# Strong Acids and Weak Acids

Classification Scheme based on pKa

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

 (1) HA  =  H+ + A- with   Ka = [H+][A-] / [HA]

Thus, a classification based on Ka or pKa values seems natural.

Unlike weak acids, strong acids dissociate completely in water. Let us consider a monoprotic acid specified by Ka and the amount CT ≡ [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]/CT and a1 = [A-]/CT 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, HNA, if we rename the acidity constant Ka by the 1st 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 pKa < 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 thdyn database.1

Example calculations with strong acids are presented here.

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

In contrast to the strong acids with negative pKa values, acids with pKa > 0 are explicitly specified in the thdyn database 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 pKa < 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 Ka (which is a thermodynamic property of the acid that nobody can change), while the second relies on the amount CT 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 values, as indicated by the pK-CT diagram below. (Note: For polyprotic acids, pK refers to the 1st dissociation step.)

Appendix — Undissociated Fraction of Acid

Given is an N-protic acid HNA characterized by N acidity constants K1 to KN. 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 & 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 J Johnson at LLNL, in Geochemist’s Workbench format. Converted to PhreeqC format by G Anderson with help from D 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, Mar 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

1. Nonetheless, all strong-acid calculations are de facto exact (see examples here, here, here, and here).

2. The thdyn database wateq4f contains only the 2nd and 3rd dissociation step of phosphoric acid. The missing species “H2PO4” was extra implemented into aqion (in addition to the already present species H2PO4-, HPO4-2 and PO4-3).

3. It is common in hydrochemistry to use the composite carbonic acid, H2CO3* = CO2(aq) + H2CO3 instead of the true carbonic acid, H2CO3. In the thdyn database wateq4f (and in aqion) the composite carbonic acid is abbreviated by CO2

4. Acid-Base Systems – Mathematical Background of Simple Closed-Form Expressions (Short Lecture 2023), for a summary see here