AP®ChemistryCollege BoardStudy GuidesUnit 8: Acids & BasespH & pOHThe Ionic Product of Water

The Ionic Product of Water (College Board AP® Chemistry): Study Guide

Philippa Platt

Written by: Philippa Platt

Reviewed by: Stewart Hird

Updated on

The ionic product of water

The autoionization constant of water, Kw

  • pH, pOH, [H3O+] and [OH–] are all related to one another

  • Water autoionizes: a very small fraction of water molecules transfer a proton to other water molecules, forming hydronium and hydroxide ions

2H2O (l) ⇌ H3O+ (aq) + OH– (aq)

OR

H2O (l) ⇌ H+ (aq) + OH– (aq)

  • The equilibrium expression for this is:

Kw = [H3O+][OH–] = 1.0 × 10-14 at 25 °C

  • In a neutral solution [H3O+] = [OH–]

  • In pure water, [H3O+] can be calculated as √Kw

    • At 25 °C the value of Kw is 1.0 × 10-14

  • Taking the negative log for the equilibrium will give

pKw = pH + pOH = 14.00 at 25 °C

How does temperature affect Kw?

  • The ionization of water is an endothermic process

2H2O (l) ⇌ H3O+  (aq) + OH- (aq) 

  • In accordance with Le Châtelier's principle, an increase in temperature will result in the forward reaction being favored

    • This causes an increase in the concentrations of the hydronium and hydroxide ions

    • This leads to the magnitude of Kw increasing

    • Therefore, the pH will decrease

  • Increasing the temperature decreases the pH of pure water, but the water stays neutral because [H3O+] = [OH–] at every temperature

  • Decreasing the temperature increases the pH of pure water, and the water is still neutral

Examiner Tips and Tricks

Kw = 1.0 × 10−14 and pKw = 14.00 only at 25 °C. At another temperature, you should use the Kw you are given.

In pure water:

[H3O+] = √Kw

Kw = 3.0 × 10−14 at 40 °C

This gives:

[H3O+] = 1.7 × 10−7 M

pH = 6.76

The water is still neutral, because [H3O+] = [OH−].

Kw and the pH of pure water at different temperatures

Temperature (°C)

Kw

pH of pure water

0

1.1 × 10-15

7.48

10

2.9 × 10-15

7.27

25

1.0 × 10-14

7.00

40

3.0 × 10-14

6.76

50

5.5 × 10-14

6.63

100

5.1 × 10-13

6.15

  • As temperature increases, Kw increases, so the pH of pure water decreases

  • The water stays neutral because [H3O+] = [OH–]

Relationship between H+ (H3O+), OH–, pH and pOH

Cycle diagram linking pH, H+(aq), OH−(aq) and pOH: [H+] = 10 to the power −pH; pH = −log10[H+]; [OH−] = Kw ÷ [H+]; [H+] = Kw ÷ [OH−]; pOH = −log10[OH−]; [OH−] = 10 to the power −pOH; pH + pOH = pKw

To make a conversion, follow the arrow and equation given, so to convert OH– (aq) to pOH use pOH = −log [OH–] 

Worked Example

Convert between [H3O+], [OH–], pH and pOH.

Complete the following table for solutions at 25 °C, giving pH and pOH values to 2 decimal places.

[H3O+]

[OH–]

pH

pOH

2.40 × 10-4

 

 

 

 

4.60 × 10-5

 

 

 

 

10.36

 

 

 

 

3.21

Answer:

As shown below there are different ways to arrive at the correct answer

[H3O+]

[OH–]

pH

pOH

2.40 × 10-4

1.00×10−142.40×10−4

= 4.17 × 10-11

−log (2.40 × 10-4)

= 3.62

14.00 − pH

= 10.38

1.00×10−144.60×10−5

= 2.17 × 10-10

4.60 × 10-5

14.00 − pOH

= 9.66

−log (4.60 × 10-5)

= 4.34

10-10.36

= 4.37 × 10-11

1.00×10−144.37×10−11

= 2.29 × 10-4

10.36

14.00 − pH

= 3.64

1.00×10−146.17×10−4

= 1.62 × 10-11

10-3.21 

= 6.17 × 10-4

14.00 − pOH

= 10.79

3.21

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Philippa Platt

Author: Philippa Platt

Expertise: Chemistry Content Creator

Philippa has worked as a GCSE and A level chemistry teacher and tutor for over thirteen years. She studied chemistry and sport science at Loughborough University graduating in 2007 having also completed her PGCE in science. Throughout her time as a teacher she was incharge of a boarding house for five years and coached many teams in a variety of sports. When not producing resources with the chemistry team, Philippa enjoys being active outside with her young family and is a very keen gardener

Stewart Hird

Reviewer: Stewart Hird

Expertise: Chemistry Content Creator

Stewart has been an enthusiastic GCSE, IGCSE, A Level and IB teacher for more than 30 years in the UK as well as overseas, and has also been an examiner for IB and A Level. As a long-standing Head of Science, Stewart brings a wealth of experience to creating Topic Questions and revision materials for Save My Exams. Stewart specialises in Chemistry, but has also taught Physics and Environmental Systems and Societies.