# Calcium carbonate

Calcium carbonate
Names
IUPAC name
Calcium carbonate
Other names
Identifiers
471-34-1
ChEBI CHEBI:3311
ChEMBL ChEMBL1200539
ChemSpider 9708
EC Number 207-439-9
Jmol 3D model Interactive image
Interactive image
KEGG D00932
PubChem 10112
RTECS number FF9335000
UNII H0G9379FGK
Properties
CaCO3
Molar mass 100.0869 g/mol
Appearance Fine white powder; chalky taste
Odor odorless
Density 2.711 g/cm3 (calcite)
2.83 g/cm3 (aragonite)
Melting point 1,339 °C (2,442 °F; 1,612 K) (calcite)
825 °C (1517 °F; 1,098 K) (aragonite) [1]
Boiling point decomposes
0.013 g/L (25 °C)[2][3]
3.3×109[4]
Solubility in dilute acids soluble
Acidity (pKa) 9.0
1.59
Structure
Trigonal
32/m
Thermochemistry
93 J·mol−1·K−1[5]
−1207 kJ·mol−1[5]
Pharmacology
A02AC01 (WHO) A12AA04 (WHO)
Hazards
Safety data sheet ICSC 1193
NFPA 704
Flash point 825 °C (1,517 °F; 1,098 K)
Lethal dose or concentration (LD, LC):
6450 mg/kg (oral, rat)
US health exposure limits (NIOSH):
PEL (Permissible)
TWA 15 mg/m3 (total) TWA 5 mg/m3 (resp)[6]
Related compounds
Other anions
Calcium bicarbonate
Other cations
Magnesium carbonate
Strontium carbonate
Barium carbonate
Related compounds
Calcium sulfate
Except where otherwise noted, data are given for materials in their standard state (at 25 °C [77 °F], 100 kPa).
verify (what is  ?)
Infobox references
Crystal structure of calcite

Calcium carbonate is a chemical compound with the formula CaCO3. It is a common substance found in rocks as the minerals calcite and aragonite (most notably as limestone) and is the main component of pearls and the shells of marine organisms, snails, and eggs. Calcium carbonate is the active ingredient in agricultural lime and is created when calcium ions in hard water react with carbonate ions to create limescale. It is medicinally used as a calcium supplement or as an antacid, but excessive consumption can be hazardous.

## Chemistry

Calcium carbonate shares the typical properties of other carbonates. Notably,

CaCO3(s) + 2H+(aq) → Ca2+(aq) + CO2(g) + H2O (l)
CaCO3 (s) → CaO (s) + CO2 (g)

Calcium carbonate will react with water that is saturated with carbon dioxide to form the soluble calcium bicarbonate.

CaCO3 + CO2 + H2O → Ca(HCO3)2

This reaction is important in the erosion of carbonate rock, forming caverns, and leads to hard water in many regions.

An unusual form of calcium carbonate is the hexahydrate, ikaite, CaCO3·6H2O. Ikaite is stable only below 6 °C.

## Preparation

The vast majority of calcium carbonate used in industry is extracted by mining or quarrying. Pure calcium carbonate (e.g. for food or pharmaceutical use), can be produced from a pure quarried source (usually marble).

Alternatively, calcium carbonate is prepared from calcium oxide. Water is added to give calcium hydroxide then carbon dioxide is passed through this solution to precipitate the desired calcium carbonate, referred to in the industry as precipitated calcium carbonate (PCC):[7]

CaO + H2O → Ca(OH)2
${\displaystyle {\ce {{Ca(OH)2}+CO2->CaCO3(v)+H2O}}}$

## Structure

The thermodynamically stable form of CaCO3 under normal conditions is hexagonal β-CaCO3, (the mineral calcite).[8] Other forms can be prepared, the denser,(2.83 g/cc) orthorhombic λ-CaCO3 ( the mineral aragonite) and μ-CaCO3, occurring as the mineral vaterite.[8] The aragonite form can be prepared by precipitation at temperatures above 85 °C, the vaterite form can be prepared by precipitation at 60 °C.[8] Calcite contains calcium atoms coordinated by 6 oxygen atoms, in aragonite they are coordinated by 9 oxygen atoms.[8] The vaterite structure is not fully understood.[9] Magnesium carbonate MgCO3 has the calcite structure, whereas strontium and barium carbonate (SrCO3 and BaCO3) adopt the aragonite structure, reflecting their larger ionic radii.[8]

## Occurrence

Calcium carbonate chunks from clamshell

### Geological sources

Calcite, aragonite and vaterite are pure calcium carbonate minerals. Industrially important source rocks which are predominantly calcium carbonate include limestone, chalk, marble and travertine.

