According to Wikipedia, the conjugate acid of LDA has a pKa of about 35 - which is in line with figures I've seen elsewhere.
How then can such a weak acid's pKa be determined? If the determination is made in water, how is that even possible? Water would be a stronger acid by far and couldn't it easily mask the acidity of LDA's conjugate acid?
Is LDA's pKa value even determined in water?
Similarly, how are extremely strong acids' pKa values determined? Wouldn't the leveling effect come into play as one introduces, say, tosic acid into water? How then can we determine the strength of an acid stronger than hydronium ion in water?
Answer
Sure enough, such extreme pKa values can't be determined in water for the very reason you've specified (the so-called leveling effect). Now, pretty much every textbook containing the phrase "leveling effect" would also provide a word of explanation as to how can we move beyond the common pH range of water. Even the link above does that; please, read it till the words "discrimination window", at least.
Long story short, we abandon water altogether and move to another solvent (more acidic, like acetic acid, if we are interested in super-strong acids, or more basic, like liquid ammonia, if we want to deal with super-weak acids and super-strong bases). We take our compound in question which is too acidic (or too basic) to be measured in water, pit it against some known compound which is less acidic (or basic) so that its pKa (or pKb) is known from the measurements in water, measure the constant of equilibrium between them and thus derive the unknown pKa. If our compound is too strong for that solvent, we step further to another solvent. Thus we build a kind of ladder, much like the ladder of years in dendrochronology or the ladder of distances in astronomy. And that's how the wild values of pKa like -20 or +40 can be reached.
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