# Strong Acids and Weak Acids

Classification Scheme based on pKa

The dissociation of an acid HA is determined by its acidity constant Ka:

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

Strong acids dissociate completely in water, while weak acids do not dissociate completely. A classification based on acidity constants or pKa values seems natural.

Let’s denote the total amount of the acid by 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-]

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 literature, there is no sharp border line 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, very weak acids etc. 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 idea remains valid even for N-protic acids, HNA. The acidity constant Ka should only be replaced by the 1st dissociation constant K1. The mathematical description is straightforward (see Appendix):

 (3) undissociated fraction  =  $$\dfrac{1}{1+K_1/x}$$ with  x = [H+] = 10-pH

The diagram below displays the undissociated fraction of some common acids (based on 3). The small circles mark the corresponding pK1 values. As expected, strong acids are completely dissolved in real-world applications (pH > 0). 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 explicitly contained in the thermodynamic 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 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 pKa < 0 (e.g. HI, HBr, HCl, H2SO4, HNO3) are not present in this table (and database). In addition, acidity constants of many organic acids are presented here.

These 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 no one 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

You cannot make a weak acid strong, but you can change the degree of dilution (or concentration) as you like. 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-CT diagram below. (Note: For polyprotic acids pK refers to the first 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: T.J. 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 Lawrence Livermore National Laboratory, 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: J.D. Allison, D.S. Brown, K.J. 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: J.W. Ball and D.K. 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 thermodynamic 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 thermodynamic database wateq4f (and in aqion) the composite carbonic acid is abbreviated by CO2

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