5.8: Enthalpy of Hydration
- Page ID
- 444403
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The formation of a solution involves the interaction of solute with solvent molecules. Many different liquids can be used as solvents for liquid solutions, and water is the most commonly used solvent. When water is used as the solvent, the dissolving process is called hydration. The interaction between water molecules and sodium ion is illustrated in Figure \(\PageIndex{1}\). This is a typical ion-dipole interaction. At the molecular level, the ions interact with water molecules from all directions in a 3-dimensional space. Figure \(\PageIndex{1}\) also shows hydrogen-bonding, dipole-dipole, ion-induced dipole, and dipole-induced dipole interactions. In the absence of these interactions, solvation takes place due to dispersion.
Enthalpy of Hydration
Enthalpy of hydration, \(\Delta H_{hyd}\), of an ion is the amount of heat released when a mole of the ion dissolves in a large amount of water forming an infinitely dilute solution in the process,
\[M^{z+}_{(g)} + mH_2O \rightarrow M^{z+}_{(aq)} \label{1}\]
where Mz+(aq) represents ions surrounded by water molecules and dispersed in the solution. The approximate hydration energy of some common ions are listed in Table \(\PageIndex{1}\).
| Ion | \(\Delta H_{hyd}\) | Ion | \(\Delta H_{hyd}\) | Ion | \(\Delta H_{hyd}\) |
|---|---|---|---|---|---|
| H+ | -1130 | Al3+ | -4665 | Fe3+ | -4430 |
| Li+ | -520 | Be2+ | -2494 | F- | -505 |
| Na+ | -406 | Mg2+ | -1921 | Cl- | -363 |
| K+ | -322 | Ca2+ | -1577 | Br- | -336 |
| Rb+ | -297 | Sr2+ | -1443 | I- | -295 |
| Cs+ | -276 | Ba2+ | -1305 | ClO4- | -238 |
| Cr2+ | -1904 | Mn2+ | -1841 | Fe2+ | -1946 |
| Co2+ | -1996 | Ni2+ | -2105 | Cu2+ | -2100 |
| Zn2+ | -2046 | Cd2+ | -1807 | Hg2+ | -1824 |
Hydration of an ion occurs in two steps. First, the solvent coordinates with the ion as energy is released. The energy released is called the enthalpy of ligation, \(\Delta H_{lig}\). Second, the hydrated ions are dispersed into the solvent. The energy change associated with this step is called energy of dispersion, \(\Delta H_{disp}\).
\[M^{z+} + nL \rightarrow ML_n^{z+} \;\;\; \Delta H_{lig} \label{2}\]
\[ML_n^{z+} + solvent \rightarrow ML^{z+}_{n(sol)} \;\;\; \Delta H_{disp} \label{3}\]
\[\Delta H_{hyd} = \Delta H_{disp} + \Delta H_{lig} \label{4}\]
Factors affecting the size of hydration enthalpy
Hydration enthalpy is a measure of the energy released when attractions are set up between positive or negative ions and water molecules.
- With positive ions, there may only be loose attractions between the slightly negative oxygen atoms in the water molecules and the positive ions, or there may be formal dative covalent (co-ordinate covalent) bonds.
- With negative ions, hydrogen bonds are formed between lone pairs of electrons on the negative ions and the slightly positive hydrogen atoms in water molecules.
The size of the hydration enthalpy is governed by the amount of attraction between the ions and the water molecules.
- The attractions are stronger the smaller the ion. For example, hydration enthalpies fall as you go down a group in the Periodic Table. The small lithium ion has by far the highest hydration enthalpy in Group 1, and the small fluoride ion has by far the highest hydration enthalpy in Group 7. In both groups, hydration enthalpy falls as the ions get bigger.
- The attractions are stronger the more highly charged the ion. For example, the hydration enthalpies of Group 2 ions (like Mg2+) are much higher than those of Group 1 ions (like Na+).
Contributors and Attributions
Chung (Peter) Chieh (Professor Emeritus, Chemistry @ University of Waterloo)