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 Dissolution may refer to: Arts and entertainment Books * ''Dissolution'' (''Forgotten Realms'' novel), a 2002 fantasy novel by Richard Lee Byers * ''Dissolution'' (Sansom novel), a 2003 historical novel by C. J. Sansom Music * Dissolution, in mu ...

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 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 o ...

. 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 exis ...

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 Le Chatelier's principle (pronounced or ), also called Chatelier's principle (or the Equilibrium Law), is a principle of chemistry used to predict the effect of a change in conditions on chemical equilibria. The principle is named after French ...

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

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 the ...

. 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 wit ...

, 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 defi ...

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

of an ideal solution 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 electrolytes 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 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_ = \sum_i \nu_i RT \ln \gamma_i \left( 1 + \frac\frac \right)

References

External links