13.5 The Coupled Chemical Equilibria
In nature there are some chemical coupled chemical equilibria can go simultaneously without the dependence on each other: Example of such coupled chemical equilibria is given below:
Reference: https://chem.libretexts.org/Courses/CSU_San_Bernardino/CHEM_2100%3A_General_Chemistry_I_(Mink)/15%3A_Equ ilibria_of_Other_Reaction_Classes/15.03%3A_Coupled_Equilibria
Another example is the coupling between increasing acidity of the oceans due to CO2 gas emission which can combine itself with water to produce carbonic acid H2CO3 and the solubility of calcium carbonate in the ocean leading to acidification on the health of the ocean’s coral reefs and killing millions of corals which can lead to food mangle to many marines’ lives taking refuge on or surrounding the coral reefs. Calcium carbonate is needed for the coral to live and grow.
At the coral reefs:
CaCO3(s) 
Ca 2+ (aq) + CO3 2- (aq) K sp = 8.7 x 10 – 9
At atmospheric environment:
| K a2 = 4.7 x 10 -11 |
Reference: https://chem.libretexts.org/Courses/CSU_San_Bernardino/CHEM_2100%3A_General_Chemistry_I_(Mink)/15%3A_Equ ilibria_of_Other_Reaction_Classes/15.03%3A_Coupled_Equilibria
Looking at all these equilibrium, one can conclude that carbonate ions are coupled in the dissolution equilibrium of calcium carbonate as well as in the increase of acidification of the oceans.
Now combining the dissolution of calcium carbonate with K SP with reverse reaction of the acid hydrolysis of bicarbonate ion 1 / K a2, one obtains the relationship between the coupled chemical equilibrium:
CaCO3(s) Ca 2+ (aq) + CO3 2- (aq) K sp = 8.7 x 10 – 9
H+ (aq) + CO3 2- (aq) HCO3 – (aq) K’ = 1 / K a2 = 1 / 4.7 x 10 -11 = 2.127 x 10 +11
The combined chemical equilibrium:
CaCO3(s) + H+ (aq) Ca 2+ (aq) + HCO3 – (aq) with K = Ksp x K’ = [8.7 x 10 – 9] x [1 / 4.7 x 10 -11] =
K = Ksp x K ‘ = [8.7 x 10 – 9] x [4.7 x 10 -11] = 185.106 = 185
The videos below illustrate the concept of the coupled equilibria in some details: