Chemistry lesson: calcium carbonate solubility

The big equations:
CaCO₃ ⇌ Ca²⁺ + CO₃^2-
CaCO₃ (s) + H₂CO₃ (aq) ⇌ Ca²⁺ (aq) + 2HCO₃^- (aq)

For refreshers on chemistry concepts like Qc and Kc, see these websites:

• The Equilibrium Constant
• Difference Between K And Q
• SkepticalScience on ocean acidification (make sure you go through all of the mini-pages)

Ω: what we have

$$\Omega = \frac{\text{have}}{\text{need for saturation}} = \frac{\text{[Ca}^{2+}\text{ present}][\text{CO}_{3}^{2-} \text{ present}]}{\text{[Ca}^{2+}\text{ needed}][\text{CO}_{3}^{2-} \text{ needed}]}$$

CaCO₃ ⇌ Ca²⁺ + CO₃^2-
Note: Ca²⁺ is supplied by weathering.

Ω tells us how much we have relative to what we need for a saturated solution.
Ω tells us how CaCO₃ will behave.
Ω > 1 Precipitation
Ω = 1 Equilibrium
Ω < 1 Dissolution

Modern Sea Surface Ω ≈ 2-5
Sea surface is supersaturated with respect to CaCO₃,
but calcium carbonates are not constantly precipitating.

In the ocean, Ω decreases with depth.

Image credit: http://www.skepticalscience.com/print.php?n=933

K_c: what we want

At 25° C:
Calcite K_c = 10^-8.35
Aragonite K_c = 10^-8.22

$$\Omega = \frac{\text{[Ca}^{2+}][\text{CO}_{3}^{2-}] }{[\text{CaCO}_3]} = \frac{1}{10^{8.35}} = 10^{-8.35}$$

When the concentration ratio of products (numerator) to reactants (denominator) is equal to K_c, the reaction is at equilibrium; the concentrations of the products and reactants remain the same. The reaction is not favored in either the forward or backward direction.

What if Ω > K?

$$\Omega = \frac{[\text{products}]}{[\text{reactants}]} = \frac{\text{[Ca}^{2+}][\text{CO}_{3}^{2-}] }{[\text{CaCO}_3]} = \frac{10}{1}$$

In this example, the balance is "top heavy" compared to the equilibrium value (K_c), where there are 1 products for every 10^8.35 reactants.

This means that in our example, where we have 10 products for every 1 reactant, there are too many products (Ca²⁺ and CO₃^2-) compared to K_c. To achieve equilibrium, the amount of CaCO₃ must increase, and it will increase until it reaches the number that will give us a ratio of 1:10^8.35. So, in our example, the reaction will run backward -- toward CaCO₃. Therefore, CaCO₃ will precipitate when Ω > K.

CaCO₃ ⇌ Ca²⁺ + CO₃^2-

Extra CaCO₃ stops precipitating when equilibrium is reached:

$$\Omega = \text{K} = \frac{[\text{products}]}{[\text{reactants}]} = \frac{\text{[Ca}^{2+}][\text{CO}_{3}^{2-}] }{[\text{CaCO}_3]} = \frac{10}{10^{9.35}} = \frac{1}{10^{8.35}}$$

If we switched the values so that Ω < K -- in other words, we had too much CaCO_{3 --} then the reaction runs forward: CaCO₃ will dissolve.

How do we get carbonate?

Total Dissolved Inorganic Carbon =
[CO₂] + [HCO₃^-] + [CO₃^2-] + [H₂CO₃]
carbon dioxide + bicarbonate + carbonate + carbonic acid

CO₂ (g) ⇌ CO₂ (aq)
CO₂ (aq) + H₂O (l) ⇌ H₂CO₃ (aq)
H₂CO₃ (aq) ⇌ HCO₃^- (aq) + H⁺ (aq)
HCO₃^- ⇌ CO₃^2- (aq) + H⁺ (aq)

The last two reactions release H⁺, so,
CO₂ in water lowers pH
CO₂ out of water raises pH

The Ideal Gas Law states that:
PV=nRT
pressure × volume = amount (moles) × ideal gas constant × temperature

When pressure is higher, more CO₂ dissolves into the water .
When temperature is lower, more CO₂ dissolves into the water.
(At lower pressures and higher temperatures, CO₂ can escape as a gas.)

