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

change associated with the dissolution of a substance in a

solvent A solvent (from the Latin language, Latin ''wikt:solvo#Latin, solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a Solution (chemistry), solution. A solvent is usually a liquid but can also be a solid, a gas ...

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 up of three parts: the

endothermic An endothermic process is a chemical or physical process that absorbs heat from its surroundings. In terms of thermodynamics, it is a thermodynamic process with an increase in the enthalpy (or internal energy ) of the system.Oxtoby, D. W; Gillis, ...

breaking of bonds within the

solute In chemistry, a solution is defined by IUPAC as "A liquid or solid phase containing more than one substance, when for convenience one (or more) substance, which is called the solvent, is treated differently from the other substances, which are ...

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

ideal solution 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. The vapor pressures of all components obey R ...

has a null

enthalpy of mixing In thermodynamics, the enthalpy of mixing (also heat of mixing and excess enthalpy) is the enthalpy liberated or absorbed from a substance upon mixing. When a substance or compound is combined with any other substance or compound, the enthalpy ...

. For a non-ideal solution, it is an

excess molar quantity In chemical thermodynamics, excess properties are properties of mixtures which quantify the non- ideal behavior of real mixtures. They are defined as the difference between the value of the property in a real mixture and the value that would exist ...

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 the solution.

Steps in dissolution

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

), for instance,

lattice energy In chemistry, the lattice energy is the energy change (released) upon formation of one mole of a crystalline compound from its infinitely separated constituents, which are assumed to initially be in the gaseous state at 0 K. It is a measure of ...

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

hydrogen bonding In chemistry, a hydrogen bond (H-bond) is a specific type of molecular interaction that exhibits partial covalent character and cannot be described as a purely electrostatic force. It occurs when a hydrogen (H) atom, Covalent bond, covalently b ...

. # 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 (e ...

), in

solvation Solvations 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 the solute, includi ...

. 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 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, but does not form hydrates. It is predominantly us ...

in water is endothermic. The energy released by the 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 utili ...

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 is the continuous analog of a Summation, sum, which is used to calculate area, areas, volume, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental oper ...

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

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

where is the infinitesimal variation, or differential, of the

mole number The mole (symbol mol) is a unit of measurement, the base unit in the International System of Units (SI) for ''amount of substance'', an SI base quantity proportional to the number of elementary entities of a substance. One mole is an aggregate ...

of the solute during dissolution. The integral heat of dissolution is defined as 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^\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

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 ...

or vaporisation. For non-ideal solutions of

electrolyte An electrolyte is a substance that conducts electricity through the movement of ions, but not through the movement of electrons. This includes most soluble Salt (chemistry), salts, acids, and Base (chemistry), bases, dissolved in a polar solven ...

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 vacuum permittivity, electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric co ...

through the following formula:

Gustav Kortüm Gustav Ferdinand Albert Kortüm (14 June 1904 to 1 December 1990) was a German physical chemist and electrochemist. Kortüm was the son of a pastor and studied chemistry at Karlsruhe Institute of Technology from 1922. In 1928 he received his doct ...

, Elektrolytlösungen, Akademische Verlagsgesellschaft m. b. H., Leipzig 1941, p. 124.

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

References

External links