# Equilibrium Positions of Acid-Base Reactions

### Acid-Base Equilibrium

Acid-base reactions most often exist in a state of equilibrium in which the rates of the forward and reverse reactions are equal.

Acid-base reactions quickly attain equilibrium, the state in which the rates of the forward and reverse reactions are equal, and the position of this equilibrium is determined using one of two methods: pKa or ARIO. One method compares the pKa values, or the negative log of Ka where Ka is the acid dissociation constant, of the reactant acid and the conjugate acid of the base. A conjugate acid is the molecule or ion formed when a Brønsted-Lowry base has accepted a proton. A conjugate base is the molecule or ion remaining after a Brønsted-Lowry acid donates its proton to another molecule or ion. The equilibrium will swing toward the weaker acid. The pKa provides a quantitative method to determine the strength of an acid.

ARIO is another method to determine the relative strength of an acid. ARIO stands for atom effects, resonance delocalization, inductive effect, and orbital bearing the charge (hybridization). These effects are based on the size and electronegativity of the atom (atom effect); the presence of resonance (resonance delocalization); the presence and location of electronegative atoms, which form a dipole (inductive effect); and the hybridization directly impacting the strength of the acid or base (orbital bearing the charge or hybridization).

Periodic trends can be used to dictate acid strength based on the atom to which the hydrogen is attached. The presence of resonance structures and/or the inductive effect in the conjugate base of an acid will weaken and stabilize the conjugate base, which makes the acid stronger. The hybridization of the atom attached to the hydrogen alters the acidity of the acid. Triple bonds have sp-hybridized carbons and are more acidic than double bonds, which have sp2-hybridized carbons. In turn, double bonds are more acidic than single bonds, which have sp3-hybridized carbons.

A strong acid is an acid that completely dissociates and has a pH around 1 to zero. Strong acids have a large Ka and dissociate to produce stable and weak conjugate bases. The resulting weak conjugate base is stabilized by ARIO factors. A weak acid is an acid in which only a fraction of the molecules dissociates when dissolved in water, resulting in a low concentration of H+ and a more neutral pH, around 5 or 6. A weaker acid will have a larger pKa. Weak acids dissociate to produce strong conjugate bases, which are not stabilized by ARIO factors. Strong acids produce weak conjugate bases, and weak acids produce strong conjugate bases.

A strong base is a base that completely dissociates and has a pH around 13 to 14. Strong bases have a large Kb. A weak base is one in which only a fraction of the molecules deprotonates in water. This results in a low concentration of OH ions and a more neutral pH, around 8 or 9. A weaker base will have a smaller pKa. Weak bases dissociate to produce strong conjugate acids, which are not stabilized by ARIO factors. Strong bases produce weak conjugate acids, and weak bases produce strong conjugate acids.
\begin{aligned}\text{Strong acid}&\rightarrow{\text{Weak conjugate base}}\\{\text{Weak acid}}&\rightarrow{\text{Strong conjugate base}}\\{\text{Strong base}}&\rightarrow{\text{Weak conjugate acid}}\\{\text{Weak base}}&\rightarrow\text{Strong conjugate acid}\end{aligned}
${\rm{HCl}\atop{\text{Strong}\atop\text{acid}}}+{\rm{NH_3}\atop{\text{Weak}\atop\text{base}}}\rightarrow{\rm{Cl^-}\atop{\text{Weak}\atop\text{conjugate base}}}+{\rm{{NH_4}\atop{\text{Strong}\atop\text{conjugate acid}}}}$
The ARIO method examines the molecular structures of the reaction acid and the conjugate acid of the base. The molecular structure is the three-dimensional shape of a molecule that takes into account bonding and nonbonding electron pairs and molecular rotations to minimize their interactions. By comparing the different overall structural effects on acidity, a determination is made as to which acid is weaker and to which direction the equilibrium swings. This determination is verified using pKa values if they are available for the selected acids.

### Using pKa to Predict Equilibrium

The direction that an acid-base reaction proceeds can be determined by comparing the reactant acid to the conjugate acid of the other component. The reaction will always proceed towards the acid with a higher pKa.

