Some pH, pOH, [H+], [OH-], and Kw Relationships

Intro

When dealing with acid/base chemistry some of the quantities can seem difficult to comprehend and even redundant. Try your hand at some of these relations!

Sample Problem

Solution

Some definitions first:
pH = -log[H+] and pOH = -log[OH-]

Math concepts:
if y = log(x), then x = antilog(y), where antilog(y) is merely 10^y
log(x) + log(y) = log(xy)

Using these definitions and some algebraic manipulation (multiplying both sides by -1), we get: -pH = log[H+] and -pOH = log[OH-], this might seem trivial but by undoing the log we can directly solve for [H+] and [OH-] by taking the antilog, giving us:
[H+] = antilog(-pH) = 10^-pH and [OH-] = antilog(-pOH) = 10^-pOH

Next we can further exploit logarithms even more:
We know [H+] * [OH-] = 10^-14 and by taking -log of both sides we get:
-log([H+] * [OH-]) = -log(10^-14) and by using the mathematical concept above we get:
-log[H+] + -log[OH-] = -log(10^-14) and by using definitions above and solving the right hand side log we get: pH + pOH = 14

So we now have knowledge that:
pH = -log[H+] and pOH = -log[OH-]
[H+] = antilog(-pH) = 10^-pH and [OH-] = antilog(-pOH) = 10^-pOH
[H+] * [OH-] = 10^-14 –> [H+] = (10^-14)/[OH-] and [OH-] = (10^-14)/[H+]
pH + pOH = 14 –> pH = 14 – pOH and pOH = 14 – pH

I hope this was clear enough, and that some of you get some milage out of seeing all these quantities in one place.