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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 of mixing is the consequence of the new interactions between the two substances or compounds. This enthalpy, if released exothermically, can in an extreme case cause an explosion. Enthalpy of mixing can often be ignored in calculations for mixtures where other heat terms exist, or in cases where the mixture is ideal. The sign convention is the same as for enthalpy of reaction: when the enthalpy of mixing is positive, mixing is endothermic, while negative enthalpy of mixing signifies exothermic mixing. In ideal mixtures, the enthalpy of mixing is null. In non-ideal mixtures, the thermodynamic activity of each component is different from its concentration by multiplying with the activity coefficient. One approximation for calculating the heat of mixing is Flory–Huggins solution theory for polymer solutions. For a liquid, enthalpy of mixing can be defined as follows Where: H(mixture) is the total enthalpy of the system after mixing ΔHmix is the enthalpy of mixing xi is the mole fraction of component i in the system Hi is the enthalpy of pure i Enthalpy of mixing can also be defined using Gibbs free energy of mixing However, Gibbs free energy of mixing and entropy of mixing tend to be more difficult to determine experimentally. As such, enthalpy of mixing tends to be determined experimentally in order to calculate entropy of mixing, rather than the reverse. Enthalpy of mixing is defined exclusively for the continuum regime, which excludes molecular-scale effects (However, first-principles calculations have been made for some metal-alloy systems such as Al-Co-Cr or β-Ti). When two substances are mixed the resulting enthalpy is not an addition of the pure component enthalpies, unless the substances form an ideal mixture. The interactions between each set of molecules determines the final change in enthalpy.

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Enthalpy of mixing

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 (or macroscopically equivalent, the enthalpy change of solution and volume variation in mixing is zero) and, as a result, properties of the mixtures can be expressed directly in terms of simple concentrations or partial pressures of the substances present e.g. Raoult's law.

Partial molar property

In thermodynamics, a partial molar property is a quantity which describes the variation of an extensive property of a solution or mixture with changes in the molar composition of the mixture at constant temperature and pressure. It is the partial derivative of the extensive property with respect to the amount (number of moles) of the component of interest. Every extensive property of a mixture has a corresponding partial molar property. The partial molar volume is broadly understood as the contribution that a component of a mixture makes to the overall volume of the solution.

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