The outcome of an acid-base reaction results from the position of an equilibrium. The equilibrium will move in the direction of the more stable species.The more stable species have the lowest potential energy—the energy of an object based on its position—or Gibbs free energy. The formation of the weaker acid and the weaker base is favored in acid-base reactions. These species have lower potential energy than the stronger acid and stronger base and are therefore the more stable species.

The acidity constant (Ka), or acid dissociation constant, is a measure of the strength of an acid in solution. As the acid dissociates in water, it releases protons. Weak acids only partially dissociate (or break apart) in water, so both the HA and A coexist in the solution. Square brackets around a species indicate concentration. The acid dissociation constant is unique to each molecule or compound (i.e., every acid will have its own Ka). The acid HA, in water, dissociates into H+ and A. To find the Ka, the concentrations of the dissociated species are multiplied together and then divided by the concentration of the acid.
\begin{aligned}{\rm{HA}}\;\rightleftarrows\;{\rm {H}}^++{\rm {A}}^-\\K_{\rm a}=\frac{\lbrack{\rm H}^+\rbrack\lbrack{\rm {A}}^-\rbrack}{\lbrack{\rm{HA}}\rbrack}\end{aligned}
Larger pKa values indicate a lesser amount of dissociation and a weaker acid. Smaller pKa values indicate greater dissociation and a stronger acid. The larger the value of pKa, the weaker the acid; the smaller the value of pKa, the stronger the acid.
${\rm {p}}K_{\rm {a}}=-\log\lbrack K_{\rm {a}}\rbrack$

### Example Ka and pKa of Various Acids

Acid Ka pKa
Hydroiodic acid, HI $3.16\times10^9$ –9.5
Sulfuric acid, H2SO4 $1.0\times10^3$ –3
Nitric acid, HNO3 $2.82\times10^1$ –1.45
Acetic acid, CH3COOH $1.75\times10^{-5}$ 4.76

Strong acids will have a very large Ka and a very small pKa. Weaker acids have a small Ka and a larger pKa.

The pKb is the negative logarithm of the base dissociation constant, Kb. It is calculated in the same manner as pKa. A smaller pKb indicates a stronger base, while a larger pKb indicates a weaker base. Base strength is usually measured by the pKa of the conjugate acid.
\begin{aligned}\rm{BOH}\;\rightleftarrows\;{\rm {B}}^++{\rm{OH}}^-\\K_{\rm {b}}=\frac{\lbrack{\rm {B}}^+\rbrack\lbrack{\rm{OH}}^-\rbrack}{\lbrack{\rm{BOH}}\rbrack}\end{aligned}
The larger the pKa, the weaker the acid and the stronger the conjugate base. Reactions will proceed in whichever direction forms the acid with the larger pKa. For example, the pKa of acetic acid is 4.76, and the pKa of the conjugate acid, NH4+, is 9.2. Because the pKa of the conjugate acid is larger than the pKa of the reactant acid, equilibrium shifts to the right (toward the larger pKa).
The pKa of acetic acid is 4.76, and the pKa of the conjugate acid, water, is 15.74. This reaction will therefore proceed toward the products.
$\begin{gathered}{\rm{CH}_3{COOH}}+{\rm{OH}}^-\rightleftarrows{\rm{CH}_3{COO}}^-+{\rm {H}_2{O}}\\{\rm {p}}K_{\rm a}=4.76 \hspace{35pt}{\rm {p}}K_{\rm a}\;=\;15.74\end{gathered}$
If the pKa values of both compounds are known, then the outcome of any acid-base reaction is predictable. Tables of pKa values are available on both the Internet and in textbooks. These tables rank an acid and its conjugate base from strongest acid to weakest acid. The strongest acid and its conjugate base, which will be very weak, have a smaller pKa. The weakest acid and its conjugate base, which will be very strong, will have a larger pKa.
Acetic acid (C2H4O2) is a weak acid that does not dissociate completely in water. Based on a comparison of the pKa values for acetic acid and hydronium ion (H3O+), acetic acid is the weaker acid and therefore more stable species. This means the equilibrium for this reaction moves toward the formation of acetic acid and away from the formation of the hydronium ion.