### Biological sources

Eggshells, snail shells and most seashells are predominantly calcium carbonate and can be used as industrial sources of that chemical. [10] Oyster shells have enjoyed recent recognition as a source of dietary calcium, but are also a practical industrial source.[11][12] While not practical as an industrial source, dark green vegetables such as broccoli and kale contain dietarily significant amounts of calcium carbonate.[13]

### Extraterrestrial

Beyond Earth, there is strong evidence that Calcium carbonate was detected on the planet Mars at more than one location (notably at Gusev and Huygens craters), providing evidence for the past presence of liquid water.[14][15]

## Geology

Carbonate is found frequently in geologic settings and constitute an enormous carbon reservoir. Calcium carbonate occurs as aragonite, calcite and dolomite. The carbonate minerals form the rock types: limestone, chalk, marble, travertine, tufa, and others.

In warm, clear tropical waters corals are more abundant than towards the poles where the waters are cold. Calcium carbonate contributors, including plankton (such as coccoliths and planktic foraminifera), coralline algae, sponges, brachiopods, echinoderms, bryozoa and mollusks, are typically found in shallow water environments where sunlight and filterable food are more abundant. Cold-water carbonates do exist at higher latitudes but have a very slow growth rate. The calcification processes are changed by ocean acidification.

Where the oceanic crust is subducted under a continental plate sediments will be carried down to warmer zones in the asthenosphere and lithosphere. Under these conditions calcium carbonate decomposes to produce carbon dioxide which, along with other gases, give rise to explosive volcanic eruptions.

### Carbonate compensation depth

The carbonate compensation depth (CCD) is the point in the ocean where the rate of precipitation of calcium carbonate is balanced by the rate of dissolution due to the conditions present. Deep in the ocean, the temperature drops and pressure increases. Calcium carbonate is unusual in that its solubility increases with decreasing temperature. Increasing pressure also increases the solubility of calcium carbonate. The carbonate compensation depth can range from 4–6 km below sea level.

### Role in taphonomy

Calcium carbonate can preserve fossils through permineralization. Most of the vertebrate fossils of the Two Medicine Formation—a geologic formation known for its duck-billed dinosaur eggs—are preserved by CaCO3 permineralization.[16] This type of preservation preserves high levels of detail, even down to the microscopic level. However, it also leaves specimens vulnerable to weathering when exposed to the surface.[16]

## Uses

### Industrial applications

The main use of calcium carbonate is in the construction industry, either as a building material or limestone aggregate for road building or as an ingredient of cement or as the starting material for the preparation of builder's lime by burning in a kiln. However, because of weathering mainly caused by acid rain,[17] calcium carbonate (in limestone form) is no longer used for building purposes on its own, but only as a raw/primary substance for building materials.

Calcium carbonate is also used in the purification of iron from iron ore in a blast furnace. The carbonate is calcined in situ to give calcium oxide, which forms a slag with various impurities present, and separates from the purified iron.[18]

In the oil industry, calcium carbonate is added to drilling fluids as a formation-bridging and filtercake-sealing agent; it is also a weighting material which increases the density of drilling fluids to control the downhole pressure. Calcium carbonate is added to swimming pools, as a pH corrector for maintaining alkalinity and offsetting the acidic properties of the disinfectant agent.[citation needed]

It is also used as a raw material in the refining of sugar from sugar beet; It is calcined in a kiln with anthracite to produce calcium oxide and carbon dioxide. This burnt lime is then slaked in sweet water to produce a calcium hydroxide suspension for the precipitation of impurities in raw juice during carbonatation.[19]

Calcium carbonate has traditionally been a major component of blackboard chalk. However, modern manufactured chalk is mostly gypsum, hydrated calcium sulfate CaSO4·2H2O. Calcium carbonate is a main source for growing Seacrete, or Biorock. Precipitated calcium carbonate (PCC), pre-dispersed in slurry form, is a common filler material for latex gloves with the aim of achieving maximum saving in material and production costs.[20]

