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Wize University Chemistry Textbook > Acids and Bases

Autoionization of Water (Kw)

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Autoionization of Water (Kw)

Two water molecules can react with themselves in an autoionization reaction as follows:

2H2O(l)↔H3O(aq)++OH(aq)−2H_2O_{(l)}\leftrightarrow H_3O_{(aq)}^++OH_{(aq)}^-

Kw=[H3O(aq)+][OH(aq)−]=1×10−14 (25oC)\boxed{K_w=[H_3O_{(aq)}^+][OH_{(aq)}^-]=1\times10^{-14}\ (25^oC)}
Here is the reaction in action!


Photo by Rice University / CC BY

Label whether each reactant and product in the above reaction is acting as an acid/base or conjugate acid/conjugate base.

Water is amphoteric: it can act as an acid or a base!

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Other Key Relationships

Kw = [H+][OH-] = 1x10-14, [H+]= 1x10-7M and [OH-]= 1x10-7M at 25oC

This is why the pH (and pOH) of neutral water is 7

Kw=[H3O(aq)+][OH(aq)−]=(Ka)(Kb)=1×10−14 (25oC)\boxed{K_w=[H_3O_{(aq)}^+][OH_{(aq)}^-]=(Ka)(Kb)=1\times10^{-14}\ (25^oC)}
*Ka and Kb have to be the K values for an acid and its conjugate base (or a base and its conjugate acid)


If [H+] goes higher, what do you think would happen to [OH-]? Goes higher/lower:
lower


Practice: Solve for [H+]

A solution of HBr has a pOH of 12.2, what is the [H+] concentration?
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Example: pH Problem

If 0.2 mols of HCl(s)\text{HCl}_{(s)} are dissolved in 1.8 L of water, what is the pH?
HCl → H+ + Cl-

Since HCl\text{HCl} is a strong acid, we will be adding 0.2 mols of H+\text{H}^+ to 1.8 L of water.

[H+]=0.2mol1.8L=0.11mol/L[\text{H}^+]=\dfrac{0.2mol}{1.8L}=0.11mol/L

pH=−log⁡[H+]=0.95pH=-\log[\text{H}^+]=0.95

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Example: pH Problem

C6H5COOH ⇌ H+ + C6H5COO-

Ka of C6H5COOH = 6.5 x 10-7 and the concentration of C6H5COOH is 0.01 M, what is the pH of the solution?

Write Out An ICE Table

I 0.01M 0 0
C -x +x +x
E 0.01-x x x

Write a K expression and Solve for x

Ka = x²/(0.01 - x) Ka = x²/0.01
We can ignore the "-x" part since y/K > 400

x² = Ka·0.01
x² = (6.5 x 10-7)(0.01) x² = 6.5 x 10-9 x = 8.06 x 10-5
x=[H+]

Find pH

pH = -log[H+] pH = -log(8.06 x 10-5) pH = 4.09



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pH Scale

The pH scale is a logarithmic scale used to measure the concentration of [H+] in a solution, since this value can vary over many orders of magnitude. It ranges from 0 to 14, with 7 representing neutral pH

Note: There are some exceptions to this. For example, an acid could have a negative pH! These aren't commonly seen.

Photo by OpenStax College / CC BY

A lower pH indicates that a substance is more (acidic/basic)
acidic
and has a (higher/lower)
higher
[H+]
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We also have Ka and pKa equations:

pKa=−log⁡⁡Ka and Ka=10−pKapK_a=-\log⁡K_a\ and\ K_a=10^{-pK_a}
As well as Kb and pKb equations:

pKb=−log⁡⁡Kb and Kb=10−pKbpK_b=-\log⁡K_b\ and\ K_b=10^{-pK_b}

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What does it mean to be a logarithmic scale?

How does the [H+] change as the pH goes from 1 to 2 or 1 to 3??



Wize Concept
Since pH is a logarithmic scale, each 1 unit change in pH corresponds to a 10-fold change in [H+]!


