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

Aug 14, 2017

Because its first ${\text{pK}}_{a}$ is known to be about $3.5$, which is on the order of a weak acid. The ${\text{pK}}_{a}$ 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 ${\text{pK}}_{a}$ below $0$ (i.e. ${K}_{a} > 1$) is generally considered a so-called "strong acid".

And its $\text{pH}$ can easily be measured by experiment...

Stick a $\text{pH}$ probe into a given solution of aspirin dissolved as a given concentration, and knowing that ${K}_{a 1} = {10}^{- 4.75} = 1.78 \times {10}^{- 5}$, which is small, the small $x$ approximation can be used to predict the $\text{pH}$ before trying the experiment.

${\text{HAsp"(aq) + "H"_2"O"(l) rightleftharpoons "Asp"^(-)(aq) + "H"_3"O}}^{+} \left(a q\right)$

${K}_{a 1} = 1.78 \times {10}^{- 5} = {x}^{2} / \left(\left[\text{HAsp"] - x) ~~ x^2/(["HAsp}\right]\right)$

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

$x = \left[\text{H"^(+)] = sqrt(K_(a1)["HAsp}\right]$

And so, the $\text{pH}$ would be...

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

as one could verify by experiment.