The H₂CO₃ / HCO₃^- / CO₃^2- equilibrium

Once you have learned to solve the H₂CO₃/HCO₃^-/CO₃^2- equilibrium like below, finding [CO₂], [ HCO₃^-] or [ CO₃^2-], most equilibrium calculations will be easy.

You can also start by exploring the easier NH₄⁺/NH₃ equilibrium or you can go and watch the video-presentations.

The H₂CO₃/HCO₃^-/CO₃^2- equilibrium is typical of biological systems like lakes and the ocean. It acts as a buffer. H⁺ reacts with CO₃^2- and acidification is prevented. OH^- reacts with H₂CO₃ or CO₂ and increasing pH-values are prevented.

The first thing to know before solving the concentrations of the three compounds, is the equilibrium between CO₂ and H₂CO₃ which is heavily favored towards CO₂. There's around 400 times more CO₂ than H₂CO₃ in seawater.

Therefore, in reality, the carbonate equilibrium could look like CO₂/HCO₃^-/CO₃^2-. The only problem is that CO₂ doesn't seem to be carrying any hydrogen atoms. But because of the equilibrium between CO₂ and H₂CO₃ one can think of CO₂ like having hydrogen.

H₂CO₃ is a medium strong acid with a pK_a value of 3,7 while CO₂, because of its equilibrium with H₂CO₃ is regarded as a weak acid, with a pK_a value of 6,35. This also explains why the K_a value of H₂CO₃ sometimes is denoted as K_a(CO₂*). This can be confusing, but just think of H₂CO₃ as a small pool of H₂CO₃ and a larger pool of CO₂.

To calculate the amounts of H₂CO₃ (or CO₂), HCO₃^- and CO₃^2- some calculations are needed.

First we define some K_a-values. If you want to know more about how this is done, click here.

As an intermediate result we shall use both the sum of the two expressions multiplied:

and the fact that (quite easy to calculate - try it):

In order to calculate the concentrations, let T_BIK = [CO₂] + [HCO₃^-] + [CO₃^2-]. Now we have the following three results:

Now both [CO₂], [HCO₃^-] and [ CO₃^2-] can be easily calculated. We start by calculating [CO₂] by rewriting the first of the three results above.

Now [H⁺] is put into the denominator

With [H⁺] in one part of the denominator and the expression for the sum of the multiplied K_a-values and the sum of [CO₂] divided by [CO₃^2-], [CO₂] can be rewritten as:

The same principles is applied when calculating [HCO₃^-] and [ CO₃^2-]. 

[ HCO₃^-]

A bit more difficult:

From the beginning of this page we have:

This again can be rewritten as:

Once more we can put [H⁺] into the denominator. This time we do it twice.

We now how the K_a-values are defined:

which are easily substituted into the equation. This gives the result that [HCO₃^-] equals:

The same principles can be used when calculating [CO₃^2-]. 

[ CO₃^2-]

For the sake of completeness the sum of [CO₃^2-] is:

As you can see it's very easy to calculate the concentrations of [CO₂], [ HCO₃^-] and [CO₃^2-].

 

If this was to difficult you can either go and see how too work out the ammonia / ammonium equilibrium or go and see this as a video.

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