Note that carbon speciates in the water depending on the water pH:

Image credit: Pedersen et al. (2013)

So what controls CaCO₃ solubility?

Lower solubility means more CaCO₃ precipitates!

↑ Concentration CaCO₃ = Solubility ↓
↑ Temperature = Solubility ↓
↓ Pressure = Solubility ↓
↓ Other Ions in Solution* = Solubility ↓

*The increasing availability of ions that can tie up either Ca²⁺ or CO₃^2- will lowers the effective concentration of Ca²⁺ or CO₃^2- and increases solubility, making it more difficult for Ca²⁺ and CO₃^2- to combine and precipitate. Examples: CaCl₂, CaSO₄, MgCO₃, Na₂CO₃

Modern seawater has lots of dissolved ions!

Putting it all together

The big equation:
CaCO₃ (s) + H₂CO₃ (aq) ⇌ Ca²⁺ (aq) + 2HCO₃^- (aq)

To dissolve calcium carbonate

CaCO₃ (s) + H₂CO₃ (aq) ⇌ Ca²⁺ (aq) + 2HCO₃^- (aq)

To dissolve calcium carbonate:

1. Increase pressure or decrease temperature
2. Per the ideal gas law, this allows more CO₂ to enter the water
3. The extra CO₂ creates more H₂CO₃
4. There is too much H₂CO₃ for equilibrium
5. The reaction must go to the right to get rid of the extra H₂CO₃
6. CaCO₃ dissolves

To precipitate calcium carbonate

CaCO₃ (s) + H₂CO₃ (aq) ⇌ Ca²⁺ (aq) + 2HCO₃^- (aq)

To precipitate calcium carbonate:

1. Decrease pressure or increase temperature
2. Per the ideal gas law, this drives CO₂ out of the water
3. H₂CO₃ breaks down to release the CO₂
4. There is too little H₂CO₃ for equilibrium
5. The reaction must go to the left to replace the lost H₂CO₃
6. CaCO₃ precipitates

How can we decrease pressure?

Bernoulli's principle states that:

Pressure + Kinetic Energy + Potential Energy = Constant
P + ½ρ² + ρgh = Constant

So if you increase kinetic energy (waves), then pressure must go down.

Coral connection

As producers of calcium carbonate (this is what comprises their skeletons), corals like conditions that favor CaCO₃ precipitation. Corals like:

1. Wave action drives off CO₂ by lowering pressure.
2. High temperatures drives off CO₂ by lowering pressure.
3. Less acidic means less carbon is in CO₂ form.
4. They also require sunlight for their nutrient-sharing symbionts to photosynthesize, so they like shallow and clear water.

What about beackrock cementation?

Beachrock is a limestone that forms underwater along the shoreline. It usually dips seaward. It mostly occurs along tropical-temperate, windward coasts. Its formation is still being debated!

1. Direct precipitation from seawaters and sea sprays
   • CaCO₃ precipitates due to intertidal alternate wetting and drying, which allows seawater to evaporate
   • High energy in certain coastal areas favors precipitation
   • Nucleation around pre-existing beach sediments
   • Issues: beachrock in arid areas
2. Precipitation due to marine and fresh water mixing in coastal water tables
   • Solubility of CaCO₃ decreases with salinity, as pure water has less ions to tie up Ca²⁺and CO₃^2-
     Issues: beachrock on islands too small to have freshwater tables
3. Precipitation due to CO₂ de-gassing of coastal groundwater
   • As groundwater reaches the surface (lower pressure) and experiences tidal pumping, CO2 de-gasses
4. Biological activity
   • For example, carbon fixation by cyanobacteria removes dissolved inorganic carbon from the water, raising the local pH

Summarized, in part, from my handwritten notes taken during Dr. Terri Woods' GEOL 540 course at ECU in Fall 2014.