Acid strength

Strong acids

A strong acid is an acid that dissociates according to the reaction

HA + S ⇌ SH⁺ + A⁻

where S represents a solvent molecule, such as a molecule of water or dimethyl sulfoxide (DMSO), to such an extent that the concentration of the undissociated species HA is too low to be measured. For practical purposes a strong acid can be said to be completely dissociated. An example of a strong acid is perchloric acid.

HClO₄ → H⁺ + ClO−4 (in aqueous solution)

Any acid with a ${\displaystyle \mathrm{p}{K}_a}$ value which is less than about −2 behaves as a strong acid. This results from the very high buffer capacity of solutions with a pH value of 1 or less and is known as the leveling effect.

The following are strong acids in aqueous and dimethyl sulfoxide solution. As mentioned above, because the dissociation is so strongly favored, the concentrations of HA and thus the values of ${\displaystyle \mathrm{p}{K}_a}$ cannot be measured experimentally. The values in the following table are average values from as many as 8 different theoretical calculations.

Also, in water

• Nitric acid HNO₃ ${\displaystyle \mathrm{p}{K}_a=-1.6}$
• Sulfuric acid H₂SO₄ (first dissociation only, ${\displaystyle \mathrm{p}{K}_{a1}\approx -3}$)

The following can be used as protonators in organic chemistry

• Fluoroantimonic acid H[SbF₆]
• Magic acid H[FSO₃SbF₅]
• Carborane superacid H[CHB₁₁Cl₁₁]
• Fluorosulfuric acid H[FSO₃] (${\displaystyle \mathrm{p}{K}_a=-6.4}$)

Sulfonic acids, such as p-toluenesulfonic acid (tosylic acid) are a class of strong organic oxyacids. Some sulfonic acids can be isolated as solids. Polystyrene functionalized into polystyrene sulfonate is an example of a substance that is a solid strong acid.

Weak acids

A weak acid is a substance that partially dissociates or partly ionizes when it is dissolved in a solvent. In solution, there is an equilibrium between the acid, HA, and the products of dissociation.

HA ⇌ H⁺ + A⁻

The solvent (e.g. water) is omitted from this expression when its concentration is effectively unchanged by the process of acid dissociation. The strength of a weak acid can be quantified in terms of a dissociation constant, ${\displaystyle K_a}$, defined as follows, where ${\displaystyle [\text{X}]}$ signifies the concentration of a chemical moiety, X. $${\displaystyle K_a=\frac{[{\mathrm{H}}^{+}][{\mathrm{A}}^{-}]}{[\mathrm{H}\mathrm{A}]}}$$ When a numerical value of ${\displaystyle K_a}$ is known it can be used to determine the extent of dissociation in a solution with a given concentration of the acid, ${\displaystyle T_H}$, by applying the law of conservation of mass. $${\displaystyle \begin{array}{cc}{T}_H& =[{\mathrm{H}}^{+}]+[\mathrm{H}\mathrm{A}]\\ & =[{\mathrm{H}}^{+}]+\frac{[{\mathrm{A}}^{-}][{\mathrm{H}}^{+}]}{K_a}\\ & =[{\mathrm{H}}^{+}]+\frac{[{\mathrm{H}}^{+}{]}^2}{K_a}\end{array}}$$ where ${\displaystyle T_H}$ is the value of the analytical concentration of the acid. When all the quantities in this equation are treated as numbers, ionic charges are not shown and this becomes a quadratic equation in the value of the hydrogen ion concentration value, [H⁺]. $${\displaystyle \frac{[{\mathrm{H}}^{+}{]}^2}{K_a}+[{\mathrm{H}}^{+}]-T_H=0}$$ This equation shows that the pH of a solution of a weak acid depends on both its ${\displaystyle K_a}$ value and its concentration. Typical examples of weak acids include acetic acid and phosphorous acid. An acid such as oxalic acid (HOOC−COOH) is said to be dibasic because it can lose two protons and react with two molecules of a simple base. Phosphoric acid (H₃PO₄) is tribasic.

For a more rigorous treatment of acid strength see acid dissociation constant. This includes acids such as the dibasic acid succinic acid, for which the simple method of calculating the pH of a solution, shown above, cannot be used.

Experimental determination

The experimental determination of a ${\displaystyle \mathrm{p}{K}_a}$ value is commonly performed by means of a titration. A typical procedure would be as follows. A quantity of strong acid is added to a solution containing the acid or a salt of the acid, to the point where the compound is fully protonated. The solution is then titrated with a strong base

HA + OH⁻ → A⁻ + H₂O

until only the deprotonated species, A⁻, remains in solution. At each point in the titration pH is measured using a glass electrode and a pH meter. The equilibrium constant is found by fitting calculated pH values to the observed values, using the method of least squares.

Conjugate acid/base pair

It is sometimes stated that "the conjugate of a weak acid is a strong base". Such a statement is incorrect. For example, acetic acid is a weak acid which has a ${\displaystyle K_a=1.75\times {10}^{-5}}$. Its conjugate base is the acetate ion with ${\displaystyle K_b={10}^{-14}}$ and ${\displaystyle K_a=5.7\times {10}^{-10}}$ (from the relationship ${\displaystyle K_a\times K_b={10}^{-14}}$), which certainly does not correspond to a strong base. The conjugate of a weak acid is often a weak base and vice versa.

Acids in non-aqueous solvents

The strength of an acid varies from solvent to solvent. An acid which is strong in water may be weak in a less basic solvent, and an acid which is weak in water may be strong in a more basic solvent. According to Brønsted–Lowry acid–base theory, the solvent S can accept a proton.

HA + S ⇌ A⁻ + HS⁺

For example, hydrochloric acid is a weak acid in solution in pure acetic acid, HO₂CCH₃, which is less basic than water.

HO₂CCH₃ + HCl ⇌ (HO)₂CCH+3 + Cl⁻

The extent of ionization of the hydrohalic acids decreases in the order HI > HBr > HCl. Acetic acid is said to be a differentiating solvent for the three acids, while water is not.

An important example of a solvent which is more basic than water is dimethyl sulfoxide, DMSO, (CH₃)₂SO. A compound which is a weak acid in water may become a strong acid in DMSO. Acetic acid is an example of such a substance. An extensive bibliography of ${\displaystyle \mathrm{p}{K}_a}$ values in solution in DMSO and other solvents can be found at Acidity–Basicity Data in Nonaqueous Solvents.

Superacids are strong acids even in solvents of low dielectric constant. Examples of superacids are fluoroantimonic acid and magic acid. Some superacids can be crystallised. They can also quantitatively stabilize carbocations.

Lewis acids reacting with Lewis bases in gas phase and non-aqueous solvents have been classified in the ECW model, and it has been shown that there is no one order of acid strengths. The relative acceptor strength of Lewis acids toward a series of bases, versus other Lewis acids, can be illustrated by C-B plots. It has been shown that to define the order of Lewis acid strength at least two properties must be considered. For the qualitative HSAB theory the two properties are hardness and strength while for the quantitative ECW model the two properties are electrostatic and covalent.

Factors determining acid strength

The inductive effect

In organic carboxylic acids, an electronegative substituent can pull electron density out of an acidic bond through the inductive effect, resulting in a smaller ${\displaystyle \mathrm{p}{K}_a}$ value. The effect decreases, the further the electronegative element is from the carboxylate group, as illustrated by the following series of halogenated butanoic acids.

Effect of oxidation state

In a set of oxoacids of an element, ${\displaystyle \mathrm{p}{K}_a}$ values decrease with the oxidation state of the element. The oxoacids of chlorine illustrate this trend.

† theoretical