Three Context-Dependent Forms of CTSP: Implications for Osmosis Education and Research

Background and Objective: Physiology textbooks traditionally distinguish osmolarity (total solute particle concentration) from effective osmolarity (impermeant solute particle concentration), and this dual usage has long contributed to confusion in understanding tonicity. Our article, “Unravelling tonicity: Causes of confusion and pathways to clarity” (Curr. Res. Physiol., 2025), resolved this issue by introducing a single, membrane-dependent definition of osmotic concentration (OC) and showing that what textbooks call “osmolarity” is not true OC but the molar concentration of total solute particles (TSP), which should be designated CTSP. Our subsequent article, “A unified framework for van ’t Hoff’s law: addressing the complexity of osmotic concentration” (RSOS, 2025), further demonstrated the effectiveness of the redefined OC in unifying multiple forms of van ’t Hoff’s law through OC 0 . This abstract supplements the RSOS article by explicitly addressing the three context-dependent forms of CTSP (CTSP 1 , CTSP 2 , CTSP 3 ) and clarifying their applications in osmosis study. Hypothesis: Distinguishing the three forms of CTSP is necessary for accurate modeling and interpretation of osmotic phenomena. Methods: Using a mixed aqueous solution containing NaCl, glucose, and MgSO 4 as a conceptual example, we derived three forms of CTSP. CTSP 1 (ideal theoretical form) is the total solute particle (TSP) count: CTSP 1 = ΣgjCj, where C is the molar concentration of molecule j and gj is the number of particles produced by full dissociation. CTSP 2 (non-ideal theoretical form) incorporates solute molecule-specific osmotic coefficients Φj, which quantify deviations from ideal behavior: CTSP 2 = = ΣgjΦjCj. CTSP 3 , the empirical form, is measured using a freezing point osmometer (FPO) and captures full non-ideal interactions among all ions and molecules. Results: (1) CTSP 1 , the ideal particle count, is appropriate for theoretical derivations or models assuming ideality; for the sample solution, CTSP 1 = 2[NaCl] + [Glu] + 2[MgSO 4 ]. (2) CTSP 2 incorporates solute-specific non-ideal contributions: CTSP 2 = 2 ΦNaCl[NaCl] + ΦGlu[Glu] + 2 ΦMgSO 4 [MgSO 4 ]. It is useful when non-ideality is not negligible but cross-solute interactions are unknown. (3) CTSP 3 , measured by FPO, reflects the true colligative behavior of the solution and fully incorporates all non-ideal interactions. Conclusions: CTSP is not a single fixed quantity but a context-dependent metric with three distinct forms. The osmotic system coefficient θ, introduced in the RSOS article, links the ideal theoretical CTSP to its measured value (CTSP 3 /CTSP 1 ) when the membrane is permeable only to water. Proper recognition and application of CTSP 1 , CTSP 2 , and CTSP 3 are essential for accurate modeling, prediction, and teaching of osmotic behavior in biological systems. This abstract was presented at the American Physiology Summit 2026 and is only available in HTML format. There is no downloadable file or PDF version. The Physiology editorial board was not involved in the peer review process.