Overview Activity Chem Equilibrium Acids Carbonate System Mineral Phases

Strong Acids and Weak Acids

Classification Scheme based on pK_a

The dissociation of a monoprotic acid HA is controlled by its acidity constant K_a:

(1)

HA  =  H+ + A-

with   Ka = [H+][A-] / [HA]

Thus, a classification based on K_a or pK_a values seems natural.

Unlike weak acids, strong acids dissociate completely in water. Let us consider a monoprotic acid specified by K_a and the amount C_T ≡ [HA]_T (which is de facto the acid’s initial concentration before it dissolves). In the equilibrium state, the total concentration splits into its undissociated and dissociated parts:

(2)

CT  =  [HA] + [A-]

or

1 = a0 + a1

where a₀ = [HA]/C_T and a₁ = [A^-]/C_T are the “ionization fractions”. Strong and weak acids then differ as follows (greatly simplified):

		strong acid	weak acid
acidity constant:		Ka ≫ 1	Ka ≤ 1
pKa = -log Ka		pKa < 0	pKa > 0
[H+] = 10-pH		[H+]  ≈  CT	[H+]  ≪  CT
undissociated acid:		[HA]  ≈  0	[HA]  ≈  CT
dissociated acid:		[A-]  ≈  CT	[A-]  ≪  CT

In the literature, there is no sharp borderline between what we call a strong acid and what we call a weak acid. More refined classification schemes distinguish even between very strong acids, strong acids, weak acids, and very weak acids. Concerning aqion, however, we prefer the simple division into two groups:

	strong acids:	acids with pKa < 0
	weak acids:	acids with pKa > 0

Polyprotic Acids. The classification scheme in the table above can also be applied to N-protic acids, H_NA, if we rename the acidity constant K_a by the 1^st dissociation constant K₁. (More about polyprotic acids is provided in the review article.)

Undissociated Fraction

Weak acids are characterized by a non-negligible amount of undissociated acid. Mathematically, the undissociated part is equivalent to the ionization fraction a₀ (see Appendix):

(3)

undissociated fraction   a0 = \(\dfrac{1}{1+K_1/x}\)

with  x = [H+] = 10-pH

The diagram below displays the undissociated fraction of some common acids (based on 3). As expected, strong acids are completely dissolved in real-world applications (where pH > 0). The small circles mark the position of the corresponding pK₁ values (which are the inflection points of a₀).

Group 1:  Strong Acids with pK_a < 0

Strong acids used in aqion are:

hydroiodic acid	HI	pKa = -10
hydrobromic acid	HBr	pKa = -9
hydrochloric acid	HCl	pKa = -6
sulfuric acid (1st dissociation step)	H2SO4	pKa = -3
selenic acid (1st dissociation step)	H2SeO4	pKa = -3
nitric acid	HNO3	pKa = -1.32
chromic acid	H2CrO4	pKa = -0.86

Note: Due to the fact that HI, HBr, HCl, H₂SO₄, H₂SeO₄, and HNO₃ virtually do not exist in undissociated form their first dissociation step is not contained in the thermodynamic database.¹

Example calculations with strong acids are presented here.

Group 2:  Acids with pK_a > 0  (Weak Acids)

In contrast to the strong acids with negative pK_a values, acids with pK_a > 0 are explicitly defined in the thermodynamic database of aqion by their log K values. Here are some examples listed in the order of decreasing strength (valid for standard conditions at 25 and 1 atm):

Reaction Formula	log K	pK	Ref.
HSeO4- = H+ + SeO4-2	-1.66	1.66	[W]
HSO4- = H+ + SO4-2	-1.988	1.988	[W]
H3PO4 = H+ + H2PO4-	-2.147	2.147 2	[M]
Fe+3 + H2O = H+ + FeOH+2	-2.19	2.19	[W]
H3AsO4 = H+ + H2AsO4-	-2.3	2.3	[W]
H3Citrate = H+ + H2Citrate-	-3.128	3.128	[M]
H2SeO3 = H+ + HSeO3-	-3	3	[W]
HF = H+ + F-	-3.18	3.18	[W]
HNO2 = H+ + NO2-	-3.22	3.22	[E,L]
HFormate = H+ + Formate-	-3.753	3.753	[M]
H2Se = H+ + HSe-	-3.8	3.8	[W]
HLactate = H+ + Lactate-	-3.863	3.863	[E,L]
H2MoO4 = H+ + HMoO4-	-3.865	3.865	[M]
HMoO4- = H+ + MoO4-2	-4.290	4.290	[M]
HAcetate = H+ + Acetate-	-4.757	4.757	[M]
H2Citrate- = H+ + HCitrate-2	-4.761	4.761	[M]
Al+3 + H2O = H+ + AlOH+2	-5.0	5.0	[W]
H2CO3* = H+ + HCO3-	-6.351	6.351 3	[W]
HCitrate-2 = H+ + Citrate-3	-6.396	6.396	[M]
HCrO4- = H+ + CrO4-2	-6.509	6.509	[M]
H2S = H+ + HS-	-6.994	6.994	[W]
H2AsO4- = H+ + HAsO4-2	-7.16	7.16	[W]
H2PO4- = H+ + HPO4-2	-7.207	7.207	[W]
HSeO3- = H+ + SeO3-2	-8.5	8.5	[W]
H3AsO3 = H+ + H2AsO3-	-9.15	9.15	[W]
H3BO3 = H+ + H2BO3-	-9.24	9.24	[W]
NH4+ = H+ + NH3	-9.252	9.252	[W]
H4SiO4 = H+ + H3SiO4-	-9.83	9.83	[W]
HCO3- = H+ + CO3-2	-10.329	10.329	[W]
HAsO4-2 = H+ + AsO4-3	-11.65	11.65	[W]
HPO4-2 = H+ + PO4-3	-12.346	12.346	[W]
HS- = H+ + S-2	-12.918	12.918	[W]
H3SiO4- = H+ + H2SiO4-2	-13.17	13.17	[W]

