# Buffers

Buffer Maker (buffer calculator)

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## Buffer lectures » constant ionic strength

When researching reactions in water solutions for the best results we have not only to control pH of the solution, but also its ionic strength. Changes in both pH and activity coefficients can substantially change ratio of concentrations of acids and their conjugate bases, changing in turn reaction equilibria and kinetics, rendering experimental results irreproducible and useless.

Let's assume we need to do some tests in two solutions, of pH 4.25 and 5.25. Typically we want to change as small number of parameters as possible, so it would make sense to use in both cases the same buffer - and acetic buffer, for which both solutions are exactly half pH unit from pKa, looks like a good candidate. Let's try 0.1 M buffer - at pH 4.25 ionic strength is 0.027 and at pH 5.25 ionic strength is 0.081 - change by 0.054. While it doesn't look large in absolute numbers, it is in fact a threefold change per one pH unit - and that's quite a lot.

The most obvious and simple way of keeping ionic strength of the solution constant (at least approximately), its to add a huge excess of some inert salt. While it doesn't guarantee the ionic strength will be constant, changes of ionic strength will be masked by the excess ions, and the relative change will be quite small. In the case of the acetic buffer mentioned above, if we add enough NaCl to make ionic strength of the solution equal to 1, change by 0.054 means just a few percent, which is quite acceptable.

How much NaCl to add to 0.1 M acetic buffer pH 4.75 to make its ionic strength equal 1?

This is not an easy problem, as adding inert salt and changing the ionic strength of the solution we are also changing practical dissociation constant value, so the buffer equilibrium shifts, changing its own ionic strength. So it is better to put the problem slightly different - calculate buffer composition assuming ionic strength of 1, use calculated concentrations to calculate ionic strength of the buffer itself, and then calculate how much inert salt must be added. Unfortunately even then solution is not easy, as it is hard to find practical dissociation constant for acetic acid in solutions with IS=1, and the concentration pKa (known to be 4.57) is useless as long as we don't know activity coefficient for H+.

Alternatively we can simply assume ionic strength of the buffer is low enough that it can be ignored, and make the solution 1 M in NaCl - we will be wrong by about 6%, which is often acceptable. Or even better, we can calculate ionic strength of the buffer ignoring activity coefficients at all (pKa=4.75, so at pH=4.75 0.1 M acetic buffer has ionic strength of 0.05) and add enough NaCl to increase the ionic strength to 1 (so the solution has to be 0.95 M in NaCl). This approach is far from being exact, but for sure it is better than the previous ones.

Unfortunately, adding excess neutral salt has its obvious drawbacks - we are introducing additional ions, which don't have to be neutral for the system being tested and can interfere, plus by forcing the ionic strength to some high level we can get far from the typical ionic strength in which the reaction typically takes place. There is another, clever approach that makes situation slightly better - it calls for preparation of solutions keeping amount of ions constant.

While it may sound slightly tautological (keeping amount of ions constant to keep ionic strength constant) and impossible to be done, in the simplest form it is very easy to implement. Imagine we start with a 0.1 M solution of sodium acetate - its ionic strength is exactly 0.1. Now, to convert it into a buffer of required pH, we will add HCl solution, protonating acetate ions:

Acetate- + HCl → HAcetate + Cl-

The reaction as written is in general wrong (HCl is fully dissociated), but it was written this way for a purpose - note, that amount of ions on both sides is identical - there is exactly one ion. While HCl is dissociated and technically there are three ions on the left, it doesn't matter, as added HCl was not part of the solution before adding hydrochloric acid. Assuming we managed to add it without changing the volume substantially (we could start with more concentrated solution and dilute it up to some volume to make sure final total concentration of acetic acid and acetate ions concentration is exactly 0.1 M), each Acetate- was replaced by Cl- - so concentrations of ions have not changed, and the ionic strength of the solution is always the same!

Example shown here allows us to keep the ionic strength of the buffer constant in relatively narrow pH range (pKa±1, so about 2 pH units). We can make the situation even better using several components.  