# 6.3.6: Thermodynamics of Gas Phase Brønsted Acidity and Basicity

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## Proton Affinity and Gas Phase Acidity/Basicity Describe Thermodynamic Aspects of Hydrogen Ion Transfer

Defining acidity in terms of hydrogen ion donation and acceptance within the Brønsted-Lowry acid base concept allows for the understanding of acidity and basicity in a variety of liquid, solid, and gaseous media. The latter are particularly important for understanding the thermodynamics of hydrogen ion donation and acceptance since the energies of gas phase species are uninfluenced by solvation factors. These reactions are perhaps best thought of in terms of the association of a hydrogen ion and a base, $$\ce{B}$$.

Formally the gas phase proton affinity (PA) of $$\ce{B}$$ is defined as the negative of the enthalpy change for the its association with hydrogen:

$\ce{H^{+}(g) + B(g) <=> BH^{+}(g)} \label{eq1}$

where $$\Delta H_{rxn}$$ is the Proton Affinity of $$\ce{B}$$.

However, it is simpler to think about the PA in terms of the reverse reaction of Equation \ref{eq1}, which describes the dissociation of $$\ce{BH^{+}}$$:

$\ce{BH^{+}(g) <=> H^{+}(g) + B(g)} \nonumber$

where $$\Delta H_{rxn}$$ is the PA of $$\ce{B}$$ and is also the heterolytic bond dissociation enthalpy, from which it can be seen that the proton affinity is just the enthalpy for heterolytic cleavage of the $$\ce{H-B}$$ bond.

The absolute or gas phase basicity (GB) of $$\ce{B}$$ is the negative of the Gibb's free energy change for the same reaction:

$\ce{H^{+}(g) + B(g) <=> BH^{+}(g)} \nonumber$

where $$\Delta~G_{rxn}$$ is the negative of the Absolute or Gas phase basicity of $$\ce{B}$$.

Again, it is simpler to think about the GB of $$\ce{B}$$ as the free energy change upon heterolytic dissociation of the $$\ce{B-H}$$ bond in $$\ce{BH^{+}}$$:

$\ce{BH^+(g) ⇌ H^{+}(g) + B(g)} \nonumber$

where $$\Delta G_{rxn}$$ is the Absolute or Gas phase basicity of $$\ce{B}$$ and is also the free energy for heterolytic bond dissociation.

Because both PA and GB values correspond to heterolytic bond dissociation, more positive values of the PA and GB correspond to higher thermodynamic affinity between $$\ce{B}$$ and $$\ce{H^{+}}$$.

Note that the gas phase acidity (GA) is a very similar quantity to the gas phase basicity, being defined for an acid of formula $$\ce{HA}$$ as the Gibb's free energy change for:††

$\ce{HA(g) <=> H^{+}(g) + A^{-}(g)} \nonumber$

where $$\Delta G_{rxn}$$ is the Absolute or Gas phase acidity of $$\ce{HA}$$.

Since $$\ce{A^{-}}$$ and $$\ce{B}$$ are just both convenient shorthand notations for a Brønsted base gas phase acidity and gas phase basicity, both refer to ionization of a gas phase acid. The quantities only differ in that gas phase acidities correspond to ionization of a neutral acid, $$\ce{HA}$$, while gas phase basicities correspond to ionization of a monocationic base, $$\ce{BH^{+}}$$. For many purposes this difference may be ignored.

Gas phase proton affinities and acidities/basicities have been determined for a large number of species and are available through the NIST chemistry webbook. Selected values are given in Table $$\PageIndex{1}$$. As can be seen from the data in Table $$\PageIndex{1}$$, typical proton affinity and gas phase acidity values fall between 600 and 1750 kJ/mol, with proton affinities being slightly larger by 20-50 kJ/mol.

