Experimental Evidence Supporting a New "Osmosis Law & Theory" Derived New Formula that Improves vant Hoff Osmotic Pressure Equation

Experimental data were used to support a new concept of osmotic force and a new osmotic law that can explain the osmotic process without the difficulties encountered with van’t Hoff osmotic pressure theory. Derived new osmotic formula with curvilinear equation (via new osmotic law) overcomes the limitations and incompleteness of van’t Hoff (linear) osmotic pressure equation, $\pi=(n/v)RT$, (for ideal dilute solution only). The application of this classical theory often resulted in contradiction regardless of miscellaneous explaining efforts. This is due to the lack of a scientific concept like “osmotic force” that we believe can elaborate the osmotic process. Via this new concept, the proposed new osmotic law and derived new osmotic pressure equation will greatly complete and improve the theoretical consistency within the scientific framework of osmosis.

💡 Research Summary

The manuscript attempts to overturn the classical van’t Hoff description of osmotic pressure by introducing a new physical quantity called “osmotic force” and a corresponding “osmotic law.” The authors define osmotic force as the product of the pressure acting on a semi‑permeable membrane (including atmospheric and hydrostatic components) and an “osmotic effective area” that supposedly varies with solute concentration. They argue that the traditional van’t Hoff equation, π = (n/V)RT, is limited to ideal dilute solutions because it is derived from an inappropriate application of chemical‑potential equilibrium and because its derivation allegedly neglects higher‑order terms in a Taylor expansion.

To remedy these perceived shortcomings, the authors derive a new, curvilinear osmotic‑pressure expression (their equation 5). This formula incorporates the atmospheric pressure, the temperature ratio T/T₀ (with T₀ being the melting point of the solvent), the solute molar concentration, and a constant k (taken as 0.0224, the molar volume of an ideal gas at STP). The resulting pressure‑versus‑concentration curve is linear at very low concentrations—reproducing the van’t Hoff result—but rises sharply as concentration increases, reflecting the authors’ claim of a more “realistic” description.

The paper, however, suffers from multiple fundamental flaws:

1. Conceptual ambiguity – “Osmotic effective area” is introduced without any operational definition, measurement method, or justification for its assumed linear dependence on concentration. The claim that atmospheric pressure contributes differently on each side of the membrane because of differing effective areas is not supported by any thermodynamic analysis.

2. Misinterpretation of thermodynamics – The authors assert that the equality of chemical potentials across the membrane is invalid for osmotic equilibrium. In reality, the equality of the solvent’s electrochemical potential holds irrespective of membrane presence; the membrane merely selects which species can cross. Their criticism therefore misrepresents the foundation of the van’t Hoff derivation.

3. Faulty mathematical reasoning – The alleged “mistake” in the van’t Hoff derivation (ignoring higher‑order terms of a Taylor series) is a misunderstanding of approximation. The linear form is deliberately retained because it accurately describes dilute solutions; higher‑order terms become significant only when the solution is no longer ideal, at which point activity coefficients must be introduced—not a new fundamental law.

4. Unclear and unreadable formulae – Equation 5 is littered with non‑standard symbols, special characters, and typographical errors, making it impossible to reproduce or verify. No dimensional analysis is provided, and the role of the constant k is not physically explained.

5. Absence of experimental validation – Although the abstract promises experimental support, the manuscript provides no details on sample preparation, temperature control, pressure measurement, replication, or statistical analysis. The only graphical evidence is a theoretical curve plotted with arbitrary parameter values (p = 1 atm, k = 0.0224, etc.) without any comparison to measured data.

6. Lack of peer‑reviewed context – The authors cite a handful of recent papers that also discuss van’t Hoff limitations, but they do not engage with the extensive literature on osmotic pressure corrections (e.g., virial expansions, activity coefficients, Pitzer equations). Their “new law” therefore adds nothing new to the well‑established framework for non‑ideal solutions.

In summary, the manuscript proposes a novel “osmotic force” concept and a non‑linear osmotic‑pressure equation, but it fails to provide a rigorous definition, a sound thermodynamic derivation, or credible experimental evidence. The presented mathematics is obscure, the physical arguments are flawed, and the experimental section is essentially absent. Consequently, the work does not meet the standards of scientific rigor and should be regarded as speculative rather than a genuine advancement of osmotic theory.