Extra Practice
Concentration
A solution of LiOH is made by mixing an unknown amount of LiOH with 1 L of water. The pOH is measured to be 3.65, what is the concentration of LiOH?
MW Li: 7 g/mol
MW O: 16 g/mol
Calculate the pH of the solution resulting from the addition of 10.0 mL of a 0.10 M NaOH to 50.0 mL of 0.10 M HCN (Ka = 4.9 x 10-10) solution
Diet cola drinks have a pH of about 3.0, while milk has a pH of about 7.0. How many times greater is the H3O+ concentration in diet cola than in milk?
Acids and Bases: Ka
The following occurs when HCl is placed in water:
HCl <----> H+ + Cl-
The Ka for this reaction is known to be Ka = 5.64 once it reaches equilibrium. At equilibrium, 1.35 x 10-7 M of HCl and 1.2 M of Cl- can be found. What is the pH of the solution at equilibrium?
Acids and Bases: pH
100 mL100\ mL of a 0.5 M0.5\ M solution of Hydrochloric acid (HCl\rm HCl) was added to 48 mL48\ mL of a 0.410 M0.410\ M solution of sodium benzoate (C6H5COONa\rm C_6H_5COONa) the conjugate base of benzoic acid (C6H5COOH\rm C_6H_5COOH Ka=6.6×10−5\rm K_a = 6.6 \times 10^{-5}). Calculate the pH\rm pH of the resulting solution.
An aqueous solution only contains a 0.050 M in a weak base. Which of the following statements would be true about the solution?
Lactic acid, shown below, is added to many beverages, including some sour beers. What is the pH of a 0.050M lactic acid solution in 0.50M hydrochloric acid? (Ka for lactic acid=1.38x10-4)
What is the hydroxide ion (OH-) concentration of a solution with a pH of 6.1?
Calculate the pH of the solution resulting from the addition of 10.0 mL of a 0.10 M NaOH to 50.0 mL of 0.10 M HCN (Ka = 4.9 x 10-10) solution
Diet cola drinks have a pH of about 3.0, while milk has a pH of about 7.0. How many times greater is the H3O+ concentration in diet cola than in milk?
What is the pH of a solution prepared by mixing 50 mL of a 0.10 M HCl solution with 150 mL of pure water?
What is the pH of a 1.1M solution of nitrous acid (HNO2). The Ka of nitrous acid is 7.2 x 10-4
Diet cola drinks have a pH of about 3.0, while milk has a pH of about 7.0. How many times greater is the H3O+ concentration in diet cola than in milk?
Concentration
A solution of LiOH is made by mixing an unknown amount of LiOH with 1 L of water. The pOH is measured to be 3.65, what is the concentration of LiOH?
MW Li: 7 g/mol
MW O: 16 g/mol
pH: Neutralization
A student adds 11.6 mL of a 3.7M KOH solution, to 29 mL of a 1.4 M HCl. What is the final pH after the addition?
To 4.00 L of water was added 100 mg of HF (6.6 x 10-4). What is the pH?
CH3COOH is a weak acid with a Ka of 1.8 x 10-5. In what pH range would you most likely an aqueous solution of Na(CH3COO).
To 150 mL of water was added 0.18 moles of ammonia (NH3 Kb= 2.3 x 10-5) calculate the pH.
Acids and Bases: Henderson Hasselbalch
To a solution of acetic acid (Ka=1.8×10−5\rm K_a = 1.8 \times 10^{-5}) was added 0.1 mol of NaOH\rm NaOH. After the addition of NaOH\rm NaOH the volume was 1.4L and the pH\rm pH was 5.2.
a) This solution a buffer? (True/False)
b) Calculate the number of moles of acetic acid that were originally in solution. Report your answer in moles to three significant figures. Do not include units in the answer field
What is the pH of a solution made by mixing 22g of NaOH in 3.1 L of water?
Molecular formula: Concentration
A solution of HBr has a pOH of 12.2, what is the [H+] concentration?
What is the pH of a solution of 0.1 M sodium acetate (NaCH3CO2) given that the Ka for acetic acid is 1.8×10−5?
Calculate the pH of the solution resulting from the addition of 10.0 mL of a 0.10 M NaOH to 50.0 mL of 0.10 M HCN (Ka = 4.9 x 10-10) solution
To a 90 mL90\ mL of 0.17 M0.17\ M of HF\rm HF is added 25 mL25\ mL of 0.06 M0.06\ M NaOH\rm NaOH. The KaK_a of HF\rm HF is 7.2×10−47.2 \times 10^{-4}. Calculate the pH\rm pH of the solution.
What is the pH of pure, neutral water at 37°C? At 37°C, Kw = 2.4x10-14.
A student titrated 10.00 mL of 0.10 M sodium acetate (CH3COONa) with HCℓ and determined that 10.00 mL of HCℓ was needed to reach the equivalence point. At equivalence, what is the expected pH?
Ka of CH3COOH = 1.8×10-5
Calculate the pH of the solution resulting from the addition of 10.0 mL of a 0.10 M NaOH to 50.0 mL of 0.10 M HCN (Ka = 4.9 x 10-10) solution
What is the pH of a solution prepared by mixing 50 mL of a 0.10 M HCl solution with 150 mL of pure water?
The equilibrium constant for the auto-ionization of water at 10 °C is 3.0 x 10-15. What is the concentration of H3O+ ions in pure water at this temperature?
If the pH of pure water is 6.80 at 37 °C, calculate Kw pOH and [OH- ] at this temperature.
Equilibrium: Auto-ionization of water
Given the equilibrium information for water below, what is the concentration of hydroxide ions in a solution of 1.5 M HCl?
2 H2O (l) ⇌ H3O+ (aq) + OH- (aq), Kc = 1x10-14 at 20oC
Equilibrium: ICE Tables and Auto-ionization of Water
Given the equilibrium information for water below, what is the concentration of hydroxide ions in water?
2 H2O (l) ⇌ H3O+ (aq) + OH- (aq), Kc = 1x10-14 at 20oC
If the pH of pure water is 6.80 at 37 °C, calculate Kw pOH and [OH- ] at this temperature.
The compound fluoroacetic acid (shown), has a pKa value of 2.59. What is pKb of its conjugate base?
A solution of [CH3NH3][CH3COO] is made in an undergraduate laboratory. Use the information below to predict the acidity of the solution.
CH3COOH: Ka = 1.8 x 10-5
CH3NH3+: Ka = 2.3 x 10-11
Auto-ionization of Water: pH
If the pH of pure water is 6.80 at 37 °C, calculate Kw pOH and [OH- ] at this temperature.
If an answer has an exponent (ex. 1.6x103), input it as: 1.6e3
The equilibrium constant for the auto-ionization of water at 10 °C is 3.0 x 10-15. What is the concentration of H3O+ ions in pure water at this temperature?