Unification of the Multiple Forms of van 't Hoff’s Law into One General Form
Authors: Kuang Serena Y. , Walter Stefan , Yang Xiaoqi , Li Xiaonan 
Published: May 2022

IntroductionThe first Nobel Prize in Chemistry was awarded to Jacobus Henricus van 't Hoff in 1901 for his discoveries of the laws of chemical dynamics and osmotic pressure (π) in solutions. The original form of van 't Hoff’s law illustrates the relationship between π and the molar concentration (C) of a solution (S) facing a membrane (m) that separates the S and water compartments and is only permeable to water: π = C·RT, where R is the gas constant and T is the absolute temperature. However, in reality, both biological and artificial membranes can be extremely complex, so that facing different m, the resulting fractions of the impermeant solute particles (imp‐SP) contributing to πis different. The composition of the total solute particles (TSP that includes imp‐SP and permeant SP (p‐SP)) in S and their interactions may also be complex. For these reasons, multiple forms of van 't Hoff’s law have been developed over time to adapt to the different levels of complexity of solutions and/or membranes. In our previous works, we have done the following: 1) Defined the osmosis setting above as a simple osmosis system (S‐m‐H2O) and the setting of S1‐m‐S2 as a composite osmosis system that can be deconstructed into two mirrored simple osmosis systems: S1‐m‐H2O and H2O‐m‐S21, 2. 2) Addressed the many problems in the current definitions of osmolarity (osmotic concentration, OC) and tonicity1‐6. 3) Reasoned out what real osmolarity is: the osmotic concentration (OC, the concentration of the imp‐SP resulting from the interaction between the composition of S and m) in S‐m‐H2O1. OC in boldface is differentiated from OC in regular face. OC is a m‐dependent variable during osmosis whose initial value before osmosis occurs (i.e,, time = 0) is OC0, a constant of practical use. 4) Proved the correctness and effectiveness of OC0 in eliminating all the problems we addressed with the current definitions of osmolarity and tonicity1‐6. Moreover, by applying OC0 to van 't Hoff’s law, the multiple forms of the law can be unified into one general form. This presentation demonstrates 1) how this unification occurs; 2) how the unified form can be applied to a composite S1‐m‐S2.MethodLogical reasoningResults1. Multiple forms ofvan 't law and their unificationTable 1 shows the unification of the multiple forms of the law into one general form: π = OC0·RT.2. Applying the unified form ofvan 'tHoff’s law to a composite osmosis system (S1‐m‐S2)Figure. 1 illustrates the application of the unified form of the law in S1‐m‐S2: ∆π = ∆OC0·RT.ConclusionsThe unification of the multiple forms of van 't Hoff’s law using OC0 into a general form (π = OC0·RT) is a significant theoretical development of the law. The original form of the law is a special case of the general form.References1. Kuang et al., The Concept of Osmolarity: Problems and Resolutions. The FASEB Journal, 2020, 34(S1).2. Kuang et al., The Concept of Osmotic Pressure: Two Common Misunderstandings and Resolutions. The FASEB Journal, 2021, 35(S1).3. Kuang et al., The Problems with the Concepts of Osmole and Osmotically Active Particles. The FASEB Journal, 2020, 34(S1).4. Kuang et al., The Concept of Tonicity: Problems and Resolutions. The FASEB Journal, 2020 34(S1).5. Kuang et al., A Resolution for the Inconsistency in the Definitions of Tonicity [Abstract], submitted to EB2022.6. Kuang et al., Resolutions to the Problems Caused by Introducing both Osmolarity and Effective Osmolarity [Abstract], submitted to EB2022.