Salinity

A lot of people, even scientist, isn't aware of the fact, that salinity has a quite large effect on equilibriums in water by changing the K_a-values, and hence pK_a-values. In very saline environments this can cause unpleasant calculation errors if neglected - for instance in a computer model.

To calculate the effect of salinity on a given equilibrium relation, we first need to know the ionic strength of our medium.

This knowledge can be used to adjust K_a-values so they fit with reality.

Calculating Ionic Strength (I)

This is the easiest part. Lets take an example. Imagine a solution containing 1 mM NH₄⁺ and 5 mM SO₄^2-. In real life we would have HSO₄^- also, but for the sake of this example we haven't calculated the concentration of HSO4-. The concentration HSO₄^- can be calculated the same way as for the equilibrium between CO₂, HCO₃^- and CO₃^2-.

The ionic strength (I) of the solution mentioned above is:

½ * (0.001 * (1)^2) + 0.005 * (2)^2) = 0.0105

According to the calculation, the uncharged or neutral charged species doesn't count when calculating the ionic strength.

Correcting the pK_a-value

When we know the ionic strength (I) in our medium we can correct our pK_a-values and K_a-values accordingly. Remember the simple relationship between K_a- and pK_a- values as outlined in the section about pK_a and K_a.

To do this we use one of the three approximation formulas below which refer to different situations regarding ionic strength.

Güntelberg		I < 0.1
Davies		I < 0.5

Notice: The 0.5 in the formula represents conditions at 25 degrees Celcius.

Z_HB means charge acid and Z_B means charge base. For instance the charge of H₂CO₃ is zero but the charge of HCO₃^- is minus one. Do remember that the square of -1 is 1.

We can take an example using Davies approximation formula.

Problem:

Calculate the pK_a of NH₄⁺ in a solution with an ionic strength of 0.25 at 25 degrees Celcius.

Answer: In pure water the pK_a-value of NH₄⁺is 9.24. The salinity is more than 0.1 so we use Davies formula to calculate the new pK_a-value at ionic strength 0.25.

= 9.33

As you can see the equilibrium shifts towards relatively more NH₄⁺ compared to NH₃ by increasing salinity.

Know this is a kind of special example since most corresponding acids are negatively charged while the charge of the acid is neutral.

Generally speaking you should use Davies formula under most environmental conditions.

In the scientific literature, you can find other ways of calculating the pK_a of NH₄⁺. I've made an Excel spreadsheet with an example of this. It can be downloaded by clicking here.

If you disagree with any of the above mentioned, please contact me immediately.

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