Solvent levelling

It is very hard to discriminate between strong acids in water since they are fully deprotonated, so a mol of HI and a mol of HBr each act like one mol of H₃O⁺. A solvent which is a weaker proton acceptor is needed to tell the difference.

The same logic applies to strong bases, one mole of any strong base can be treated as one mole of hydroxyl ions.

This is called the leveling effect - the limitation by the solvent of how strong acids or bases can be.

If two weak acids are put into a solvent which is a strong proton acceptor, such as ammonia, it is likewise hard to tell the difference between the two acids, since they will both act like a mol of ammonium ions. So the leveling effect changes with the solvent.

So a solvent HSol has a range for the allowed pH of a dissolved compound. Any acid stronger than the range will act like H₂Sol⁺, and any base stronger than this range will act like Sol^-. This is called the acid–base discrimination window:

The width of each bar is actually proportional to the pK_w of the solvents, we can see why below.

For a solute acting as an acid:

Notice that pK_{a depends on the solvent.}

An acid is considered strong at pK_a < 0, which corresponds to K_a > 1

So an acid with pK_a < 0 in a particular solvent has an acidity at the limit allowed by the leveling effect of the solvent, which is the same acidity as [H2Sol⁺]

For a solute acting as a base:

A base is considered strong at pK_b < 0, which corresponds to K_b > 1

So a base with pK_b < 0 has a basicity at the limit allowed by the leveling effect of the solvent, which is the same basicity as [Sol^-]

Now for the clever bit. The relationship between pK_a and pK_b is:

Therefore all bases with pK_a > pK_sol give a negative value of pK_b thus they behave like pure [Sol^-]

So the upper limit (strongest base) of pK_a is pK_sol

The lower limit (strongest acid) of pK_a is 0

Hence the windows of strengths that are not leveled in the solvent are is from pK_a = 0 to pK_a = pK_sol

Which explains why the window size is proportional to pK_w.

You may have difficulty grasping intuitively why a substance bad at protonating itself (high pK_w, so a small autopyrolysis constant) is also good at discriminating between acids. I have never been able to grasp it intuitively either. This explanation just shows you from the equations.