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Enthalpy of Hydration

Discussion Questions

Hydration

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 as one of the diagram below. 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. This diagram depicts the concept of interaction only.

The above diagram also display hydrogen-bonding, dipole-dipole, ion-induced dipole, and dipole-induced dipole interactions. In the absence of these interactions, solvation takes place due to dispersion. Definitions of these terms are obvious from the diagrams. The meaning of the words used in the term also hints the nature of the interactions.

What is the energy of hydration?

Enthalpy of hydration, Hhyd, of an ion is the amount of energy released when a mole of the ion dissolves in a large amount of water forming an infinite dilute solution in the process, Mz+(g) + mH2O ® Mz+(aq) where Mz+(aq) represents ions surrounded by water molecules and dispersed in the solution. The approximate hydration energies of some typical ions are listed here. The table illustrates the point that as the atomic numbers increases, so do the ionic size, leading to a decrease in absolute values of enthalpy of hydration.
Enthalpy of Hydration (Hhyd kJ/mol) of Some Typical Ions
Ion Hhyd       IonHhyd       Ion Hhyd
H+ -1130 Al3+ -4665 Fe3+ -4430
--
Li+ -520 Be2+ -2494 F- -505
Na+ -406 Mg2+ -1921Cl- -363
K+ -322 Ca2+ -1577Br- -336
Rb+ -297 Sr2+ -1443I- -295
Cs+ -276 Ba2+ -1305ClO4- -238
--
Cr2+ -1904 Mn2+ -1841Fe2+ -1946
Co2+ -1996 Ni2+ -2105Cu2+ -2100
Zn2+ -2046 Cd2+ -1807Hg2+ -1824

From the above table, an estimate can be made for the hydration energy of sodium chloride. This amount is very close to the energy of crystallization, Ecryst.

The hydration energy of an ionic compound consists of two inseparable parts. The first part is the energy released when the solvent forms a coordination compound with the ions. This energy released is called the energy of ligation, Hlig. The processes related to these energies are shown below:

Mz+ + nL = MLnz+,             Hlig
MLnz+ + solvent = MLnz+ (solution),     Hdisp
The second part is to disperse the ions or hydrated ions into the solvent medium, which has a dielectric constant different from vacume. This amount of energy is called energy of dispersion, Hdisp. Therefore, Hhyd = Hdisp + Hlig. This idea is brought up just to point out that the formation of aqua complex ions is part of the hydration process, even though the two energies are not separable. When stronger coordination is made between the ions and other ligands, they replace the coordinated water molecules if they are present. In the presence of NH3 molecules, they replace the water of Cu(H2O)62+: Cu(H2O)62+ + 6NH3 ® Cu(NH3)62+ + 6H2O

How is hydration energy related to enthalpy of crystallization?

In the discussion of lattice energy, we consider the ions separated into a gas form whereas in the disolution process, the ions are also separated, but this time into ions dispersed in a medium with solvent molecules between ions. The medium or solvent has a dielectric constant. The molar enthalpy of solvation, Hsolv, is the energy released when one mole solid is dissolved in a solvent. This quantity, the enthalpy of crystallization, and energy of hydration forms a cycle. Taking the salt NaCl as an example, the following relationship is obvious, Hhyd = Hcrystallization + Hsolv from the following diagram.

         -------Na+(g)+Cl-(g)--------
         |                       |
         |                       |
         |                       |Hcryst
         |Hhyd                    |
         |                       ¯
         |                 ----NaCl(s)---
         |                       |
         |                       |Hsolv
         ¯                       ¯
         -------Na+(aq)+Cl-(aq)--------
The term enthalpy of crystallization is used in this diagram instead of lattice energy so that all the arrows point downward. Note that enthalpy of crystallization Hcryst, and energy of crystallization, Ecryst referr to the same quantity, and they are used interchangably.

The energies of solvation for some salts can be positive values, in these cases the temperatures of the solution decrease as the substances dissolve. The solvation is an endothermic reaction. The energy levels of solids and solutions reverse in order of hight. The cycle is shown below.


         -------Na+(g)+Cl-(g)-------
         |                       |
         |                       |
         |                       |Hcryst
         |Hhyd                    |
         |                       |
         ¯                       |
         ---Na+(aq)+Cl-(aq )----    |
                            ­    |
                      Hsolv  |    |
                            |    ¯
                   ---------NaCl(s)--------
In these cases, the enthalpies of hydration are less negative than the enthalpies of crystallization.

What is enthalpy of solvation?

The molar enthalpy of solvation, Hsolv, is the energy released when one mole solid is dissolved in a solvent.

Note that Hsolv is also called molar heat of solution or molar energy of solution in some literature. Sometimes the enthalpy of hydration is also (mis)understood as Hsolv. When apply these values, make sure you understand the process involved. The following enthalpies of solvation are given in Chemistry by Radel and Navidi, West Publishing Co.


Enthalpy of Solvation (Hsolv kJ/mol) of Some Common Electrolytes
Substanc Hsolv             Substance Hsolv
AlCl3(s) -373.63 H2SO4(l) -95.28
LiNO3(s) -2.51 LiCl(s) -37.03
NaNO3(s) 20.50 NaCl(s) 3.88
KNO3(s) 34.89 KCl(s) -17.22
NaOH(s) -44.51 NH4Cl(s) 14.77

These values indicates that when aluminum chloride and sulfuric acid are dissolved in water, much heat is released. Due to the very small value of enthalpies of solvation, the temperature changes are hardly noticed when LiNO3 and NaCl are dissolving.

Example 1

The lattice energy of NaCl calculated from a physics view point using the Madlung constant of the NaCl structure type is 788 kJ/mol. The estimated enthalpy of hydration for sodium and chloride ions are 406 and 363 kJ/mol respectively. Estimate the enthalpy of solvation for NaCl.

Solution
Using the cycle shown above and the formula, we have

Hhyd = Hcrystallization + Hsolv
Hsolv = -769 - (-788) kJ     = 19 kJ/mol.

Discussion
A positive value indicates an endothermic reaction. However, the value is small, and depending on the source of data, the estimated value may change. This value of 19 kJ/mol is too high compared to the value given earlier for NaCl of 3.88 kJ/mol, due to a high value of lattice energy used.

Example 2

The enthalpy of crystallization for KCl is -715 kJ/mol. The enthalpies of hydration for potassium and chloride are -322 and -363 kJ/mol respectively. From these values, estimate the enthalpy of solvation for KCl.

Solution
The enthalpy of hydration for KCl is estimated to be

Hhyd= -322 + (-363)       = -685 kJ/mol Thus, the enthalpy of solvation is Hsolv= -685 - (-715)       = 30 kJ/mol

Discussion
The enthalpy of solvation given above is -17.22. The two values here indicates that the solvation is an endothermic reaction or change. Should temperature decrease or increase when KCl dissolves?

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