Sometimes you are asked to calculate pOH rather than pH. Here's a review of the pOH definition and an example calculation.

### Key Takeaways: How to Calculate pOH

- pH is a measure of acidity or hydrogen ion concentration, while pOH is a measure of alkalinity or hydroxide ion concentration.
- If you know pH, it's easy to calculate pOH because pH + pOH = 14.
- Sometimes you need to calculate pOH from the hydroxide ion concentration [OH
^{-}]. You'll need a calculator here, using the equation pOH = -log[OH-].

## Acids, Bases, pH and pOH

There are several ways to define acids and bases, but pH and pOH refer to hydrogen ion concentration and hydroxide ion concentration, respectively. The "p" in pH and pOH stands for "negative logarithm of" and is used to make it easier to work with extremely large or small values. pH and pOH are only meaningful when applied to aqueous (water-based) solutions. When water dissociates it yields a hydrogen ion and a hydroxide.

H_{2}O ⇆ H^{+} + OH^{-}

When calculating pOH, remember that [] refers to molarity, M.

K_{w} = [H^{+}][OH^{-}] = 1x10^{-14} at 25°C

for pure water [H^{+}] = [OH^{-}] = 1x10^{-7}

Acidic Solution: [H^{+}] > 1x10^{-7}

Basic Solution: [H^{+}] < 1x10^{-7}

## How to Find pOH Using Calculations

There are a few different formulas you can use to calculate pOH, the hydroxide ion concentration, or the pH (if you know pOH):

pOH = -log_{10}[OH^{-}]

[OH^{-}] = 10^{-pOH}

pOH + pH = 14 for any aqueous solution

## pOH Example Problems

**Find the [OH ^{-}] given the pH or pOH. You are given that the pH = 4.5.**

pOH + pH =14

pOH + 4.5 = 14

pOH = 14 - 4.5

pOH = 9.5

[OH^{-}] = 10^{-pOH}

[OH^{-}] = 10^{-9.5}

[OH^{-}] = 3.2 x 10^{-10} M

**Find the hydroxide ion concentration of a solution with a pOH of 5.90.**

pOH = -log[OH^{-}]

5.90 = -log[OH^{-}]

Because you're working with log, you can rewrite the equation to solve for the hydroxide ion concentration:

[OH^{-}] = 10^{-5.90}

To solve this, use a scientific calculator and enter 5.90 and use the +/- button to make it negative and then press the 10^{x} key. On some calculators, you can simply take the inverse log of -5.90.

[OH^{-}] = 1.25 x 10^{-6} M

**Find the pOH of a chemical solution if the hydroxide ion concentration is 4.22 x 10 ^{-5} M.**

pOH = -log[OH^{-}]

pOH = -log[4.22 x 10^{-5}]

To find this on a scientific calculator, enter 4.22 x 5 (make it negative using the +/- key), press the 10^{x} key, and press equal to get the number in scientific notation. Now press log. Remember your answer is the negative value (-) of this number.

pOH = - (-4.37)

pOH = 4.37

## Understand Why pH + pOH = 14

Water, whether it's on its own or part of an aqueous solution, undergoes self-ionization which can be represented by the equation:

2 H_{2}O ⇆ H_{3}O^{+} + OH^{-}

Equilibrium forms between the unionized water and the hydronium (H_{3}O^{+}) and hydroxide (OH^{-}) ions. The expression for the equilibrium constant Kw is:

K_{w} = [H_{3}O^{+}][OH^{-}]

Strictly speaking, this relationship is only valid for aqueous solutions at 25°C because that is when the value of K_{w} is 1 x 10^{-14}. If you take the log of both side of the equation:

log (1 x 10^{-14}) = log [H_{3}O^{+}] + log [OH^{-}]

(Remember, when numbers are multiplied, their logs are added.)

log (1 x 10^{-14}) = - 14

- 14 = log[H_{3}O^{+}] + log [OH^{-}]

Multiplying both sides of the equation by -1:

14 = - log [H_{3}O^{+}] - log [OH^{-}]

pH is defined as - log [H_{3}O^{+}] and pOH is defined as -log [OH^{-}], so the relation becomes:

14 = pH - (-pOH)

14 = pH + pOH