thermochemistry Thermochemistry is the study of the heat energy which is associated with chemical reactions and/or phase changes such as melting and boiling. A reaction may release or absorb energy, and a phase change may do the same. Thermochemistry focuses on ...

, the enthalpy of solution ( heat of solution or enthalpy of solvation) is the

enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...

change associated with the dissolution of a substance in a

solvent A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...

at constant pressure resulting in infinite dilution. The enthalpy of solution is most often expressed in kJ/ mol at constant temperature. The energy change can be regarded as being made of three parts: the

endothermic In thermochemistry, an endothermic process () is any thermodynamic process with an increase in the enthalpy (or internal energy ) of the system.Oxtoby, D. W; Gillis, H.P., Butler, L. J. (2015).''Principle of Modern Chemistry'', Brooks Cole. ...

breaking of bonds within the solute and within the solvent, and the formation of attractions between the solute and the solvent. An

ideal solution In chemistry, an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to ze ...

has a null enthalpy of mixing. For a non-ideal solution it is an excess molar quantity.

Energetics

Dissolution by most gases is exothermic. That is, when a gas dissolves in a liquid solvent, energy is released as heat, warming both the system (i.e. the solution) and the surroundings. The temperature of the solution eventually decreases to match that of the surroundings. The equilibrium, between the gas as a separate phase and the gas in solution, will by Le Châtelier's principle shift to favour the gas going into solution as the temperature is decreased (decreasing the temperature increases the solubility of a gas). When a saturated solution of a gas is heated, gas comes out of solution.

Steps in dissolution

Dissolution can be viewed as occurring in three steps: # Breaking solute-solute attractions (

), see for instance

lattice energy In chemistry, the lattice energy is the energy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state. It is a measure of the cohesive forces that bin ...

in salts. # Breaking solvent-solvent attractions (endothermic), for instance that of

hydrogen bonding In chemistry, a hydrogen bond (or H-bond) is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing a l ...

# Forming solvent-solute attractions (

exothermic In thermodynamics, an exothermic process () is a thermodynamic process or reaction that releases energy from the system to its surroundings, usually in the form of heat, but also in a form of light (e.g. a spark, flame, or flash), electricity ...

), in

solvation Solvation (or dissolution) describes the interaction of a solvent with dissolved molecules. Both ionized and uncharged molecules interact strongly with a solvent, and the strength and nature of this interaction influence many properties of t ...

. The value of the enthalpy of solvation is the sum of these individual steps. :

\Delta H_\text = \Delta H_\text + U_\text

Dissolving

ammonium nitrate Ammonium nitrate is a chemical compound with the chemical formula . It is a white crystalline salt consisting of ions of ammonium and nitrate. It is highly soluble in water and hygroscopic as a solid, although it does not form hydrates. It is ...

in water is endothermic. The energy released by solvation of the ammonium ions and nitrate ions is less than the energy absorbed in breaking up the ammonium nitrate ionic lattice and the attractions between water molecules. Dissolving

potassium hydroxide Potassium hydroxide is an inorganic compound with the formula K OH, and is commonly called caustic potash. Along with sodium hydroxide (NaOH), KOH is a prototypical strong base. It has many industrial and niche applications, most of which exp ...

is exothermic, as more energy is released during solvation than is used in breaking up the solute and solvent.

Expressions in differential or integral form

The expressions of the enthalpy change of dissolution can be differential or

integral In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with ...

, as function of the ratio of amounts solute-solvent. The molar differential enthalpy change of dissolution is: :

\Delta_\text^ H= \left(\frac\right)_

where is the infinitesimal variation or differential of

mole number The mole, symbol mol, is the unit of amount of substance in the International System of Units (SI). The quantity amount of substance is a measure of how many elementary entities of a given substance are in an object or sample. The mole is defin ...

of the solute during dissolution. The integral heat of dissolution is defined for a process of obtaining a certain amount of solution with a final concentration. The

change in this process, normalized by the

of solute, is evaluated as the molar integral heat of dissolution. Mathematically, the molar integral heat of dissolution is denoted as: :

\Delta_\text^ H = \frac

The prime heat of dissolution is the differential heat of dissolution for obtaining an infinitely diluted solution.

Dependence on the nature of the solution

The enthalpy of mixing of an

is zero by definition but the enthalpy of dissolution of nonelectrolytes has the value of the

enthalpy of fusion In thermodynamics, the enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a s ...

or vaporisation. For non-ideal solutions of

electrolyte An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon ...

s it is connected to the

activity coefficient In thermodynamics, an activity coefficient is a factor used to account for deviation of a mixture of chemical substances from ideal behaviour. In an ideal mixture, the microscopic interactions between each pair of chemical species are the same ...

of the solute(s) and the temperature derivative of the

relative permittivity The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insul ...

through the following formula: Gustav Kortüm Elektrolytlösungen, Akademische Verlagsgesellschaft m. b. H., Leipzig 1941, p. 124

H_ = \sum_i \nu_i RT \ln \gamma_i \left( 1 + \frac\frac \right)

References

External links