Category: Intermediate Chemistry

The standard enthalpy change of formation, ΔH_f ^o, is the change in enthalpy when one mole of a substance is formed from its elements in their reference states, which are the most stable forms of the respective elements at 100 kPa and 298.15K.

For example:

Element	Most stable form	Notes
Oxygen	O2 (g)	The oxygen radical, O, is unstable
Carbon	Graphite	Graphite is thermodynamically more stable than diamond since it has delocalised electrons
Mercury	Liquid mercury	–
Phosphorous	White phosphorous	Although not the most thermodynamically stable form, it is easier to isolate in its pure form than red and black phosphorous. This is the only exception.

Examples of standard enthalpy change of formation are as follows:

 

 

We can also say that the standard enthalpy change of formation of a substance ΔH_f ^o is the standard enthalpy change of the reaction ΔH_r ^o that forms the substance. For example,

 

 

Eq1e is a very useful formula and is a consequence of Hess’ law. In general, for a reaction involving multiple products and multiple reactants, the relationship between ΔH_r ^o, ΔH_f ^o[product] and ΔH_f ^o[reactants] is given by eq6 from the article on Hess’ law:

where P denotes the number of products and R denotes the number of reactants. v_P and v_R are the stoichiometric coefficients of the products of the respective standard enthalpy of formation reactions.

An issue arises when we want to determine the standard enthalpy change of formation of aqueous ions, which are always formed as pairs of cations and anions, e.g.

This implies that it is impossible to have a solution consisting of pure cations or anions. The problem is circumvented by defining the standard enthalpy change of formation of the aqueous hydrogen ion as zero:

The consequence of this can be illustrated by considering the ion pair of H⁺(aq) and Br^–(aq) where:

ΔH_r ^o for the above reaction is also known as ΔH_sol ^o, the standard enthalpy change of solution of HBr(g). Since HBr(aq) is fully dissociated to H⁺(aq) and Br^–(aq), we can also write eq2c as:

Using eq1e on eq2d,

Since

The standard enthalpy change in formation of other aqueous ions, e.g. Cl^–(aq), can be determined using the same approach. This results in all standard enthalpy changes in formation of aqueous ions being adjusted by the real value of .

 

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The standard enthalpy change of fusion, ΔH_fus ^o, is the change in enthalpy when one mole of a substance in the liquid state is formed from the same substance in its solid state under standard conditions.

The process of melting is always endothermic, e.g.

Most data for the standard enthalpy change of fusion of substances are quoted at the melting points of those substances instead of at 298.15 K. The standard enthalpy change of solidification of a substance, ΔH_solid ^o, is the negative value of the standard enthalpy change of fusion of that substance.

 

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The standard enthalpy change of sublimation, ΔH_sub ^o, is the change in enthalpy when one mole of a substance in the gaseous state is formed from the same substance in its solid state, without going through the liquid state, under standard conditions.

The process of sublimation is always endothermic, e.g.

The standard enthalpy change of sublimation is greater than that of vaporisation and hence greater than that of fusion. The standard enthalpy change of deposition of a substance, ΔH_dep ^o, is the negative value of the standard enthalpy change of sublimation of that substance.

 

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The standard enthalpy change of vaporisation, ΔH_vap ^o, is the change in enthalpy when one mole of a substance in the gaseous state is formed from the same substance in its liquid state under standard conditions.

Vaporisation reactions are always endothermic, e.g.

Even though ΔH_vap ^o = 44.0 kJmol^-1 is the standard enthalpy change of vaporisation of water at 298.15 K, many data sets of the standard enthalpy change of vaporisation of substances are quoted at the boiling points of those substances. In general, the standard enthalpy change of vaporisation of a substance is higher than the standard enthalpy change of fusion of that substance since molecules are separated further apart from one another from the liquid state to the gaseous state (more energy required) compared to the separation from the solid state to the liquid state. The standard enthalpy change of condensation of a substance, ΔH_con ^o, is the negative value of the standard enthalpy change of vaporisation of that substance.

 

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The standard enthalpy change of combustion ΔH_c ^o is the change in enthalpy when one mole of a substance, in its most stable form, is burnt in excess oxygen under standard conditions.

