Question

What is the hydrogen ion concentration in a urine specimen that registers a pH of 4 on a strip of pH paper?

Answer 1

Well, `[H_3O^+]=1xx10^-4*mol*L^-1.......`

Explanation:

And I didn't even need a calculator.........

By definition, `pH=-log_10[H_3O^+]`.

And if `pH=4`, then...........

`[H_3O^+]=10^-4*mol*L^-1=0.0001*mol*L^-1.`

And we know that hydroxide/hydronium ions obey the following equilibrium in aqueous solution.......

`H_3O^+ + HO^(-) rarr2H_2O`; `K_w=[H_3O^+][HO^-]=10^(-14)`. Of course, this value HAS to be measured, and here `K_w` is measured under standard conditions of `298*K` and (almost) `1*atm`.

Why do we use such an absurd definition? Well, back in the day, approx. 30-40 years ago BEFORE the proliferation of hand-held electronic calculators, students and engineers would routinely use log tables for lengthy calculation involving multiplication and division. because the product `axxb=10^(log_10a+log_10b)`, and it was easier to do additions than multiplications, even if we had to take antilogs to get the final product.

These days with a simple electronic calculator (and I bought one for a quid in a discounter's shop a couple of weeks ago) we have access to a computational power that would have astonished both Newton and Gauss (they say that Gauss in particular, a mathematical prodigy, had memorized the log tables so that he could do his calculations).