Fine ground calcium carbonate (GCC) is an essential ingredient in the microporous film used in diapers and some building films as the pores are nucleated around the calcium carbonate particles during the manufacture of the film by biaxial stretching. GCC or PCC is used as a filler in paper because they are cheaper than wood fiber. In terms of market volume, GCC are the most important types of fillers currently used.[21] Printing and writing paper can contain 10–20% calcium carbonate. In North America, calcium carbonate has begun to replace kaolin in the production of glossy paper. Europe has been practicing this as alkaline papermaking or acid-free papermaking for some decades. PCC used for paper filling and paper coatings is precipitated and prepared in a variety of shapes and sizes having characteristic narrow particle size distributions and equivalent spherical diameters of 0.4 to 3 micrometres.[citation needed]

Calcium carbonate is widely used as an extender in paints,[22] in particular matte emulsion paint where typically 30% by weight of the paint is either chalk or marble. It is also a popular filler in plastics.[22] Some typical examples include around 15 to 20% loading of chalk in unplasticized polyvinyl chloride (uPVC) drain pipe, 5 to 15% loading of stearate coated chalk or marble in uPVC window profile. PVC cables can use calcium carbonate at loadings of up to 70 phr (parts per hundred parts of resin) to improve mechanical properties (tensile strength and elongation) and electrical properties (volume resistivity).[citation needed] Polypropylene compounds are often filled with calcium carbonate to increase rigidity, a requirement that becomes important at high use temperatures.[23] Here the percentage is often 20–40%. It also routinely used as a filler in thermosetting resins (sheet and bulk molding compounds)[23] and has also been mixed with ABS, and other ingredients, to form some types of compression molded "clay" poker chips.[citation needed] Precipitated calcium carbonate, made by dropping calcium oxide into water, is used by itself or with additives as a white paint, known as whitewashing.[citation needed]

Calcium carbonate is added to a wide range of trade and do it yourself adhesives, sealants, and decorating fillers.[22] Ceramic tile adhesives typically contain 70 to 80% limestone. Decorating crack fillers contain similar levels of marble or dolomite. It is also mixed with putty in setting stained glass windows, and as a resist to prevent glass from sticking to kiln shelves when firing glazes and paints at high temperature.[citation needed]

In ceramics/glazing applications, calcium carbonate is known as whiting,[22] and is a common ingredient for many glazes in its white powdered form. When a glaze containing this material is fired in a kiln, the whiting acts as a flux material in the glaze. Ground calcium carbonate is an abrasive (both as scouring powder and as an ingredient of household scouring creams), in particular in its calcite form, which has the relatively low hardness level of 3 on the Mohs scale of mineral hardness, and will therefore not scratch glass and most other ceramics, enamel, bronze, iron, and steel, and have a moderate effect on softer metals like aluminium and copper. A paste made from calcium carbonate and deionized water can be used to clean tarnish on silver.[24]

### Health and dietary applications

500-milligram calcium supplements made from calcium carbonate

Calcium carbonate is widely used medicinally as an inexpensive dietary calcium supplement or gastric antacid.[25] It may be used as a phosphate binder for the treatment of hyperphosphatemia (primarily in patients with chronic renal failure). It is also used in the pharmaceutical industry as an inert filler for tablets and other pharmaceuticals.[26]

Calcium carbonate is used in the production of calcium oxide as well as toothpaste and has seen a resurgence as a food preservative and color retainer, when used in or with products such as organic apples or food.[27]

Excess calcium from supplements, fortified food and high-calcium diets, can cause milk-alkali syndrome, which has serious toxicity and can be fatal. In 1915, Bertram Sippy introduced the "Sippy regimen" of hourly ingestion of milk and cream, and the gradual addition of eggs and cooked cereal, for 10 days, combined with alkaline powders, which provided symptomatic relief for peptic ulcer disease. Over the next several decades, the Sippy regimen resulted in renal failure, alkalosis, and hypercalcaemia, mostly in men with peptic ulcer disease. These adverse effects were reversed when the regimen stopped, but it was fatal in some patients with protracted vomiting. Milk-alkali syndrome declined in men after effective treatments for peptic ulcer disease arose. During the past 15 years, it has been reported in women taking calcium supplements above the recommended range of 1.2 to 1.5 g daily, for prevention and treatment of osteoporosis, and is exacerbated by dehydration. Calcium has been added to over-the-counter products, which contributes to inadvertent excessive intake. Excessive calcium intake can lead to hypercalcemia, complications of which include vomiting, abdominal pain and altered mental status.[28]

As a food additive it is designated E170;[29] INS number 170. Used as an acidity regulator, anticaking agent, stabiliser or colour it is approved for usage in the EU,[30] USA[31] and Australia and New Zealand.[32] It is used in some soy milk and almond milk products as a source of dietary calcium; one study suggests that calcium carbonate might be as bioavailable as the calcium in cow's milk.[33] Calcium carbonate is also used as a firming agent in many canned or bottled vegetable products.

