Editing Calcium carbonate (section)

===Solubility in a strong or weak acid solution===
Solutions of [[strong acid|strong]] ([[hydrochloric acid|HCl]]), moderately strong ([[sulfamic acid|sulfamic]]) or [[weak acid|weak]] ([[acetic acid|acetic]], [[citric acid|citric]], [[sorbic acid|sorbic]], [[lactic acid|lactic]], [[phosphoric acid|phosphoric]]) acids are commercially available. They are commonly used as [[descaling agent]]s to remove [[limescale]] deposits. The maximum amount of {{chem2|CaCO3}} that can be "dissolved" by one liter of an acid solution can be calculated using the above equilibrium equations.
* In the case of a strong monoacid with decreasing acid concentration [A] = [{{chem2|A−}}], we obtain (with {{chem2|CaCO3}} molar mass = 100&nbsp;g/mol):
::{| class="wikitable"
! [A] (mol/L)
| 1
| 10<sup>−1</sup>
| 10<sup>−2</sup>
| 10<sup>−3</sup>
| 10<sup>−4</sup>
| 10<sup>−5</sup>
| 10<sup>−6</sup>
| 10<sup>−7</sup>
| 10<sup>−10</sup>
|-
! Initial pH
| 0.00||1.00||2.00||3.00||4.00||5.00||6.00||6.79||7.00
|-
!Final pH
| 6.75||7.25||7.75||8.14||8.25||8.26||8.26||8.26||8.27
|-
! Dissolved {{chem2|CaCO3}} (g/L of acid)
| 50.0||5.00||0.514||0.0849||0.0504||0.0474||0.0471||0.0470||0.0470
|}

:where the initial state is the acid solution with no {{chem2|Ca(2+)}} (not taking into account possible {{chem2|CO2}} dissolution) and the final state is the solution with saturated {{chem2|Ca(2+)}}. For strong acid concentrations, all species have a negligible concentration in the final state with respect to {{chem2|Ca(2+)}} and {{chem2|A−}} so that the neutrality equation reduces approximately to 2[{{chem2|Ca(2+)}}] = [{{chem2|A−}}] yielding [{{chem2|Ca(2+)}}] ≈ 0.5 [{{chem2|A−}}]. When the concentration decreases, [{{chem2|HCO3−}}] becomes non-negligible so that the preceding expression is no longer valid. For vanishing acid concentrations, one can recover the final pH and the solubility of {{chem2|CaCO3}} in pure water.
* In the case of a weak monoacid (here we take acetic acid with [[Acid dissociation constant|p''K''<sub>a</sub>]] = 4.76) with decreasing total acid concentration [A] = [{{chem2|A−}}] + [AH], we obtain:

::{| class="wikitable"
![A] (mol/L)
| [{{chem2|Ca(2+)}}] ≈ 0.5 [{{chem2|A−}}]<br>{{clarify|date=May 2024}}
| 10<sup>−1</sup>
| 10<sup>−2</sup>
| 10<sup>−3</sup>
| 10<sup>−4</sup>
| 10<sup>−5</sup>
| 10<sup>−6</sup>
| 10<sup>−7</sup>
| 10<sup>−10</sup>
|-
!Initial pH
| 2.38||2.88||3.39||3.91||4.47||5.15||6.02||6.79||7.00
|-
!Final pH
| 6.75||7.25||7.75||8.14||8.25||8.26||8.26||8.26||8.27
|-
!|Dissolved {{chem2|CaCO3}} (g/L of acid)
| 49.5||4.99||0.513||0.0848||0.0504||0.0474||0.0471||0.0470||0.0470
|}
:For the same total acid concentration, the initial pH of the weak acid is less acid than the one of the strong acid; however, the maximum amount of {{chem2|CaCO3}} which can be dissolved is approximately the same. This is because in the final state, the pH is larger than the p''K''<sub>a</sub>, so that the weak acid is almost completely dissociated, yielding in the end as many {{chem2|H+}} ions as the strong acid to "dissolve" the calcium carbonate.
* The calculation in the case of [[phosphoric acid]] (which is the most widely used for domestic applications) is more complicated since the concentrations of the four dissociation states corresponding to this acid must be calculated together with [{{chem2|HCO3−}}], [{{chem2|CO3(2−)}}], [{{chem2|Ca(2+)}}], [{{chem2|H+}}] and [{{chem2|OH−}}]. The system may be reduced to a seventh degree equation for [{{chem2|H+}}] the numerical solution of which gives

::{| class="wikitable"
! [A] (mol/L)
| 1
| 10<sup>−1</sup>
| 10<sup>−2</sup>
| 10<sup>−3</sup>
| 10<sup>−4</sup>
| 10<sup>−5</sup>
| 10<sup>−6</sup>
| 10<sup>−7</sup>
| 10<sup>−10</sup>
|-
! Initial pH
| 1.08||1.62||2.25||3.05||4.01||5.00||5.97||6.74||7.00
|-
! Final pH
| 6.71||7.17||7.63||8.06||8.24||8.26||8.26||8.26||8.27
|-
! Dissolved {{chem2|CaCO3}} (g/L of acid)
| 62.0||7.39||0.874||0.123||0.0536||0.0477||0.0471||0.0471||0.0470
|}

:where [A] = {{chem2|[H3PO4] + [H2PO4−] + [HPO4(2−)] + [PO4(3−)]}} is the total acid concentration. Thus phosphoric acid is more efficient than a monoacid since at the final almost neutral pH, the second dissociated state concentration [{{chem2|HPO4(2−)}}] is not negligible (see [[phosphoric acid#pH and composition of a phosphoric acid aqueous solution|phosphoric acid]]).