5.9: Enthalpy of Solution

Enthalpy of Solution

The enthalpy change of solution is the enthalpy change when 1 mole of an ionic substance dissolves in water to give a solution of infinite dilution. Enthalpies of solution may be either positive or negative - in other words, some ionic substances dissolved endothermically (for example, NaCl); others dissolve exothermically (for example NaOH).

An infinitely dilute solution is one where there is a sufficiently large excess of water that adding any more does not cause any further heat to be absorbed or evolved. So, when 1 mole of sodium chloride crystals are dissolved in an excess of water, the enthalpy change of solution is found to be +3.9 kJ mol^-1. The change is slightly endothermic, and so the temperature of the solution will be slightly lower than that of the original water.

The process of forming a solution, or of dissolving a solid, is often referred to as the dissolution process. In the dissolution process, the solid must separate into ions and become dispersed with solvent molecules between the ions. The overall process of dissolving a solid can be treated as an energy cycle.

Dissolving as an Energy Cycle

Why is heat sometimes evolved and sometimes absorbed when a substance dissolves in water? To answer that it is useful to think about the various enthalpy changes that are involved in the process of dissolving a solid. First, the crystal lattice is first broken up into its separate gaseous ions. Then those ions become surrounded by water molecules, which is how they exist in the final solution. The energy change associated with this overall process is the molar enthalpy of solution, \(\Delta H_{sol}\).

The energy change associated with assembling a lattice from its component gaseous ions is referred to as the lattice energy, \(\ce_\Delta H_{lattice}\), and it typically has a negative value, indicating that energy is released to assemble ions into a lattice. The process of breaking a lattice apart into its component ions, is the opposite of the lattice energy and has a value of \(\ce_-\Delta H_{lattice}\), indicating that energy is required to break the lattice apart. In order to dissolve a solid, the lattice must break apart; thus, the negative of the lattice energy is used in this cycle.

The hydration enthalpy is the energy released when new bonds are made between the ions and water molecules that surround them. The hydration enthalpy is the enthalpy change when 1 mole of gaseous ions dissolve in sufficient water to give an infinitely dilute solution. Hydration enthalpies are always negative.

The enthalpy of solution is then equal to the enthalpy of hydration minus the lattice energy.

\[\Delta H_{sol} =\Delta H_{lattice} + \Delta H_{hydration} \nonumber\]

The cycle relating solution enthalpy, hydration enthalpy, and lattice energy is shown in Figure \(\PageIndex{1}\) using the salt \(\ce{NaCl}\) as an example.

Figure \(\PageIndex{1}\): Thermodynamic cycle for dissolving sodium chloride in water. (CC-BY-NC-SA 4.0, Chung (Peter) Chieh)

The enthalpies of solution for some salts can be positive values, in these cases the temperatures of the solution decrease as the substances dissolve; the dissolving is an endothermic reaction. The energy levels of solids and solutions reverse in order of height. The values in Table \(\PageIndex{1}\) indicate that when aluminum chloride and sulfuric acid are dissolved in water, much heat is released. Due to the very small value of enthalpies of solution, the temperature changes are hardly noticed when LiNO₃ and NaCl are dissolving.

Table \(\PageIndex{1}\): Enthalpy of Solution \(\Delta H_\ce{sol}\) kJ/mol) of Some Common Electrolytes

Substance	\(\Delta H_{sol}\)	Substance	\(\Delta H_{sol}\)
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

Calculating Enthalpy of Solution

The hydration enthalpies for calcium and chloride ions are given by the equations:

\[\ce_Ca^{2+}(g)+H_2O \rightarrow\ Ca^{2+}(aq), \Delta H_{hyd} =-1650 kJ/mol \nonumber\]

\[\ce_Cl^{-}(g)+H_2O \rightarrow\ Cl^{-}(aq), \Delta H_{hyd} =-364 kJ/mol \nonumber\]

The following cycle is for calcium chloride, and includes a lattice energy of -2258 kJ mol^-1 (+2258 kJ mol^-1 to disassemble the lattice). We have to use double the hydration enthalpy of the chloride ion because we are hydrating 2 moles of chloride ions.

\[\ce_\Delta H_{sol} = -\Delta H_{lattice} + \Delta H_{hyd, Ca} + 2\times \Delta H_{hyd, Cl} \nonumber\]

\[\ce_\Delta H_{sol} = -(-2258 \,kJ/mol) + (-1650 \,kJ/mol) + (2\times -364 \,kJ/mol) \nonumber\]

Whether an enthalpy of solution turns out to be negative or positive depends on the relative sizes of the lattice enthalpy and the hydration enthalpies. In this particular case, the negative hydration enthalpies more than made up for the positive lattice dissociation enthalpy.

Figure \(\PageIndex{2}\): Thermodynamic cycle for dissolving calcium chloride in water. (CC-BY-NC 4.0, Jim Clark)

Problems

Exercise \(\PageIndex{1}\)

The lattice energy of NaCl 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.

Answer

Using the cycle in Figure \(\PageIndex{2}\), we have

\[\Delta H_{hyd} = \Delta H_{lattice} + \Delta H_{sol} \nonumber\]

\[\Delta H_{sol} = -769 - (788)\; kJ = -19\, kJ/mol \nonumber\]

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.

Exercise \(\PageIndex{2}\)

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 solution for KCl.

Answer

The enthalpy of hydration for KCl is estimated to be

\[\Delta H_{hyd}= -322 + (-363) = -685 kJ/mol \nonumber\]

Thus, the enthalpy of solution is

\[\Delta H_{sol}= -685 - (-715) = 30 kJ/mol \nonumber\]

The enthalpy of solution given above is -17.22. The two values here indicates that dissolving \(\ce{KCl}\) into water is an endothermic reaction or change. Should temperature decrease or increase when \(\ce{KCl}\) dissolves?

Contributors and Attributions

• Jim Clark (Chemguide.co.uk)