Table $$\PageIndex{1}$$: Gas phase proton affinity and acidity values for selected species. Data are taken from the NIST Chemistry Webbook. When more than one value is available, the number presented below represents the average of those reported (after rejection of outliers at the 90% confidence interval using a G-test).
Base Proton Affinity (kJ/mol) Gas Phase Acidity (kJ/mol)
hexafluorobenzene $$C_6F_6$$ 648
$$H_2O$$ 691
benzene 750
$$NH_3$$ 854 819
aniline 882 851
pyridine 930 898
triethylamine 982 951
$$ClO_4^-$$ 1238 1201
$$ClO_3^-$$ 1310 1284
$$I^-$$ 1313 1293
$$Br^-$$ 1349 1328
$$NO_3^-$$ 1368 1330
$$Cl^-$$ 1390 1367
$$NO_2^-$$ 1424 1396
$$ClO_2^-$$ 1488 1461
$$anilide^-$$ 1537 1506
$$F^-$$ 1555 1524
$$CH_3O^-$$ 1573 1570
$$O^-$$ 1601 1576
$$H:^-$$ 1675 1649
$$NH_2:^-$$ 1686 1656
$$FCH_2:^-$$ 1734 1676
$$CH_3CH_2:^-$$ 1758 1723

## Proton Affinity and Gas Phase Acidity/Basicity Data are Consistent with Expected Acidity Trends but also Illuminate the Role of Solvation and Dissociation Entropy in Solution Phase Acid-Base Behavior

Two lessons may be derived from gas phase acidity and proton affinity data:

1. The gas phase proton affinities and acidities of neutral and anionic bases are large, positive, and strongly disfavor acid ionization. As shown in Figure 6.3.3.1, acid ionization is driven by the high solvation energy of the hydrogen ion ($$\Delta H^o = -1091\, \text{kJ/mol}$$) with smaller contributions from solvation of the acid's conjugate base.
2. Trends in gas phase proton affinities and acidities indicate the importance of solvation for acid-base behavior in solution. As can be seen from the data in Table $$\PageIndex{1}$$, water is a very weak base in the gas phase. In fact, water's proton affinity is even lower than the proton affinity of the conjugate bases of most strong acids. This means that transfer of hydrogen ion from most strong acids to water is endothermic in the gas phase. For instance, for

$\ce{HCl(g) + H_2O(g) -> H_3O^{+}(g) + Cl^{-}(g)} \quad \quad {\Delta H = +699 kJ/mol} \nonumber$

In other words, based on the thermodynamics of hydrogen ion transfer in the gas phase, most strong Brønsted acids should not act as Brønsted acids towards water. Nevertheless they do act as strong acids. This means that the solvation energy terms in the thermodynamic cycle of Figure 6.3.3.1 (possibly assisted by entropic effects) are driving hydrogen ion transfer in solution.

This is confirmed by the values for the proton affinities and hydration energies for the hydrohalic acids given in Table $$\PageIndex{2}$$ . For these acids the solvation energies for the hydrogen ion (-1130 kJ/mol) and anions (e.g., for Cl-, -363 kJ/mol) are much larger than the hydration energies of the neutral acids and contribute towards an overall exothermic enthalpy of acid dissociation in water.

Table $$\PageIndex{2}$$ Contribution of heterolytic bond dissociation and hydration (hyd) energies to the enthalpy of dissociation for the hydrohalic acids.1
Acid

Proton Affinity (PA)

$$H-A(g) → H^+(g) + A^-(g)$$

(kJ/mol)

$$\Delta H_{hyd}~for~HX$$

$$HX(aq) → HX(g)$$

(kJ/mol)

$$\Delta~H_{hyd}~for~H^+$$

$$H^+(g) → H^+(aq)$$

(kJ/mol)

$$\Delta~H_{hyd}~for~X^-$$

$$X^-(g) → X^-(aq)$$

(kJ/mol)

Total (acid dissociation enthalpy)

$$H-A(aq) → H^+(aq) + A^-(aq)$$

(kJ/mol)