### Agricultural use

Agricultural lime, powdered chalk or limestone, is used as a cheap method for neutralising acidic soil, making it suitable for planting.[34]

### Environmental applications

In 1989, a researcher, Ken Simmons, introduced CaCO3 into the Whetstone Brook in Massachusetts.[35] His hope was that the calcium carbonate would counter the acid in the stream from acid rain and save the trout that had ceased to spawn. Although his experiment was a success, it did increase the amount of aluminium ions in the area of the brook that was not treated with the limestone. This shows that CaCO3 can be added to neutralize the effects of acid rain in river ecosystems. Currently calcium carbonate is used to neutralize acidic conditions in both soil and water.[36][37][38] Since the 1970s, such liming has been practiced on a large scale in Sweden to mitigate acidification and several thousand lakes and streams are limed repeatedly.[39]

Calcium carbonate is also used in flue gas desulfurisation applications eliminating harmful SO2 and NO2 emissions from coal and other fossil fuels burnt in large fossil fuel power stations.[36]

## Calcination equilibrium

Calcination of limestone using charcoal fires to produce quicklime has been practiced since antiquity by cultures all over the world. The temperature at which limestone yields calcium oxide is usually given as 825 °C, but stating an absolute threshold is misleading. Calcium carbonate exists in equilibrium with calcium oxide and carbon dioxide at any temperature. At each temperature there is a partial pressure of carbon dioxide that is in equilibrium with calcium carbonate. At room temperature the equilibrium overwhelmingly favors calcium carbonate, because the equilibrium CO2 pressure is only a tiny fraction of the partial CO2 pressure in air, which is about 0.035 kPa.

At temperatures above 550 °C the equilibrium CO2 pressure begins to exceed the CO2 pressure in air. So above 550 °C, calcium carbonate begins to outgas CO2 into air. However, in a charcoal fired kiln, the concentration of CO2 will be much higher than it is in air. Indeed, if all the oxygen in the kiln is consumed in the fire, then the partial pressure of CO2 in the kiln can be as high as 20 kPa.[40]

The table shows that this partial pressure is not achieved until the temperature is nearly 800 °C. For the outgassing of CO2 from calcium carbonate to happen at an economically useful rate, the equilibrium pressure must significantly exceed the ambient pressure of CO2. And for it to happen rapidly, the equilibrium pressure must exceed total atmospheric pressure of 101 kPa, which happens at 898 °C.

Equilibrium pressure of CO2 over CaCO3 (P) vs. temperature (T).[41]
P (kPa) 0.055 0.13 0.31 1.80 5.9 9.3 14 24 34 51 72 80 91 101 179 901 3961
T (°C) 550 587 605 680 727 748 777 800 830 852 871 881 891 898 937 1082 1241

## Solubility

### With varying CO2 pressure

Travertine calcium carbonate deposits from a hot spring

Calcium carbonate is poorly soluble in pure water (47 mg/L at normal atmospheric CO2 partial pressure as shown below).

The equilibrium of its solution is given by the equation (with dissolved calcium carbonate on the right):

 CaCO3 ⇌ Ca2+ + CO32− Ksp = 3.7×10−9 to 8.7×10−9 at 25 °C

where the solubility product for [Ca2+][CO32−] is given as anywhere from Ksp = 3.7×10−9 to Ksp = 8.7×10−9 at 25 °C, depending upon the data source.[41][42] What the equation means is that the product of molar concentration of calcium ions (moles of dissolved Ca2+ per liter of solution) with the molar concentration of dissolved CO32− cannot exceed the value of Ksp. This seemingly simple solubility equation, however, must be taken along with the more complicated equilibrium of carbon dioxide with water (see carbonic acid). Some of the CO32− combines with H+ in the solution according to:

 HCO3− ⇌ H+ + CO32− Ka2 = 5.61×10−11 at 25 °C

HCO3 is known as the bicarbonate ion. Calcium bicarbonate is many times more soluble in water than calcium carbonate—indeed it exists only in solution.

