A noniterative, implicit, mass-conserving, unconditionally stable, positive-definite numerical scheme that solves nonequilibrium air-ocean transfer equations for any atmospheric constituent and time step is derived. The method, referred to as the Ocean Predictor of Dissolution (OPD) scheme, is coupled with EQUISOLV O, a new ocean chemical equilibrium module based on the EQUISOLV II atmospheric aerosol solver. EQUISOLV O converges iteratively, but is unique because it is positive-definite and mass and charge conserving, regardless of the number of iterations taken or equations solved. Two advancements of EQUISOLV O were the development of a new method to initialize charge and a noniterative solution to the water dissociation equation. Here OPD-EQUISOLV O is used to calculate air and ocean composition and ocean pH among dozens of species in the Na-Cl-Mg-Ca-K-H-O-Li-Sr-C-S-N-Br-F-B-Si-P system. The modules are first used in a one-dimensional ocean/two-compartment atmospheric model driven by emission to examine the historic change in atmospheric CO2 and ocean composition from 1751 to 2004 and the possible future change in CO2 and ocean composition from 2004 to 2104. CO2 estimates from the historic simulation compare well with the measured CO2 record. Whereas surface ocean pH is estimated to have dropped from near 8.25 to near 8.14 between 1751 and 2004, it is forecasted to decrease to near 7.85 in 2100 under the SRES A1B emission scenario, for a factor of 2.5 increase in H+ in 2100 relative to 1751. This ocean acidification is calculated to cause a nontrivial transfer of ammonia from the atmosphere to the ocean and a smaller transfer of hydrochloric acid, nitric acid, and sulfurous acids from the ocean to the atmosphere. The existence and direction of these feedbacks are almost certain, suggesting that CO2 buildup may have an additional impact on ecosystems. Computer time of the module in the GATOR-GCMOM global model with a 10-layer-ocean was less than two hours per simulation year on a modern single processor.