Kuang Serena Y, Li Xiaonan, Yang Xiaoqi, Jones Eric
Foundational Medical Studies, Oakland University William Beaumont School of Medicine, Rochester, MI, USA.
Children Healthcare, Children Hospital of Nanjing Medical University, Nanjing, Jiangsu, People's Republic of China.
R Soc Open Sci. 2025 Sep 15;12(9):250622. doi: 10.1098/rsos.250622. eCollection 2025 Sep.
The original van 't Hoff's law established the theoretical foundation for osmosis but applies only to ideal solutions and membranes. To address real-world complexities (non-ideal solutions, diverse membranes, etc.), multiple variations have emerged over a century. In resolving osmosis-related conceptual issues, our previous work introduced several new fundamental concepts to fill gaps in the study of osmosis and redefined osmotic concentration (OC) as a membrane-dependent, osmosis system-level parameter, not a parameter of any isolated solution. This article examines the multiple factors influencing the initial OC (OC) before osmosis occurs and demonstrates that the multiple forms of van 't Hoff's law can be unified using OC into one general form through mathematical reasoning. Building upon this unified framework, we further propose an extended formulation to accommodate more complex osmosis systems. These general forms of van 't Hoff's law overcome the limitations of the original and may be widely applied to real-world dilute solutions and membranes. We also perform an initial validation of our work using measured data in the literature. This work represents a significant theoretical advance in the understanding of osmosis and has potential to impact multiple disciplines that teach and research it, including physics, chemistry, physiology and clinical disciplines.
最初的范特霍夫定律为渗透作用奠定了理论基础，但仅适用于理想溶液和膜。为了解决现实世界中的复杂性问题（非理想溶液、多种膜等），在过去的一个世纪里出现了多种变体。在解决与渗透作用相关的概念问题时，我们之前的工作引入了几个新的基本概念，以填补渗透作用研究中的空白，并将渗透浓度（OC）重新定义为一个依赖于膜的、渗透系统层面的参数，而非任何孤立溶液的参数。本文研究了在渗透作用发生之前影响初始OC（OC₀）的多个因素，并通过数学推理证明，范特霍夫定律的多种形式可以用OC统一为一种通用形式。基于这个统一的框架，我们进一步提出了一个扩展公式，以适应更复杂的渗透系统。这些范特霍夫定律的通用形式克服了原始定律的局限性，可能广泛应用于现实世界中的稀溶液和膜。我们还利用文献中的实测数据对我们的工作进行了初步验证。这项工作代表了在理解渗透作用方面的一项重大理论进展，有可能影响多个教授和研究渗透作用的学科，包括物理学、化学、生理学和临床学科。
