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 [H3O+]
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, H2CO3, 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 CO2 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 $4.0×10^{-3}\;M$. What are the corresponding values of pOH and pH?
Answer:
pOH = 11.6, pH = 2.4