondary zinc-air batteries is revived, which are commercialized as primary hearing aid batteries. One of the main obstacles for making zinc-air batteries rechargeable is their poor lifetime due to the degradation of alkaline electrolyte in contact with atmospheric carbon dioxide. In this article, we present a continuum theory of a commercial Varta PowerOne button cell. Our model contains dissolution of zinc and nucleation and growth of zinc oxide in the anode, thermodynamically consistent electrolyte transport in porous media, and multi-phase coexistance in the gas diffusion electrode. We perform electrochemical measurements and validate our model. Excellent agreement between theory and experiment is found and novel insights into the role of zinc oxide nucleation and growth and carbon dioxide dissolution for discharge and lifetime is presented. We demonstrate the implications of our work for the development of rechargeable zinc-air batteries.