## pH & pOH

pH is a unitless number used to convey the acidity of a substance without having to deal with numbers in scientific notation. You must use an extra significant digit when calculating it (and drop a digit when you are going from pH to concentration). You can go between pH and concentration with these equivalent formulae:

"pH" = - log["H"^+] qquad <=> qquad ["H"^+] = 10^(-"pH").

The pH value tells us about the acidity of a solution:

• "pH" = 7 => neutral
• "pH" < 7 => acidic
• "pH" > 7 => basic

pOH is just like pH, except it uses the hydroxide ion concentration:

"pOH" = - log["OH"^-] qquad <=> qquad ["OH"^-] = 10^(-"pOH").

If you have one of pH and pOH, you can easily find the other (at SATP):

"pH" + "pOH" = 14.

### Example

Calculate the concentrations of H+(aq) and OH(aq) and the values of pH and pOH for a 0.042 mol/L H2SO4(aq) solution.

H2SO4(aq) is a strong acid, so finding the H+(aq) concentration is trivial:

["H"^+] = 2["H"_2"SO"_4] = 2(0.042\ "mol/L") = 0.084\ "mol/L".

Now we can use this to calculate pH. Remembering to keep an extra significant digit, we have

"pH" = - log["H"^+] = - log(0.084\ "mol/L") = 1.08,

and then we can calculate pOH with

"pOH" = 14 - "pH" = 14 - 1.08 = 12.9.

From that we can get the hydroxide ion concentration, remembering to drop the extra significant digit:

["OH"^-] = 10^(-"pOH") = 10^(-12.9) = 1.2xx10^-13\ "mol/L".

We could have also used the ion product constant for water to get from H+ concentration to OH concentration, but this way is faster.