Revisiting Bugarszky’s 1895 Chemical Equilibrium Study: Mercury Speciation Correction, Temperature-Corrected Thermodynamics, and Improved Accuracy with Sodium Bromide

We present a comprehensive thermodynamic reanalysis of István Bugarszky’s landmark 1895 study of the heterogeneous equilibrium 2MBr(aq) + HgO(s) + H2O ⇌ 2MOH(aq) + HgBr2(aq) (M = K, Na) at 12.50 °C. Bugarszky observed that his classical mass-action quotient KGW = (p − ξ)/ξ2 increases by a factor of 66 across a 15-fold dilution range, in apparent violation of the Guldberg–Waage law. We resolve this 130-year-old puzzle by demonstrating that Bugarszky’s gravimetric mercury determination measured total dissolved mercury, dominated by HgBr42−, rather than free HgBr2. Applying NIST mercury–bromide speciation constants and extended Debye–Hückel activity corrections reduces the coefficient of variation (CV) of the equilibrium constant from 132% (Kapp) to 7.3% (Kcorr, KBr), fully rehabilitating the law of mass action. The speciation mechanism itself is model-dependent, resting on critically evaluated formation constants; the empirical exponent z = 1.284 ≈ 4/3, obtained directly from the raw data, provides the principal model-independent support, and direct spectroscopic confirmation (Raman/UV–Vis) of the HgBrn distribution is identified as future work. After van‘t Hoff temperature corrections to 12.50 °C, the fully corrected Kcorr(KBr) = (4.61 ± 0.31)∙10−8 exceeds the thermodynamic reference value Klit(12.5 °C) = 4.17∙10−8 by +10.4%. To probe cation-specific effects, we replicated the protocol at five bromide concentrations using sodium bromide. The NaBr system yields Kcorr(NaBr) = (4.37 ± 0.42)∙10−8 (CV = 9.7%), deviating from Klit by +4.6% (the KBr–NaBr difference is not statistically significant; Welch’s t-test, p = 0.28). We consider possible origins of this difference in terms of the extended Debye–Hückel activity model and known structural differences between Na+ and K+ electrolyte environments; a kinetic explanation is also conceivable but remains a working hypothesis requiring direct experimental validation. We also discuss the optical properties of HgBr2 and the implications of the equilibrium analysis for its synthesis.