HF +1555 +48 -1091 -524 -12
HCl +1390 +18 -1091 -378 -61
HBr +1349 +21 -1091 -348 -69
HI +1313 +23 -1091 -308 -63

Although solvation plays a crucial role in determining a substance's acid-base behavior in solution, an acid's strength cannot be predicted from solvation energies alone. This is because it is difficult to predict the relative importance of the large proton affinity and conjugate base hydration enthalpy terms (and to a lesser extent the acid hydration enthalpy) in a given case. This is also illustrated by the data in Table $$\PageIndex{2}$$. The hydrohalic acid bond dissociation energy and halide hydration enthalpy both decrease in magnitude by approximately the same amount on going from HCl to HI, so that the acid dissociation enthalpies remain approximately constant. While proton affinities and hydration enthalpies often change in tandem, it is not always the case that they change by similar magnitudes. This may be seen by comparing the data shown for HF with those for the other hydrohalic acids in Table $$\PageIndex{2}$$. In the case of HF, the 165 kJ/mol increase in proton affinity between HCl and HF is not compensated for by the -146 kJ/mol decrease in hydration energy on going from Cl- to F- (due to fluorine's ability to form hydrogen bonds), leading HF to exhibit an anomalously small ionization enthalpy.

##### How Gas phase acidity values are measured

Gas phase acidities can be conveniently determined thermochemically relative to a standard by measuring the relative affinity of a hydrogen ion for two bases, $$B_1$$ & $$B_2$$, by using mass spectrometry to follow the equilibrium of the hydrogen ion transfer reaction:

$HB_1^+ + B_2 → B_1 + HB_2^+ \nonumber$

The free energy change of this reaction may be found from the relative populations of $$HB_1^+$$ and $$HB_2^+$$ using mass spectrometry:

$\Delta G = \dfrac{[B_1][HB_2^+]}{[HB_1^+][B_2]} \nonumber$

and the enthalpies and entropies of reaction from the temperature dependence of the free energies (since $$\Delta G = \Delta H - T \times \Delta S$$.

Gas phase acidity values determined from hydrogen ion transfer equilibrium values are called relative acidities. In contrast, absolute acidities are those which can be traced back to the standard forms of the elements at standard temperature and pressure. Absolute acidities can be found from relative ones as long as the absolute acidity of at least one of the bases is known. Fortunately, the absolute affinities of a number of gas phase acidity standards have been determined thermochemically. For instance, the gas phase proton affinity of H-A corresponds to the sum of the following processes:

$H-A(g) ⇌ H(g) + A(g)~~~~~~~ { \Delta H=Bond~Dissociation~Energy~of~HA,~BDE_{HA}} \nonumber$

$H(g) ⇌ H^+(g) + e^-(g)~~~~~~~~~~~~~~ { \Delta H=Ionization~Energy~of~H,~IE_H}\nonumber$

$A(g) + e^-(g) ⇌ A^-(g)~~~~~~~~~~~~~~~ { \Delta H=Electron~Affinity~of~A^-,~IE_A}\nonumber$

$$\rule{10 cm}{0.03 cm}$$

$HA(g) ⇌ H^+(g) + A^-(g)~~~~~~~~~~~ { \Delta H_{rxn} = Proton~affinity~of~A^-}\nonumber$

so that

${ Proton~Affinity~of~A^- = Delta H_{rxn} = BDE_{HA} + IE_H - EA_A}\nonumber$

For a more detailed explanation of how gas phase acidities are found see the gas phase ion thermochemistry page at the NIST chemistry webbook.

## References

1. Proton affinities are taken from the NIST NIST Chemistry Webbook. Hydration enthalpies are from Dasent, W. E. Inorganic Energetics: An Introduction, 2nd ed. Cambridge University Press, 1982, pp. 168-170.

6.3.6: Thermodynamics of Gas Phase Brønsted Acidity and Basicity is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Stephen M. Contakes.