There are two common calculations you will encounter with pH and pOH: Finding pX from [X] (and vice versa) and finding pH knowing pOH (or vice versa).

Calculation of pH from [H_{3}O^{+}]

What is the pH of stomach acid, a solution of HCl with a hydronium ion concentration of $1.2×10^{−3}\;M$?

Solution

$$pH=-log[H_3O^+]$$ $$pH=-log(1.2×10^{-3})$$ $$pH=-(-2.92)=2.92$$(The use of logarithms is explained the review chapter. Sig fig rules for logarithms are reviewed here.)

### Check Your Learning

Water exposed to air contains carbonic acid, H

_{2}CO

_{3}, due to the reaction between carbon dioxide and water: $$CO_2\;(aq)+H_2O\;(l)⇌H_2CO_3\;(aq)$$

Air-saturated water has a hydronium ion concentration caused by the dissolved CO_{2} of $2.0×10^{-6}\;M$, about 20-times larger than that of pure water. Calculate the pH of the solution at 25 °C.

## Answer:

5.70

### Calculation of Hydronium Ion Concentration from pH

Calculate the hydronium ion concentration of blood, the pH of which is 7.3.

Solution

$$pH=-log[H_3O^+]=7.3$$ $$log[H_3O^+]=-7.3$$ $$[H_3O^+]=10^{-7.3}\;or\;[H_3O^+]=antilog\;of\;-7.3$$ $$[H_3O^+]=5×10^{-8}\;M$$

(On a calculator take the antilog, or the “inverse” log, of −7.3, or calculate 10^{−7.3}.)

### Check Your Learning

Calculate the hydronium ion concentration of a solution with a pH of −1.07.

## Answer:

12 *M*

Calculation of pOH

What are the pOH and the pH of a 0.0125-*M* solution of potassium hydroxide, KOH?

Solution

Potassium hydroxide is a highly soluble ionic compound and completely dissociates when dissolved in dilute solution, yielding [OH^{−}] = 0.0125 *M*:

The pH can be found from the pOH:

$$pH+pOH=14.00$$ $$pH=14.00-pOH=14.00-1.903=12.10$$### Check Your Learning

The hydronium ion concentration of vinegar is approximately $4×10^{-3}\;M$. What are the corresponding values of pOH and pH?

## Answer:

pOH = 11.6, pH = 2.4