This article describes a mathematical model of the acid-base chemistry of blood. The model is formulated from first principles by considering the "components" of blood and the reaction equations in the plasma and erythrocyte fractions. Equations are formulated to describe the total concentration of blood components, the physicochemical properties, and the equilibrium position of reactions. The model includes 28 equations and 12 parameters. All equations can be solved from six variables included in the model. The model uses simple mathematics, without introducing intermediate concepts or linear coefficients necessary for algebraic solution. Model equations are solved simultaneously using numerical methods. Model parameters are estimated and the model verified for plasma, fully oxygenated blood, and deoxygenated blood. Published data are used to estimate model parameters and normal conditions and to verify model simulations. The model reproduces experimental results, including addition or removal of CO2, or strong acid to plasma; CO2, strong acid or haemoglobin to blood; and the effects of deoxygenating blood. The model can also be used as the basis for models of whole body CO2 transport as illustrated in the accompanying article. As such, it is possible to simulate the effects on blood of physiological changes in ventilation or metabolism.