Combustion reactions are always exothermic, e.g.

The standard enthalpy change of combustion of iron is also the standard enthalpy change of formation of iron (III) oxide and the standard enthalpy change of reaction between iron and oxygen to give iron (III) oxide.

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The standard enthalpy change of atomisation, ΔH_at ^o, is the change in enthalpy when one mole of atoms in the gaseous state is formed from the most stable form of its element under standard conditions.

The atomisation process is always endothermic. Some examples are:

The standard enthalpy of atomisation of an atom is the same as the standard enthalpy of formation of that atom and the standard enthalpy of the reaction to form that atom. The standard enthalpy of atomisation of a species that exist as a homonuclear diatomic molecule under standard conditions, e.g. O₂, is also the bond enthalpy of that species. So,

 

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The standard enthalpy change of ionisation, ΔH_ion^o, is the change in enthalpy for removing one mole of electrons from one mole of atoms or ions in the gaseous state under standard conditions.

When one mole of electrons is removed from atoms to form one mole of monovalent cations, the change in enthalpy is called the first ionisation enthalpy, e.g.

When one mole of electrons is removed from monovalent cations to form one mole of divalent cations, the change in enthalpy is called the second ionisation enthalpy, e.g.

The standard enthalpy change of ionisation of a substance is calculated from the substance’s ionisation energy (the two are not the same, as ionisation energy is defined at absolute zero). Ionisation energies are determined experimentally using photoelectron spectroscopy (PES), where the known energy of an incident photon on an atom equals to the atom’s first ionisation energy plus the measured kinetic energy of the ionised electron. These ionisation energies are then converted to ionisation energies at absolute zero before converting to standard enthalpies of ionisation, with both conversions using Kirchhoff’s law.

 

 

 

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The standard enthalpy change of electron gain, ΔH_eg^o, is the change in enthalpy when one mole of electrons is attached to atoms or anions in the gaseous state to form one mole of anions under standard conditions.

When one mole of electrons is attached to atoms to form one mole of monovalent anions, the change in enthalpy is called the first electron gain enthalpy, e.g.

When one mole of electrons is attached to monovalent anions to form one mole of divalent anions, the change in enthalpy is called the second electron gain enthalpy, e.g.

The standard enthalpy change of electron gain of a substance is calculated from the substance’s electron affinity (the two are not the same, as electron affinity is defined at absolute zero) using Kirchhoff’s law, or from the relationship:

which states that the standard enthalpy change of electron gain of a species is the negative of the standard enthalpy change of ionisation of that species with an additional electron attached, e.g.

Substituting eq3 from the previous section in eq5,

Electron affinities are determined experimentally using photoelectron spectroscopy (PES) where the known energy of an incident photon on an anion equals to the atom’s electron affinity plus the measured kinetic energy of the ionised electron. These electron affinities are then converted to electron affinities at absolute zero, which are then converted to standard enthalpies of electron gain, with both conversions using Kirchhoff’s law. It is easier to measure ionisation energies than electron affinities and therefore standard enthalpies of electron gain of substances are usually calculated using eq4.

 

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The standard enthalpy change of hydration, ΔH_hyd^o, is the change in enthalpy when one mole of an ion in the gaseous state dissolves in water to form an infinitely dilute solution under standard conditions. This means that we need to dissolve the solute in excess water until there is no change in the energy absorbed or released by the system.

Some examples are:

The standard enthalpy of hydration is always exothermic (negative) and increases (more negative) for ions with higher charge densities, i.e. higher charge-to-radius ratios.

 

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The standard enthalpy change of solution, ΔH_sol^o, is the change in enthalpy when one mole of a solute dissolves in a solvent to form an infinitely dilute solution under standard conditions. This means that we need to dissolve the solute in excess solvent until there is no change in the energy absorbed or released by the system.

Some examples are:

Since KOH(aq) and HCl(aq) are fully dissociated in water, we can also write the above equation as:

ΔH_sol^o can be positive or negative. Compounds with large positive ΔH_sol^o are relatively insoluble.

 

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