Autoionization of Water

Although water is a molecular substance, very low concentrations of hydronium ions and hydroxides ions are formed by autoionization.

Autoinization

H O

H

+ H O

H

H O+ H

H

+H O -

Autoionization of Water

Autoionization: the process in which water spontaneously

forms low concentrations of H+ and OH - ions by proton transfer from one water molecule to another

At any given time only a very small number of water molecules are ionized.• If every letter in our text represented a water

molecule, you would have to look through about 50 texts to find one H3O+!

2 H2O (l) H3O+ (aq) + OH- (aq)

Autoionization of Water

An equilibrium constant expression can be written for the autoionization of water:

2 H2O (l) H3O+ (aq) + OH - (aq)

Kw = [H3O+] [OH -] = [H+ ] [OH- ]

where Kw = ionization constant for water= ion-product constant= 1.00 x 10-14 at 25oC

Autoionization of Water

The value of Kw (and all other equilibrium constants) varies with temperature:Kw = 1.14 x 10-15

at 0oCKw = 1.00 x 10-14

at 25oCKw = 9.61 x 10-14 at 60oC

You should assume 25oC unless otherwise stated in a problem.

Autoionization of Water

By definition:

Neutral solution: [H+ ] = [OH- ]

Acidic solution: [H+ ] > [OH- ]

Basic solution: [H+ ] < [OH- ]

Autoionization of Water

Example: Calculate the [H+ ] and [OH- ] in a neutral solution at 25oC.

Autoionization of Water

Example: What is the [H+ ] at 25oC for a solution in which [OH- ] = 0.010 M.

Autoionization of Water

Example: What is the [OH- ] at 25oC in a solution in which [H+ ] = 2.5 x 10-6 M.

pH

Since the [H+] is usually very small in aqueous solutions, we normally express the [H+] in terms of pH.

pH = - log10 [H+]

Sig Figs and logs: only the digits after the decimal point are significant.

pH

Example: Calculate the pH of a solution with [H+] = 2.52 x 10-5.

pH

Example: Calculate the pH of a solution with [OH-] = 6.5 x 10-5.

pH

The negative log is also used to express the magnitude of other small quantities:

pOH = - log [OH- ]

pH and pOH are related by the following equation that is derived by taking the negative log of the expression for Kw

pH + pOH = 14.00 at 25oC

pH

Example: Calculate the pOH of a solution with [OH - ] = 2.5 x 10-3 M.

pH

Example: Calculate the pH of a solution with [OH - ] = 2.5 x 10-3 M.

Approach 1:

pH

Approach # 2:

pH

Given the pH of a solution, you can also find the [H+] and the [OH-].

Since pH = - log [H+],

[H+] = 10 –pH

Since pOH = - log [OH-],

[OH-] = 10 -pOH

pH

Example: What are the [H+] and [OH-] for a solution with a pH of 2.50 at 25oC?

Strong Acids

Strong acid:Strong electrolyteIonizes completely in aqueous solution

HNO3 (aq) H + (aq) + NO3 – (aq)

The only significant source of H+ ion in an aqueous solution of a strong acid is usually the strong acid.

HNO3 (aq) H + (aq) + NO3 – (aq)

In a 0.05 M HNO3 (aq) solution,

[H+] = 0.05 mol HNO3 x 1 mol H+ = 0.05 ML 1 mol HNO3

Strong Acids

Consequently, the [H+] in a solution of a strong monoprotic acid can be determined easily using the concentration of the strong acid itself.

Strong Acids

Example: What is the pH of a 0.25 M HCl (aq) solution?

Strong Bases

Strong Basestrong electrolyte ionizes completely in aqueous solution

NaOH (aq) Na+ (aq) + OH- (aq)

Common strong basesalkali metal hydroxideshydroxides of Ca, Sr, and Ba

Strong Bases

The pH of an aqueous solution of a strong base can be determined using the concentration of the strong base

NaOH (aq) Na+ (aq) + OH- (aq)

A 0.25 M solution of NaOH has an [OH-] of 0.25 M:

0.25 mol NaOH x 1 mol OH- = 0.25 ML 1 mol NaOH

Strong Bases

The pH of the base solution can then be found in two ways:

Calculate pOH use pH + pOH = 14.00 to determine pH

Calculate [H+]use [H+] [OH-] = 1.00 x 10-14

Then calculate pH

Step 1: Determine [OH-]

Strong Bases

Example: Calculate the pH of a 0.25 M Ca(OH)2 (aq) solution.