Some of the HCO3 combines with H+ in solution according to:

 H2CO3 ⇌ H+ + HCO3− Ka1 = 2.5×10−4 at 25 °C

Some of the H2CO3 breaks up into water and dissolved carbon dioxide according to:

 H2O + CO2(dissolved) ⇌ H2CO3 Kh = 1.70×10−3 at 25 °C

And dissolved carbon dioxide is in equilibrium with atmospheric carbon dioxide according to:

 ${\displaystyle {\frac {P_{\ce {CO2}}}{[{\ce {CO2}}]}}\ =\ k_{\ce {H}}}$ where kH = 29.76 atm/(mol/L) at 25 °C (Henry constant), ${\displaystyle P_{\ce {CO2}}}$ being the CO2 partial pressure.

For ambient air, ${\displaystyle P_{\ce {CO2}}}$ is around 3.5×10−4 atmospheres (or equivalently 35 Pa). The last equation above fixes the concentration of dissolved CO2 as a function of ${\displaystyle P_{\ce {CO2}}}$, independent of the concentration of dissolved CaCO3. At atmospheric partial pressure of CO2, dissolved CO2 concentration is 1.2×10−5 moles/liter. The equation before that fixes the concentration of H2CO3 as a function of [CO2]. For [CO2]=1.2×10−5, it results in [H2CO3]=2.0×10−8 moles per liter. When [H2CO3] is known, the remaining three equations together with

Calcium ion solubility as a function of
CO2 partial pressure at 25 °C (Ksp = 4.47×10−9)
${\displaystyle \scriptstyle P_{{\ce {CO}}_{2}}}$ (atm) pH [Ca2+] (mol/L)
10−12 12.0 5.19 × 10−3
10−10 11.3 1.12 × 10−3
10−8 10.7 2.55 × 10−4
10−6 9.83 1.20 × 10−4
10−4 8.62 3.16 × 10−4
3.5 × 10−4 8.27 4.70 × 10−4
10−3 7.96 6.62 × 10−4
10−2 7.30 1.42 × 10−3
10−1 6.63 3.05 × 10−3
1 5.96 6.58 × 10−3
10 5.30 1.42 × 10−2
 H2O ⇌ H+ + OH− K = 10−14 at 25 °C

(which is true for all aqueous solutions), and the fact that the solution must be electrically neutral,

2[Ca2+] + [H+] = [HCO3] + 2[CO32−] + [OH]

make it possible to solve simultaneously for the remaining five unknown concentrations (note that the above form of the neutrality equation is valid only if calcium carbonate has been put in contact with pure water or with a neutral pH solution; in the case where the initial water solvent pH is not neutral, the equation is modified).

The table on the right shows the result for [Ca2+] and [H+] (in the form of pH) as a function of ambient partial pressure of CO2 (Ksp = 4.47×10−9 has been taken for the calculation).

• At atmospheric levels of ambient CO2 the table indicates the solution will be slightly alkaline with a maximum CaCO3 solubility of 47 mg/L.
• As ambient CO2 partial pressure is reduced below atmospheric levels, the solution becomes more and more alkaline. At extremely low ${\displaystyle P_{\ce {CO2}}}$, dissolved CO2, bicarbonate ion, and carbonate ion largely evaporate from the solution, leaving a highly alkaline solution of calcium hydroxide, which is more soluble than CaCO3. Note that for ${\displaystyle P_{\ce {CO2}}=10^{-12}\mathrm {atm} }$, the [Ca2+][OH]2 product is still below the solubility product of Ca(OH)2 (8×10−6). For still lower CO2 pressure, Ca(OH)2 precipitation will occur before CaCO3 precipitation.
• As ambient CO2 partial pressure increases to levels above atmospheric, pH drops, and much of the carbonate ion is converted to bicarbonate ion, which results in higher solubility of Ca2+.

The effect of the latter is especially evident in day-to-day life of people who have hard water. Water in aquifers underground can be exposed to levels of CO2 much higher than atmospheric. As such water percolates through calcium carbonate rock, the CaCO3 dissolves according to the second trend. When that same water then emerges from the tap, in time it comes into equilibrium with CO2 levels in the air by outgassing its excess CO2. The calcium carbonate becomes less soluble as a result and the excess precipitates as lime scale. This same process is responsible for the formation of stalactites and stalagmites in limestone caves.

