Compare a solution with a pH of 13 to a solution with a pH of 4. Which of the following are correct statements about the two solutions?

Question

1. The solution with a pH of 13 has a pOH of 1.0, while the solution with a pH of 4 has a pOH of 10.

2. The solution with a pH of 13 has a pOH of 13 while, the solution with a pH of 4 has a pOH of 4.

3. The solution with the pH of 4 has a [H3O+] of 1 x 10-10 M.

4. The solution with the pH of 13 has a [OH-] of 1 x 10-1 M.

2 and 4

1 and 4

1 and 3

2 and 3

Answer 1

Answer: statements 1 and 4.

One formatting note first, because it changes what the statements actually say. The numbering ran together when this was posted: statement 1 ends with "...has a pOH of 10" and the "2" stuck to it is the label for statement 2, which is why it looks like "10.2". Same with "4.3" - that is statement 2 ending in "a pOH of 4", then the "3" label. Read that way all four statements are coherent and one of the offered pairs comes out correct, which is the tell that this is the right reading.

Two relationships do all the work here: pH + pOH = 14, and pH = -log[H3O+] with pOH = -log[OH-].

Statement 1 - CORRECT. 14 - 13 = 1.0, so the pH 13 solution has a pOH of 1.0. And 14 - 4 = 10, so the pH 4 solution has a pOH of 10.

Statement 2 - WRONG. It simply repeats each pH as though it were the pOH. If pH 13 had a pOH of 13, then pH + pOH would be 26 instead of 14.

Statement 3 - WRONG. For pH 4, [H3O+] = 10^-4 = 1 x 10-4 M, not 1 x 10-10 M. The 1 x 10-10 M figure is a real number for that solution, but it is the HYDROXIDE concentration (its pOH is 10). The statement has the two ions swapped, which is the most common way to miss a question like this.

Statement 4 - CORRECT. The pH 13 solution has a pOH of 1, so [OH-] = 10^-1 = 1 x 10-1 M. A tenth-molar hydroxide is strongly basic, which is exactly what a pH of 13 should look like.

So the correct pair is 1 and 4.

The habit worth taking away from this one: when a problem hands you a pH, write down all four numbers before you even look at the answer choices.

pH 13: pOH = 1, [H3O+] = 1 x 10-13 M, [OH-] = 1 x 10-1 M
pH 4: pOH = 10, [H3O+] = 1 x 10-4 M, [OH-] = 1 x 10-10 M

With that little table in front of you, the swap in statement 3 jumps out in a second instead of being something you have to re-derive under time pressure. One more fast check that works on any problem like this: the exponent on [H3O+] and the exponent on [OH-] always add to -14, because [H3O+][OH-] = 1 x 10-14. If a stated pair of concentrations does not satisfy that, one of the two is wrong.