The proton affinity, E_pa, of a anion or of a neutral atom or molecule is a measure of its gas-phase basicity. It is the energy released in the following reactions:

A⁻ + H⁺ → HA

B + H⁺ → BH⁺

These reactions are always exergonic in the gas phase, i.e. energy is released when the reaction advances in the direction shown. However, proton affinities are conventionally quoted with the opposite sign convention from most other thermodynamic properties, a positive E_pa indicating a release of energy by the system. This is the same sign convention as is used for electron affinity.

Acid/base chemistry

The higher the proton affinity, the stronger the base and the weaker the conjugate acid in the gas phase. The strongest known base is the methanide anion (E_pa = 1743 kJ/mol), slightly stronger than the hydride ion (E_pa = 1675 kJ/mol), making methane the weakest proton acid in the gas phase, followed by dihydrogen. The weakest known base is the helium atom (E_pa = 177.8 kJ/mol), making the hydrohelium(1+) ion the strongest known proton acid.

Hydration

Proton affinities illustrate the role of hydration in aqueous-phase Brønsted acidity. Hydrofluoric acid is a weak acid in aqueous solution (pK_a = 3.15) but a very weak acid in the gas phase (E_pa (F⁻) = 1554 kJ/mol): the fluoride ion is a strong base as SiH₃⁻ in the gas phase, but its basicity is reduced in aqueous solution because it is strong hydrated, and therefore stabilized. The contrast is even more marked for the hydroxide ion (E_pa = 1635 kJ/mol), one of the strongest known proton acceptors in the gas phase. Suspensions of potassium hydroxide in dimethyl sulfoxide (which does not solvate the hydroxide ion as strongly as water) are markedly more basic than aqueous solutions, and are capable of deprotonating such weak acids as triphenylmethane (pK_a = ca. 30).

To a first approximation, the proton affinity of a base in the gas phase can be seen as offsetting (usually only partially) the extremely favorable hydration energy of the gaseous proton (ΔE = −1530 kJ/mol), as can be seen in the following estimates of aqueous acidity:

Proton affinity

HHe+(g)

→

H+(g)

+ He(g)

+178 kJ/mol

HF(g)

→

H+(g)

+ F−(g)

+1554 kJ/mol

H2(g)

→

H+(g)

+ H−(g)

+1675 kJ/mol

Hydration of acid

HHe+(aq)

→

HHe+(g)

+973 kJ/mol

HF(aq)

→

HF(g)

+23 kJ/mol

H2(aq)

→

H2(g)

−18 kJ/mol

Hydration of proton

H+(g)

→

H+(aq)

−1530 kJ/mol

H+(g)

→

H+(aq)

−1530 kJ/mol

H+(g)

→

H+(aq)

−1530 kJ/mol

Hydration of base

He(g)

→

He(aq)

+19 kJ/mol

F−(g)

→

F−(aq)

−13 kJ/mol

H−(g)

→

H−(aq)

+79 kJ/mol

Dissociation equilibrium

HHe+(aq)

→

H+(aq)

+ He(aq)

−360 kJ/mol

HF(aq)

→

H+(aq)

+ F−(aq)

+34 kJ/mol

H2(aq)

→

H+(aq)

+ H−(aq)

+206 kJ/mol

Estimated pKa

−63

+6

+36

These estimates suffer from the fact the free energy change of dissociation is in effect the small difference of two large numbers. However, hydrofluoric acid is correctly predicted to be a weak acid in aqueous solution and the estimated value for the pK_a of dihydrogen is in agreement with the behaviour of saline hydrides (e.g., sodium hydride) when used in organic synthesis.

See also

• Proton affinity (data page)

References