Equations for O2 and CO2 solubilities in saline and plasma: combining temperature and density dependences

Solubilities of respiratory gasses in water, saline, and plasma decrease with rising temperatures and solute concentrations. Henry's Law, C = α·P, states that the equilibrium concentration of a dissolved gas is solubility times partial pressure. Solubilities in the water of a solution depend on temperature and the content of other solutes. Blood temperatures may differ more than 20°C between skin and heart, and an erythrocyte will undergo that range as blood circulates. The concentrations of O₂ and CO₂ are the driving forces for diffusion, exchanges, and for reactions. We provide an equation for O₂ and CO₂ solubilities, α, that allows for continuous changes in temperature, T, and solution density, , in dynamically changing states:a(T, sol, , , β)=[1–⋅(sol–)β]⋅(C1⋅e–k1T+C2⋅e–k2T)

This two-exponential expression with a density scalar , and a density exponent β, accounts for solubility changes due to density changes of an aqueous solution. It fits experimental data on solubilities in water, saline, and plasma over temperatures from 20 to 40°C, and for plasma densities, _sol up to 1.020 g/ml with ~0.3% error. The amounts of additional bound O₂ (to Hb) and CO₂ (bicarbonate and carbamino) depend on the concentrations in the local water space and the reaction parameters. During exercise, solubility changes are large; both _sol and T change rapidly with spatial position and with time. In exercise hemoconcentration plasma, _sol exceeds 1.02, whereas T may range over 20°C. The six parameters for O₂ and the six for CO₂ are constants, so solubilities are calculable continuously as T and _sol change.

NEW & NOTEWORTHY Solubilities for oxygen and carbon dioxide are dependent on the density of the solution, on temperature, and on the partial pressure. We provide a brief equation suitable for hand calculators or mathematical modeling, accounting for these factors over a wide range of temperatures and solution densities for use in rapidly changing conditions, such as extreme exercise or osmotic transients, with better than 0.5% accuracy.

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