User:Pjb81/draft on aqueous carbaone system

Aqueous carbonate system

The CaCO3 - CO2 - H2O System / Calcium carbonate in water

SUMMARY:

The seemingly simple solubility equilibrium of calcium carbonate in water of
 * CaCO3(S) Ca2+ + CO32-

is coupled with that of carbon dioxide in water (see carbonic acid)to create a system which is much more complex. Overall this system explains the property of retrograde solubility observed for dissolved calcium carbonate, which causes fouling (scaling) in hard water areas.

The aqueous carbonate System

The aqueous carbonate system is governed by seven equilibria in total.

The equilibrium of solid calcium carbonate with its solution is given by


 * CaCO3(S) Ca2+(aq) + CO32-(aq)           Ksp1 = 3.7 × 10-9 to 8.7 × 10-9 at 25oC

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.[17][18]- (See solubility as stands)

This seemingly simple soulubility equation, however must be taken along with the more complicated equilibrium of carbon dioxide with water, since the carbonate anion is a common species in both systems, thus two more equlibria of the system can be defined:


 * HCO3-(aq) H+(aq) + CO32-(aq) Ka2 = 5.61 × 10-11 at 25oC

and


 * H2CO3(aq) H+(aq) + HCO3-(aq) Ka1 = 2.5 × 10-4 at 25oC

Some of the H2CO3(aq) dissociates into water and dissolved carbon dioxide:

H2O(aq) + CO2(aq) H2CO3(aq) Kh = 1.70 × 10-3 at 25oC

This dissolved carbon dioxide is in equilibrium with that present within the surrounding atmosphere according to:


 * {| width="500"


 * width="45%" |$$\frac{P_{\text{CO}_2}}{[\text{CO}_2]}\ =\ k_\text{H}$$
 * where kH = 29.76 atm/(mol/L) at 25 °C (Henry constant), $$\scriptstyle P_{\text{CO}_2}$$ being the CO2 partial pressure.
 * }

This leads to two separate aqueous carbonate systems- the closed aqueous carbonate system in which the equilibrium is excluded and the open aqueous carbonate system in which the equilibrium is included. The open system is taken as having an atmosphere with a set value of PCO2 which is around 3.5 x 10-4 atmospheres (or equivalently 35Pa) for ambient air.

There are two further equlibria present within the aqueous carbonate system. The direct reaction of solid calcium carbonate with aqueous acid according to:


 * CaCO3(s) + H3O+(aq) Ca2+(aq) + HCO3-(aq)  Ksp2 = 81.3 at 25oC

And the water equilibrium according to:

H2O H+ + OH-  Kw = 10-14 at 25oC

A further condition of the system is that it must satisfy the principle of electro neutrality and therefore must be electrically neutral at all times meaning the following equation must be adhered to:

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

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 original water solvent pH is not neutral, the equation is modified. The above equations makes it possible to solve simultaneously for five unknown concentrations, provided the rest are known.

From these equations it is possible to derive an expression for the maximum dissolved concentration of calcium ions ([Ca2+]max) provided that solid calcium carbonate is present in contact with the liquid phase. This expression is:


 * $$[\text{Ca}^{2+}]_\text{max} = \frac{K_\text{sp}} {K_\text{h}K_\text{a1}K_\text{a2}k_\text{H}} \frac{[\text{H}^+]^2}{P_{\text{CO}_2}}$$

which shows a quadratic dependence in [H+] and an inverse relationship to the partial pressure of carbon dioxide.

Perturbations of the system

-pH -PCO2 -T?

Precipitation from a supersaturated solution of calcium carbonate

The aqueous carbonate system can easily become supersaturated with respect to the solubility product of calcite (the most thermodynamically stable polymorph of calcium carbonate) and this can be seen in natural waters. This supersaturated solution does not precipitate out solid calcium carbonate, but exists in a metastable state. In order to precipitate out calcium carbonate a change needs to applied to the system, so that the supersaturation is increased to the maximum solubility of one of the hydrated forms of calcium carbonate (Amorphous calcium carbonate (ACC), Monohydrated Caclium carbonate (MCC) and Ikatite). Above XXoC Ikatite is not observed to form.

Upon the onset of precipitation a drop in pH is observed and this is believed to be due to the inital precipitation being between Ca2+ and HCO3- ions, due to the high concentration of HCO3- compared to that of CO32- ions. The HCO3- ions then transform to CO32- within the crystal by the following reaction:


 * HCO3- + H2O CO32- + H3O+

Dependent upon the extent of the supersaturation at room temperate two distinct zones of precipitation are observed:

Zone A: Primary nucleation of MCC which is observed to be a slow process- it takes approximately one day. Zone B: Primary nucleation of ACC which is observed to be a rapid process- it occurs over a couple of minutes.

The Solubility product for ACC is slightly greater than that for MCC. Thus if the solubility product of ACC is exceeded then mainly ACC will be initally formed.

Due to the instability of the hydrated polymorphs of calcium carbonate, the ACC and MCC rapidly change into an anhydrous form of calcium carbonate, which has been found to depend upon the temperature of the solution. For low temperatures (14oC-30oC)a mixture of Vaterites and Calcites are observed, for high temperatures (60oC-80oC) a mixture of aragonites and calcites are observed and for medium temperatures (40oC-50oC) all three anhydrous polymoprhs are observed.

--Pjb81 (talk) 18:24, 17 August 2010 (UTC)