Acid strength

The usual measure of the strength of an acid is its acid dissociation constant (${\displaystyle K_{a}}$), which can be determined experimentally by titration methods. Stronger acids have a larger ${\displaystyle K_{a}}$ and a smaller logarithmic constant (${\displaystyle \mathrm {p} K_{a}=-\log K_{a}}$) than weaker acids. The stronger an acid is, the more easily it loses a proton, H⁺. Two key factors that contribute to the ease of deprotonation are the polarity of the H−A bond and the size of atom A, which determine the strength of the H−A bond. Acid strengths also depend on the stability of the conjugate base.

While the ${\displaystyle K_{a}}$ value measures the tendency of an acidic solute to transfer a proton to a standard solvent (most commonly water or DMSO), the tendency of an acidic solvent to transfer a proton to a reference solute (most commonly a weak aniline base) is measured by its Hammett acidity function, the ${\displaystyle H_{0}}$ value. Although these two concepts of acid strength often amount to the same general tendency of a substance to donate a proton, the ${\displaystyle K_{a}}$ and ${\displaystyle H_{0}}$ values are measures of distinct properties and may occasionally diverge. For instance, hydrogen fluoride, whether dissolved in water (${\displaystyle \mathrm {p} K_{a}=3.2}$) or DMSO (${\displaystyle \mathrm {p} K_{a}=15}$), has ${\displaystyle \mathrm {p} K_{a}}$ values indicating that it undergoes incomplete dissociation in these solvents, making it a weak acid. However, as the rigorously dried, neat acidic medium, hydrogen fluoride has an ${\displaystyle H_{0}}$ value of –15,^[1] making it a more strongly protonating medium than 100% sulfuric acid and thus, by definition, a superacid.^[2] (To prevent ambiguity, in the rest of this article, "strong acid" will, unless otherwise stated, refer to an acid that is strong as measured by its ${\displaystyle \mathrm {p} K_{{\ce {a}}}}$ value (${\displaystyle \mathrm {p} K_{{\ce {a}}}<-1.74}$). This usage is consistent with the common parlance of most practicing chemists.)

When the acidic medium in question is a dilute aqueous solution, the ${\displaystyle H_{0}}$ is approximately equal to the pH value, which is a negative logarithm of the concentration of aqueous H⁺ in solution. The pH of a simple solution of an acid in water is determined by both ${\displaystyle K_{a}}$ and the acid concentration. For weak acid solutions, it depends on the degree of dissociation, which may be determined by an equilibrium calculation. For concentrated solutions of acids, especially strong acids for which pH < 0, the ${\displaystyle H_{0}}$ value is a better measure of acidity than the pH.

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.^[3]

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.

Estimated pK_a values^[4]

Acid	Formula	in water	in DMSO
Hydrochloric acid	HCl	−5.9 ± 0.4	−2.0 ± 0.6
Hydrobromic acid	HBr	−8.8 ± 0.8	−6.8 ± 0.8
Hydroiodic acid	HI	−9.5 ± 1	−10.9 ± 1
Triflic acid	H[CF3SO3]	−14 ± 2	−14 ± 2
Perchloric acid	H[ClO4]	−15 ± 2	−15 ± 2

Also, in water

• Nitric acid HNO₃ ${\displaystyle \mathrm {p} K_{a}=-1.6}$^[5]
• Sulfuric acid H₂SO₄ (first dissociation only, ${\displaystyle \mathrm {p} K_{a1}\approx -3}$)^[6]: 171

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] (${\displaystyle \mathrm {p} K_{a}=-6.4}$)^[7]

Sulfonic acids, such as p-toluenesulfonic acid (tosylic acid) are a class of strong organic oxyacids.^[7] 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.

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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 ${\displaystyle {\ce {[X]}}}$ signifies the concentration of a chemical moiety, X. $${\displaystyle K_{a}={\frac {[\mathrm {H} ^{+}][\mathrm {A} ^{-}]}{[\mathrm {HA} ]}}}$$ 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. $${\displaystyle {\begin{aligned}T_{H}&=[\mathrm {H} ^{+}]+[\mathrm {HA} ]\\&=[\mathrm {H} ^{+}]+{\frac {[\mathrm {A} ^{-}][\mathrm {H} ^{+}]}{K_{a}}}\\&=[\mathrm {H} ^{+}]+{\frac {[\mathrm {H} ^{+}]^{2}}{K_{a}}}\end{aligned}}}$$ 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.

The experimental determination of a ${\displaystyle \mathrm {p} K_{a}}$ value is commonly performed by means of a titration.^[8] 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.

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.

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.^[6]: 217

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.^{[inappropriate external link?]}

Superacids are strong acids even in solvents of low dielectric constant.^[9] Examples of superacids are fluoroantimonic acid and magic acid. Some superacids can be crystallised.^[10] They can also quantitatively stabilize carbocations.^[11]

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.^[12] The relative acceptor strength of Lewis acids toward a series of bases, versus other Lewis acids, can be illustrated by C-B plots.^[13][14] 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.

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.

Structure	Name	pKa
	2-chlorobutanoic acid	2.86
	3-chlorobutanoic acid	4.0
	4-chlorobutanoic acid	4.5
	butanoic acid	4.5

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.^{[6]: (p. 171)}

Structure	Name	Oxidation state	pKa
	perchloric acid	7	−8†
	chloric acid	5	−1
	chlorous acid	3	2.0
	hypochlorous acid	1	7.53

† theoretical