As mentioned above, the strong acids with pK_a < 0 (e.g. HI, HBr, HCl, H₂SO₄, HNO₃) are not present in this table (and database). In addition, acidity constants of organic acids are presented here.

The acids are available as inorganic and organic reactants in the reaction tool (pH calculator). Calculated pH values for 1, 10, and 100 mM are shown in this table.

Weak Acids vs Dilute Acids

A weak acid and a dilute acid are two different things, like apples and oranges. The first relies on the acidity constants K_a (which is a thermodynamic property of the acid that nobody can change), while the second relies on the amount C_T of a given acid:

	weak acid	↔	strong acid	⇔		small Ka	↔	large Ka
	dilute acid	↔	concentrated acid	⇔		small CT	↔	large CT

One cannot make a weak acid strong, but one can change the degree of dilution (or concentration). The principal differences between the degree of strength and the degree of dilution can be summarized as follows:

		degree of strength	degree of dilution
determined by:		acidity constant Ka	amount of acid CT
relationships:		weak acid ↔ strong acid	dilute acid ↔ concentrated acid
		small Ka ↔ large Ka	small CT ↔ large CT
		(positive pKa ↔ negative pKa)
compares:		two different acids	dilution of the same acid
describes:		release of H+	dilution of H+
type:		fundamental property	control parameter
		(cannot be changed)	(can be changed)

Instead of K, the classification can also be based on pK, as indicated by the pK-C_T diagram below. (Note: For polyprotic acids pK refers to the first dissociation step.)

Appendix – Undissociated Fraction of Acid

Given is an N-protic acid H_NA characterized by N acidity constants K₁ to K_N. The sum over all acid species defines the total concentration (mass balance):

(A1)

CT ≡ [HNA]T  =  [HNA] + [HN-1A-] + … + [A-N]

The fraction of the undissociated species is expressed by the ionization fraction a₀:

(A2)

undissociated fraction:

a0  =  [HNA] / CT

Its pH dependence is given by:⁴

(A3)

\(a_0(x) \,=\, \left( 1+\dfrac{K_1}{x} + \dfrac{K_1K_2}{x^2}+ \dfrac{K_1\cdots K_N}{x^N} \right)^{-1} \approx\, \left( 1+\dfrac{K_1}{x} \right)^{-1}\)

where x is an abbreviation for [H⁺] = 10^-pH.

References

[E]	Database EQ3/6 taken from: TJ Wolery: EQ3/6, A Software Package for Geochemical Modeling of Aqueous Systems: Package Overview and Installation Guide (Version 7.0), Lawrence Livermore National Laboratory UCRL-MA-110662 PT I, Sep 1992
[L]	Database llnl taken from: ‘thermo.com.V8.R6.230’ prepared by Jim Johnson at LLNL, in Geochemist’s Workbench format. Converted to PhreeqC format by Greg Anderson with help from David Parkhurst (llnl.dat 4023 2010-02-09 21:02:42Z dlpark)
[M]	Database minteq taken from: JD Allison, DS Brown, KJ Novo-Gradac: MINTEQA2/PRODEFA2, A Geochemical Assessment Model for Environmental Systems, Version 3.0, User’s Manual, EPA/600/3-91/021, March 1991
[W]	Database wateq4f taken from: JW Ball and DK Nordstrom: WATEQ4F – User’s manual with revised thermodynamic data base and test cases for calculating speciation of major, trace and redox elements in natural waters, U.S.G.S. Open-File Report 90-129, 1991

Remarks