Buffers and Equilibriums – PHScale.net

As shortly explained in the section about how to calculate pH in a solution of dissolved NaHCO₃, a buffer has the capability of keeping pH withina certain and narrow range even if an excess of hydrogen ions H⁺or hydroxide ions OH^–are added.

In this particular page I will elaborate a bit on why buffers actually have the capabilities of resisting changes in pH when acid or base is added.

Before I move on I suggest you read the pdf documents showing how equilibriums are calculated and how pH in a NaHCO₃solution is calculated.Links are found in the margin to the left. Also notice that this webpage also has its own pdf version.

Topic:pKa& Ka

The basics

NaHCO₃considered

Consider the solution mentioned in the NaHCO₃section made up of 0.1 M NaHCO₃. We can show that unlike pure water this solution ofsodium bicarbonate is extremely good at resisting pH changes when HCl is added.

Now in order to follow the arguments an excel spreadsheet isneeded to do all the calculations. You can download the spreadsheet for this example by clicking here.

As is seen in this excel spreadsheet at the end of row 16, the pH in the solution is 8.31. Now let’s figure out what happens when 0.0005 mole HCl is added(volume change is neglected).

This starts at row 20 in the excel document. In row 29 it is seen that the pH should decrease to approximatelypH = 8.21 which is not much.

Had it been a solution of pure water the pH would have dropped to -LOG₁₀(0.0005) = 3.3.

Ions and compounds are in equilibriums with each other. A typical equilibrium is the one between ammonia (NH₃) and ammonium(NH₄⁺) discussed in the section about pKa and Ka. These types of equilibriums are dependent on pH.

pH determines how much of a compound or an ion in an equilibrium is dissociated. A simple example is already given in the pKa / Ka section, so here’s abetter one:

Topic:Ideal Gas Law

Ionic Strength

Consider the equilibrium between carbonic acid, bicarbonate and carbonic ion: H₂CO₃, HCO₃^–and CO₃^2-. First of all it should be noted that only approximately 1/400 of the carbonic acid H₂CO₃is inthe form H₂CO₃. The rest is on the form CO₂.

For this reason the carbonic acid in the “inorganic carbon equilibrium” is often denoted CO₂^*even though it at firstsight seems unreasonable that CO₂^*can dissociate into HCO₃^–.

To calculate the concentration of individual species in the equilibrium one first have to introduce a variable denoting the sum of concentrations ofCO₂^*, HCO₃^–and H₂CO₃. This variable should be called TIC – a shortcut forTotalInorganicCarbon.
TIC = [CO₂^*] + [HCO₃^–] + [CO₃^2-]
If we start by finding the [CO₂^*], CO₂^*should be isolated in the above equation. By rearranging the equationabove to:
TIC = [CO₂^*]^.(1+ [HCO₃^–] / [CO₂^*] + [CO₃^2-] /[CO₂^*])
If both sides are divided by (1+ [HCO₃^–] / [CO₂^*] + [CO₃^2-] / [CO₂^*])we get that:
[CO₂^*] = TIC / (1+ [HCO₃^–] / [CO₂^*] + [CO₃^2-] /[CO₂^*])
To move on with this equation and to see how it depend on [H⁺] we introduce [H⁺] in the denominator:
[CO₂^*] = TIC / (1+ [HCO₃^–]^.[H⁺] / [CO₂^*]^.[H⁺] +[CO₃^2-] / [CO₂^*])

Topic:Equilibriums

The pH scale

At this point it is necessary to recall the definition of the dissociation constant. A more detailed explanation on this subject can be found on the siteabout pKa and Ka.

The ionisation constant of CO₂^*is [H⁺]^.[HCO₃^–]/[CO₂^*]

This ionisation constant can be substituted into denominator of the equation for TIC:
[CO₂^*] = TIC / (1 + Ka(CO₂^*) / [H⁺] + [CO₃^2-] / [CO₂^*])
The calculation is not finished yet. [CO₃^2-] and [CO₂^*] are not known.

They cannot be substituted the same way as before. However, the ionisation constant of HCO₃^–is [H⁺]^.[CO₃^2-]/[HCO₃^–].

If this, the ionisation constant of HCO₃^–is multiplied by the ionisation constant of CO₂^*we get that:

Ka(HCO₃^–)^.Ka(CO₂^*)=[H⁺]^.[HCO₃^–]/[CO₂^*]^.[H⁺]^.[CO₃^2-]/[HCO₃^–] = [H⁺]^2.([CO₃^2-] / [CO₂^*]).But this is the same as saying that:

Ka(CO₂^*)^.Ka(HCO₃^–) / [H⁺]²= [CO₃^2-] /[CO₂^*]

This can be substituted into the equation for the [CO₂^*] from before:
[CO₂^*] = TIC / (1 + Ka(CO₂^*) / [H⁺] + Ka(HCO₃^–)^.Ka(CO₂^*) / [H⁺]²)