A non-ideal replacement for the Boyle van’t Hoff equation

A non-ideal osmotic equilibrium equation is proposed as a replacement for the Boyle van’t Hoff equation to describe the equilibrium volume of a living cell as a function of external osmolality. Contrary to common understanding, the Boyle van’t Hoff equation is only thermodynamically correct for ideal, dilute solutions. However, the Boyle van’t Hoff equation is commonly used to determine the osmotically inactive fraction of the cell. This involves extrapolating to infinite osmolality, which violates the ideal, dilute solution constraint. It has been noted that the osmotically inactive fractions obtained from the Boyle van’t Hoff equation for human erythrocytes are markedly larger than measured values of the dry volume fraction of the cell. Using the new osmotic equilibrium equation to analyze experimental osmotic equilibrium data reduces the inferred osmotically inactive fraction of human erythrocytes by approximately 20%.