Worked example 1
A solution has [OH⁻] = 2.5 × 10⁻⁴ M at 25 C. Find [H₃O⁺], pH and pOH.
Try it first: Start from Kw rather than from a pH formula.
0 of 3 steps revealed.
Acids, Bases & Aqueous EquilibriaAcids and BasesContent level: Core 18 min
Autoionization of Water, pH and pOH
What you'll be able to do: Convert freely among [H₃O⁺], [OH⁻], pH and pOH and classify a solution as acidic, neutral or basic.
Introduction
Water itself is very slightly ionized, and that tiny equilibrium sets the whole pH scale. Once you have Kw, every acid-base number in this unit connects to every other one.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Write the autoionization equilibrium and the expression for Kw
- Convert between [H₃O⁺], [OH⁻], pH and pOH
- Classify solutions as acidic, neutral or basic
- Apply significant-figure rules to logarithmic quantities
Lesson
Water ionizes itself
In any sample of pure water a very small fraction of molecules transfer a proton to a neighbour: 2 H₂O ⇌ H₃O⁺ + OH⁻. At 25 C this gives [H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ M, which is about one ionized molecule in every 500 million.
Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 C
Kw links the two ions
Kw is an equilibrium constant, so it holds in every aqueous solution, not just pure water. Add acid and [H₃O⁺] rises, which forces [OH⁻] down so the product stays 1.0 × 10⁻¹⁴. Neither ion is ever truly zero.
If you know one ion concentration, divide Kw by it to get the other.
The p-function
Because these concentrations span many orders of magnitude, chemists take negative logarithms. pH = -log[H₃O⁺], pOH = -log[OH⁻], pKw = 14.00. Taking -log of the Kw expression gives pH + pOH = 14.00 at 25 C.
pH + pOH = pKw = 14.00 at 25 C
Reading the scale
At 25 C, pH < 7 is acidic, pH = 7 is neutral and pH > 7 is basic. Each pH unit is a factor of ten in [H₃O⁺], so a solution at pH 3 is one hundred times more acidic than one at pH 5. pH values below 0 and above 14 are perfectly possible for concentrated solutions.
Temperature matters
Autoionization is endothermic, so heating water increases Kw. At 60 C, Kw is about 9.6 × 10⁻¹⁴ and neutral water has a pH near 6.5. The water is still neutral because the two ion concentrations are still equal.
Neutral is defined by [H₃O⁺] = [OH⁻], not by the number 7.
Significant figures in logs
In a pH the digits before the decimal point only encode the power of ten. [H₃O⁺] = 4.2 × 10⁻⁵ M has two significant figures, so pH = 4.38 is written with two decimal places.
Key ideas
Definition
Autoionization
Proton transfer between two water molecules producing H₃O⁺ and OH⁻.
Rule
Kw
[H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 C in every aqueous solution.
Rule
pH
pH = -log[H₃O⁺]; [H₃O⁺] = 10-pH.
Rule
pH + pOH
Equals 14.00 at 25 C only.
Rule
Neutrality
[H₃O⁺] = [OH⁻]; the pH of neutrality changes with temperature.
Equation
Ion product of water
Kw = [H₃O⁺][OH⁻]
- Kw = 1.0 × 10⁻¹⁴ at 25 C
Equation
pH definition
pH = -log[H₃O⁺]
- [H₃O⁺] = hydronium concentration in mol/L
Equation
Inverse of pH
[H₃O⁺] = 10-pH
- pH = measured or calculated pH
Worked examples
Worked example 2
What is [H₃O⁺] in a solution of pH 5.72?
Try it first: Undo the logarithm.
0 of 3 steps revealed.
Worked example 3
At 50 C, Kw = 5.5 × 10⁻¹⁴. What is the pH of pure water, and is it acidic?
Try it first: In pure water the two ion concentrations are still equal.
0 of 3 steps revealed.
Common mistakes
Assuming pH 7 is always neutral.
Why it's wrong: Kw changes with temperature, so neutral pH is 7.00 only at 25 C.
Check instead: Compare [H₃O⁺] with [OH⁻].
Treating pH as a linear scale.
Why it's wrong: Each unit is a factor of ten in concentration.
Check instead: pH 2 is 1000 times more acidic than pH 5.
Reporting pH 4.3812 from a concentration with two significant figures.
Why it's wrong: Only decimal places count in a log.
Check instead: Match decimal places to significant figures.
Saying [OH⁻] is zero in an acidic solution.
Why it's wrong: Kw forces both ions to be present at all times.
Check instead: Divide Kw by [H₃O⁺].
Using pH + pOH = 14 at other temperatures.
Why it's wrong: That sum equals pKw, which is 14.00 only at 25 C.
Check instead: Recompute pKw from the given Kw.
Practice this skill
No practice questions are available for this topic yet. You can still practice the whole unit.
What you should now know
Water autoionizes: 2 H₂O ⇌ H₃O⁺ + OH⁻, with Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 C. Because the product is fixed, knowing either ion concentration gives the other. pH = -log[H₃O⁺] and pOH = -log[OH⁻], so pH + pOH = 14.00 at 25 C. A solution is acidic when [H₃O⁺] > [OH⁻] (pH < 7 at 25 C), neutral when they are equal, and basic when [OH⁻] is larger. Neutral means equal ion concentrations, not pH exactly 7: autoionization is endothermic, so at higher temperature Kw rises and neutral pH falls below 7. In pH values only the digits after the decimal point are significant.
- Water autoionizes and Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 C
- Knowing one ion concentration always gives the other
- pH = -log[H₃O⁺] and pH + pOH = 14.00 at 25 C
- Neutral means equal ion concentrations, not pH 7
- Only decimal places are significant in a pH value
Sources and further reading
This lesson is original Chem Help content. No external sources were adapted.