In this work we present an isothermal mathematical model of a secondary zinc air battery with alkaline liquid electrolyte. The model approach is flexible and allows to analyze the impact of surrounding air composition with its relative humidity, carbon dioxide and oxygen content on battery operation. We thereby apply an idealized approach to explore general limitations which give useful predictions for practical zinc air battery operation. Galvanostatic charge and discharge simulations show that air composition strongly impacts zinc air battery operation. Water level at anode and cathode, species concentrations and cell potential are shown to vary with air-composition impact during operation and may reach critical values which reduce battery lifetime. In detail, we deduce that intermediate relative humidity values of approximately 65%, carbon dioxide concentrations below 10 ppm and pure oxygen are beneficial for high performance and long term stable zinc air battery operation at 298 K with 6M potassium hydroxide as alkaline liquid electrolyte. The presented results will give useful information on operating strategies for zinc air batteries and electrochemical energy storage systems with open air electrode. The model might be adapted for other metal air batteries with aqueous electrolyte.