Question

Why is aspirin considered to be a weak acid and how can you measure the exact pH?

Answer 1

Because its first `"pK"_a` is known to be about `3.5`, which is on the order of a weak acid. The `"pK"_a` of acetic acid is `4.75`, so aspirin is `10^(4.75-3.5) = 17.78` times stronger than acetic acid.

Nonetheless, an acid with a `"pK"_a` below `0` (i.e. `K_a > 1`) is generally considered a so-called "strong acid".

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And its `"pH"` can easily be measured by experiment...

Stick a `"pH"` probe into a given solution of aspirin dissolved as a given concentration, and knowing that `K_(a1) = 10^(-4.75) = 1.78 xx 10^(-5)`, which is small, the small `x` approximation can be used to predict the `"pH"` before trying the experiment.

`"HAsp"(aq) + "H"_2"O"(l) rightleftharpoons "Asp"^(-)(aq) + "H"_3"O"^(+)(aq)`

`K_(a1) = 1.78 xx 10^(-5) = x^2/(["HAsp"] - x) ~~ x^2/(["HAsp"])`

And thus, having a given concentration for aspirin, we obtain

`x = ["H"^(+)] = sqrt(K_(a1)["HAsp"]`

And so, the `"pH"` would be...

`color(blue)("pH" ~~ -log(sqrt(K_(a1)["HAsp"]))`

as one could verify by experiment.