1.8.10: Enthalpy of Solutions- Salts
The chemical substance \(\mathrm{NaCl}(\mathrm{s})\) is a hard crystalline solid with a high melting point, \(1074 \mathrm{K}\). All the more remarkable therefore is the observation when a few crystals are dropped into water(\(\ell\)) the crystals disintegrate into ions with no dramatic change in the temperature of the water. One concludes that the intensity of interactions between ions in the crystal is comparable to that between ions and water molecules in the aqueous solution. Not surprisingly therefore enthalpies of solutions have been extensively investigated.
The enthalpy of an aqueous solution prepared at temperature \(\mathrm{T}\) and pressure \(\mathrm{p}\) using \(\mathrm{n}_{1}\) moles of water and \(\mathrm{n}_{j}\) moles of salt is given by equation (a) where \(\phi\left(\mathrm{H}_{j}\right)\) is the apparent molar enthalpy of salt \(j\) in solution.
\[\mathrm{H}(\mathrm{aq})=\mathrm{n}_{1} \, \mathrm{H}_{1}^{*}(\ell)+\mathrm{n}_{\mathrm{j}} \, \phi\left(\mathrm{H}_{\mathrm{j}}\right) \nonumber \]
Before the solution was prepared the enthalpy of the system, \(\mathrm{H}(\mathrm{no}-\mathrm{mix})\) is given by equation (b) where \(\mathrm{H}_{\mathrm{j}}^{*}(\mathrm{~s})\) is the molar enthalpy of solid salt \(j\).
\[\mathrm{H}(\mathrm{no}-\operatorname{mix})=\mathrm{n}_{1} \, \mathrm{H}_{1}^{*}(\ell)+\mathrm{n}_{\mathrm{j}} \, \mathrm{H}_{\mathrm{j}}^{*}(\mathrm{~s}) \nonumber \]
Using an isobaric calorimeter, heat \(\mathrm{q}\) is recorded for the solution process.
\[\mathrm{q}=\mathrm{H}(\mathrm{aq})-\mathrm{H}(\mathrm{no}-\mathrm{mix})=\mathrm{n}_{\mathrm{j}} \,\left[\phi\left(\mathrm{H}_{\mathrm{j}}\right)-\mathrm{H}_{\mathrm{j}}^{*}(\mathrm{~s})\right] \nonumber \]
Or
\[\phi\left(H_{j}\right)-H_{j}^{*}(s)=q / n_{j} \nonumber \]
In many studies [1] using sensitive calorimeters (\(\mathrm{q}/\mathrm{n}_{j}\)) can be recorded for the production of quite dilute solutions such that \(\phi\left(\mathrm{H}_{j}\right)\) is effectively equal to \(\mathrm{H}_{\mathrm{j}}^{\infty}(\mathrm{aq})\). In other cases \(\Delta_{s \ln } \mathrm{H}(\mathrm{s} \rightarrow \mathrm{aq})\) is found to depend on the molality of the resultant solution. One procedure [2] fits the measured enthalpy of solution to a quadratic in the molality of salt.
\[\Delta_{s \ln } \mathrm{H}(\mathrm{s} \rightarrow \mathrm{aq})=\Delta_{\mathrm{sin}} \mathrm{H}^{0}(\mathrm{~s} \rightarrow \mathrm{aq})+\mathrm{A} \,\left(\mathrm{m}_{\mathrm{j}} / \mathrm{m}^{0}\right)+\mathrm{B} \,\left(\mathrm{m}_{\mathrm{j}} / \mathrm{m}^{0}\right)^{2} \nonumber \]
In other cases the Debye-Huckel limiting law is used as a basis for extrapolating \(\Delta_{\mathrm{s} \ln } \mathrm{H}(\mathrm{s} \rightarrow \mathrm{aq})\) to the required infinite dilution value [3].
Footnotes
[1]
- R. K. Mohanty, T. S. Sarma, S. Subramanian and J.C. Ahluwalia, Trans. Faraday Soc.,1971, 67 ,305.
- N Van Meurs, Th. W Warmerdam and G. Somsen, Fluid Phase Equilib., 1989, 49 ,263.
- M. E. Estep, D. D. Macdonald and J. B. Hyne, J. Solution Chem.,1977, 6 ,129.
[2] C. V. Krishnan and H. L. Friedman, J. Phys.Chem.,1970, 74 ,3900 .
[3] e.g. Om. N. Bhatnagar and C. M. Criss, J. Phys Chem.,1969, 73 ,174.