Two hydrated phases of calcium carbonate, monohydrocalcite, CaCO3·H2O and ikaite, CaCO3·6H2O, may precipitate from water at ambient conditions and persist as metastable phases.

### With varying pH, temperature and salinity: CaCO3 scaling in swimming pools

In contrast to the open equilibrium scenario above, many swimming pools are managed by addition of sodium bicarbonate (NaHCO3) to about 2 mM as a buffer, then control of pH through use of HCl, NaHSO4, Na2CO3, NaOH or chlorine formulations that are acidic or basic. In this situation, dissolved inorganic carbon (DIC) is far from equilibrium with atmospheric CO2. Progress towards equilibrium through outgassing of CO2 is slowed by (i) the slow reaction H2CO3 ⇌ CO2(aq) + H2O;[43] (ii) limited aeration in a deep water column and (iii) periodic replenishment of bicarbonate to maintain buffer capacity (often estimated through measurement of ‘total alkalinity’).

In this situation, the dissociation constants for the much faster reactions H2CO3 ⇌ H+ + HCO3 ⇌ 2 H+ + CO32− allow the prediction of concentrations of each DIC species in solution, from the added concentration of HCO3 (which comprises more than 90% of total DIC from pH 7 to pH 8 at 25 ˚C in fresh water.[44] Addition of HCO3 will increase CO32− concentration at any pH. Rearranging the equations given above, we can see that [Ca2+] = Ksp / [CO32−], and [CO32−] = Ka2 × [HCO3] / [H+]. Therefore, when HCO3 concentration is known, the maximum concentration of Ca2+ ions before scaling through CaCO3 precipitation can be predicted from the formula:

Ca2+max = (Ksp / Ka2) × ([H+] / [HCO3])

The solubility product for CaCO3 (Ksp) and the dissociation constants for the DIC species (including Ka2) are all substantially affected by temperature and salinity,[44] with the overall effect that Ca2+max increases from fresh to salt water, and decreases with rising temperature, pH, or added bicarbonate level, as illustrated in the accompanying graphs.

The trends are illustrative for pool management, but whether scaling occurs also depends on other factors including interactions with Mg2+, B(OH)4 and other ions in the pool, as well as supersaturation effects.[45][46] Scaling is commonly observed in electrolytic chlorine generators, where there is a high pH near the cathode surface and scale deposition further increases temperature. This is one reason that some pool operators prefer borate over bicarbonate as the primary pH buffer, and avoid the use of pool chemicals containing calcium.[47]

### Solubility in a strong or weak acid solution

Solutions of strong (HCl), moderately strong (sulfamic) or weak (acetic, citric, sorbic, lactic, phosphoric) acids are commercially available. They are commonly used as descaling agents to remove limescale deposits. The maximum amount of 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] = [A], we obtain (with CaCO3 molar mass = 100 g):
 [A] (mol/L) 1 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−10 Initial pH 0 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 CaCO3 (g per liter of acid) 50 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 Ca2+ (not taking into account possible CO2 dissolution) and the final state is the solution with saturated Ca2+. For strong acid concentrations, all species have a negligible concentration in the final state with respect to Ca2+ and A so that the neutrality equation reduces approximately to 2[Ca2+] = [A] yielding ${\displaystyle \scriptstyle [\mathrm {Ca} ^{2+}]\simeq {\frac {[\mathrm {A} ^{-}]}{2}}}$. When the concentration decreases, [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 CaCO3 in pure water.

• In the case of a weak monoacid (here we take acetic acid with pKA = 4.76) with decreasing total acid concentration [A] = [A]+[AH], we obtain:
 [A] (mol/L) 1 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−10 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 CaCO3 (g per liter 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 CaCO3 which can be dissolved is approximately the same. This is because in the final state, the pH is larger than the pKA, so that the weak acid is almost completely dissociated, yielding in the end as many 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 [HCO3], [CO32−], [Ca2+], [H+] and [OH]. The system may be reduced to a seventh degree equation for [H+] the numerical solution of which gives
 [A] (mol/L) 1 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−10 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 CaCO3 (g per liter of acid) 62 7.39 0.874 0.123 0.0536 0.0477 0.0471 0.0471 0.0470

where [A] = [H3PO4] + [H2PO4] + [HPO42−] + [PO43−] 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 [HPO42−] is not negligible (see phosphoric acid).

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