The ammonia / ammonium equilibrium

The concentrations of NH3 and NH4+ are much easier to find in the equilibrium between NH3 and NH4+ than for instance the concentration of CO32- in the equilibrium between H2CO3, HCO3- and CO32-.

The ammonia / ammonium equilibrium looks like:

NH4+ <=> NH3 + H+

The Ka-value of NH4+ and pH decides whether there's more ammonium or ammonia in a solution. At pH level below 9.24 there will be an excess of NH4+ since the pKa-value of NH4+, defined as:

is less than 9.24, where there's half NH3 and half NH4+ at pH 9.24. At pH above 9.24 there will be an excess of NH3.

We can calculate the concentrations of NH3 and NH4+ in to ways. One option is just to look at the way we define the Ka of NH4+. 

We can easily rearrange this to give us the concentration of both NH3 and NH4+.

If we multiply by NH4+ and divide by Ka on both sides of the equation we get NH4+

If we multiply by NH4+ and divide by H+ on both sides of the equation we get NH3.

If we want the concentrations of NH3 and NH4+ as a function of ([NH3] + [NH4+]) it is done the following way. This can be considered a kind of training before embarking on the more difficult carbonate system.

We start by rewriting [NH3] + [ NH4+]:

Notice that nothing has changed. If you calculate the sum above its still [NH3] + [ NH4+]. To this we multiply with [H+] in the last part of the equation. There's nothing wrong in doing this. The result is still the same. 

If we know how Ka looks, we also knows [H+] / Ka. Now we replace the last part of the equation with [H+] / Ka because its the same. The formula now looks like:

From the start we know that this equals ([NH3] + [ NH4+]). On both sides we divide by (1+[H+] / Ka) and we got:

NH3 =

As you can se it was fairly easy to solve this kind of equations.

In the section "Example and test" you can find the additional question: "How do you calculate NH4+?"

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