= Solvation thermodynamic balance
{title2=$\Delta G=\Delta H-T\Delta S$}
At fixed <temperature> and <pressure>, compare fully specified initial and final states using
$$
\Delta G=\Delta H-T\Delta S.
$$
The <entropy> change is for the whole selected system, including both <solute> and <solvent>. Dispersing a <solute> can increase accessible arrangements while orienting nearby <solvent> <molecules> restricts others. One picture of an ordered <hydration shell> cannot determine the sign of the total <entropy> change. A negative <Gibbs free energy> change favors the specified process; it does not determine its <reaction rate>.<Chemistry 2e by Paul Flowers and others/16.4 Free Energy>[Opening definition and Table 16.3]{ref}
An illustrative <enthalpy> accounting path separates <solute> constituents, reorganizes the <solvent>, and establishes their interactions:
$$
\Delta H=\Delta H_{\mathrm{separate}}+\Delta H_{\mathrm{reorganize}}+\Delta H_{\mathrm{interact}}.
$$
This is a chosen decomposition between compatible states, not a measured sequence. If a gaseous-ion-to-<chemical solution> <solvation> term already includes <solvent> reorganization, do not add that reorganization a second time. <Lattice enthalpy from solution calorimetry> gives the alternative <Hess's law> route that combines lattice separation with the complete <hydration of ions> term.<Chemistry 2e by Paul Flowers and others/11.1 The Dissolution Process>[Chemistry 2e by Paul Flowers and others; “The Formation of Solutions”, Figure 11.4]{ref}
\Image[/solvation-enthalpy-entropy-balance.png]
{title=Synthetic <dissolution> bookkeeping: <solvent> interactions change the <enthalpy> balance, while total <entropy> also enters the <Gibbs free energy>}
{id=image-solvation-enthalpy-entropy-balance}
{description=Original stipulated model for one <mole> of a hypothetical 1:1 <salt> at $300\,\mathrm K$, with two unspecified <solvents>. No plotted value is a measurement or a claim about a named <chemical substance>. The accounting path is not a <reaction coordinate> or an <activation energy>.}
The invented inputs are $+100$ for separation and $+20$ for <solvent> reorganization, in $\mathrm{kJ\,mol^{-1}}$. Interaction terms of $-150$ in <solvent> A and $-90$ in <solvent> B give $\Delta H_A=-30$ and $\Delta H_B=+30$. Stipulated total <entropy> changes of $-50$ and $+150\,\mathrm{J\,mol^{-1}\,K^{-1}}$ give $-T\Delta S_A=+15$ and $-T\Delta S_B=-45\,\mathrm{kJ\,mol^{-1}}$ at $300\,\mathrm K$. Both selected processes therefore have $\Delta G=-15\,\mathrm{kJ\,mol^{-1}}$. This deliberately constructed comparison shows why the signs of the <enthalpy> and <Gibbs free energy> changes need not agree; it does not predict either <solvent>'s <solubility>.
For incremental <dissolution> at a particular composition, the relevant <chemical potential> difference also depends on <thermodynamic activities>. At <chemical equilibrium> that driving difference vanishes. A quoted standard <Gibbs free energy> change and the finite change between arbitrary mixtures answer different questions; use compatible <standard states> and the <reaction quotient> when discussing <solubility>.
The motivating <calorimetry> experiment is especially instructive. A weighed <potassium chloride> sample dissolves in a known amount of <water> in a platinum-lined, shielded <calorimeter>; a quartz-oscillator <thermometer> and measured electrical heating provide the readouts. Electrical calibration before and after the reaction, comparison with a resistance <thermometer>, and checks on residual <water> and particle size constrain errors. The inspected authored article reports positive <enthalpy of solution> at $298.15\,\mathrm K$ for the specified dilution, despite complete <dissolution>. This is a combined <enthalpy> balance, not an isolated <solvation free energy> or direct single-ion <hydration of ions> measurement. Shield tracking and final <concentration> matter; the existing <lattice enthalpy from solution calorimetry> discussion gives the numerical result and the conversion limits.<The Enthalpy of Solution of SRM 1655 (KCl) in H2O by Marthada V. Kilday>[Abstract, §§3–4 and conclusion; inspected indexed authored text, direct PMC access challenged]{ref}
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