Step 1: Determine [OH-]

Strong Bases

Step 2: Calculate pOH

Step 3: Calculate pH

Strong Bases

Example: What is the pH of a solution prepared by mixing 10.0 mL of 0.015 M Ba(OH)2 and 30.0 mL of 7.5 x 10-3 M NaOH?

Strong Bases

Step 1: Find the total [OH-]

Strong Bases

Step 2: Find pOH

Step 3: Find pH

Weak Acids

Most acidic substances are weak acids:partially ionize in solutionthe solution contains an equilibrium

mixture of acid molecules and its component ions

CH3CO2H H+ (aq) + CH3CO2

- (aq)

Weak Acids

The extent to which a weak acid ionizes can be expressed using an equilibrium constant known as the acid-dissociation constant (Ka).

For a general reaction:HX (aq) H+ (aq) + X- (aq)

Ka = [H+][X-]

[HX]

Note: The rules for writing an expression for Ka are the same as those for Kc, Kp and Ksp.

Weak Acids

The magnitude of Ka indicates the tendency of the hydrogen ion in an acid to ionize.

The larger the value of Ka, the stronger the acid is.

The pH of a weak acid solution can be calculated using the initial concentration of the weak acid and its Ka.

Weak Acids

To calculate the pH of a weak acid solution:Write the ionization equilibrium for

the acid.Write the equilibrium constant

expression and its numerical value.Set up a table showing initial

concentration, change, equilibrium concentration.

Substitute equilibrium concentrations into the equilibrium constant expression.

Weak Acids

To calculate the pH of a weak acid solution (cont):Solve for the change in concentration.

Assume that the change in concentration is small (i.e. < 5%) compared to the initial concentration of the weak acid.

Check the validity of previous assumptions.If x/initial concentration x 100% >5.0%, you

must use the quadratic equation to solve for x.

Calculate the final concentrations and pH.

Weak Acids

Example: Calculate the pH of a 0.20 M solution of HCN. Ka = 4.9 x 10-10

Step 1: Write the equation for the ionization.

Step 2: Write the expression for Ka.

Weak Acids

Step 3: Set up a table.

Weak Acids

Step 4: Substitute equilibrium concentrations into the Ka expression.

Step 5: Assume that x << 0.20 M and solve for x.

Weak Acids

Step 6: Check the validity of our assumption.

Weak Acids

Step 7: Substitute value for x into the table to find the [H+].

Weak Acids

Step 8: Calculate the pH using the [H+]

Weak Bases

Many substances behave as weak bases in water.

Weak base + H2O conjugate acid + OH-

The extent to which a weak base reacts with water to form its conjugate acid and OH- ion can be expressed using an equilibrium constant known as the base-dissociation constant (Kb).

Weak Bases

Kb always refers to the equilibrium in which a base reacts with water to form its conjugate acid and OH- ion.

For the reaction:

NH3 (aq) + H2O (l) NH4+ (aq) + OH-

(aq)

Kb = [NH4+] [OH-]

[NH3]

Note: The rules for writing an expression for Kb are the same as those for Kc, Kp and Ksp.

Weak Base

To calculate the pH of a weak base solution:Write the ionization equilibrium for

the base.Write the equilibrium constant

expression and its numerical value.Set up a table showing initial

concentration, change, equilibrium concentration.

Substitute equilibrium concentrations into the equilibrium constant expression.

Weak Bases

To calculate the pH of a weak base solution (cont):Solve for the change in concentration.

Assume that the change in concentration is small (i.e. < 5%) compared to the initial concentration of the weak base.

Check the validity of previous assumption.

Calculate the [OH-] concentration and pOH

Use pOH to calculate pH.

Weak Bases

Example: Calculate the pH of a 0.20 M solution of methylamine, CH3NH2. Kb = 3.6 x 10-4.

Step 1: Write the equation for the ionization.

Step 2: Write the expression for Kb.

Weak Bases

Step 3: Set up a table.

Weak Bases

Step 4: Substitute equilibrium concentrations into the Kb expression.

Step 5: Assume that x << 0.20 M and solve for x.

Weak Bases

Step 6: Check the validity of our assumption.

Weak Bases

Step 7: Substitute value for x into the table to find the [OH-].

Weak Acids

Step 8: Calculate the pOH

Step 9: Calculate the pH