Recall, that water is amphoteric. That is, it can act as both an acid and a base.

HA + H2O(l) H3O+(aq) + A¯(aq)

or

B + H2O(l) BH+(aq) + OH¯(aq)

Very sensitive instruments have shown that pure water actually dissociates into ions, or ionizes, slightly. We call this process self-ionization or autoionization.

The equation for self-ionization is written as:

H2O(l) + H2O(l) H3O+(aq) + OH¯(aq)

or

H2O(l) H+(aq) + OH¯(aq)

This indicates there is an equilibrium established between hydronium and hydroxide ions.

Ion Product of Water  If an equilibrium is established between hydronium ions, hydroxide ions and water molecules, an equilibrium law can be written:

Ionization of Water  

Since water is a liquid, the product of Ka and water results in the ion product for water, Kw. The equilibrium law for water becomes:

KW = [H3O+][OH¯]

At 25°C, the concentration of the hydronium and hydroxide ions are equal at 1.0 x 10-7 mol/L.

Therefore, at 25°C, the value of KW is constant at 1.0 x 10-14.

Acidic and Basic Solutions  If the ionization of water occurs by the equation

H2O(l) + H2O(l) H3O+(aq) + OH¯(aq)

we can predict the effect of dissolving an acid or base on hydronium and hydroxide ion concentrations by using Le Chatelier's Principle.

Adding Acid

When an acid is dissolved in water, the acid produces a large amount of H3O+ ions. If the H3O+ ion concentration increases, the equilibrium will shift to the left to use up some of the added hydronium and maintain Kw at 1.0 x 10-14.

Since equilibrium shifts left, the hydroxide ion concentration is reduced. Therefore, adding a strong acid to water increases the hydronium ion concentration and reduces the hydroxide ion

concentration.

Adding Base

When a base is dissolved in water, the hydroxide ion concentration increases. According to Le Chatelier's Principle, the equilibrium shifts left to use up some of the added hydroxide and maintain KW at 1.0 x 10-14.

Since equilibrium shifts left, the hydronium ion concentration is reduced. Therefore, adding a strong base to water increases the hydroxide ion concentration and reduces the hydronium ion concentration.

Calculating Hydroxide Ion Concentration  Example 1

If 2.5 moles of hydrochloric acid is dissolved in 5.0 L of water, what is the concentration of the hydroxide ions? Assume the volume remains unchanged.

Solution

If 2.5 moles is dissolved in 5.0 L, the concentration of the HCl would be

Since HCl is a strong acid, the [H3O+] = 0.50 mol/L.

Use the equilibrium law for water, Kw, to find the concentration of the hydroxide ion:

Calculating Hydronium Ion Concentration  Example 2

O.40 g of NaOH is dissolved in water to make a solution with a volume of 1.0 L. What is the hydronium ion concentration in this solution?

Solution

First calculate the number of moles of NaOH:

NaOH = 40.0 g/mol

Since NaOH is a strong base, [OH¯] = [NaOH] = 0.010 mol/L

Substitute into the equilibrium law and solve for hydronium ion concentration:

Kw Problems

1. The [H3O+] in a nitric acid solution is 0.0020M. Write the equation for the dissociation of nitric acid. What is the [OH-]?

2. The [OH-]in a sodium hydroxide solution is 0.050M. Write the equation for the dissociation of sodium hydroxide. What is the [H3O+]?

3. 0.25 mol of hydrogen chlorine gas is dissolved in 2.0L of solution. Write the equation for the dissociation of the gas. Calculate [H3O+] and [OH-].

4. 10.0g of lithium hydroxide is dissolved in 750ml of solution. Write the dissociation equation and calculate [H3O+] and [OH-].

5. 10.0g calcium hydroxide is dissolved in 400ml of solution. Write the equation for the dissociation and calculate [H3O+] and [OH-].

6. If the [H3O+] of a barium hydroxide solution is 1.0 x 10-13 M. Write the dissociation equation for barium hydroxide. Calculate the [OH-]. How many moles of barium hydroxide must have been dissolved per liter?

7. Calculate the [H3O+] found in milk of magnesia that has an [OH-] = 1.43 x 10-4 mol/L.

We already know that in an acidic solution, [H3O+] is greater than [OH¯]. In an alkaline or basic solution, [OH¯] is greater than [H3O+]. If a solution is neutral, that is in pure water, hydronium and hydroxide ion concentrations are equal.

Most solutions chemists use have a very small hydronium ion concentration. For example, if you have a swimming pool, you must keep the hydronium ion concentration at around 4 x 10-8 mol/L, about the same as in blood. Even stomach acid is only about 0.01 mol/L HCl.

As you can see, using concentration values of hydronium ions or hydroxide ions to describe the acidity or alkalinity of a solution can be quite cumbersome.

In 1909, a Danish chemist, named Soren Sorensen (1868 - 1939), developed a simplified system for referring to the degree of acidity of a solution. He used the pH or the potenz (power) of hydrogen. Therefore, pH describes the concentration of the hydronium or hydrogen ions in solution.

pH is defined as the negative logarithm of the hydronium ion concentration, or

pH = -log[H3O+] or pH = -log[H+]

(We will use the H3O+ion and H+ ion interchangeably.)

Similarly, pOH is defined as the negative logarithm of the hydroxide ion concentration, or

pOH = -log[OH¯]The pH Scale

Defining pH

 Values for pH in most solutions range from 0.0 to 14.0. Pure water is considered to be neutral, or a pH of 7.0. The lower the pH, the more acidic the solution. The higher the pH the more alkaline or basic the solution.

pH < 7 acidic

pH = 7 neutral

pH > 7 basic(alkaline)Below is a pH scale with the pH values of some common solutions.

pH Calculations  Example 1

Calculate the pH of an HCl solution whose concentration is 5.0 x 10-6 mol/L.

Solution

Since HCl is a strong acid, it ionizes 100%. Therefore the concentration of the HCl is equal to the hydronium ion concentration.

pH = -log[H3O+]

pH = -log(5.0 x 10-6)

pH = -(-5.30) = 5.30

Calculate the log of the [H3O+] then use the change of sign button to get the negative log.

We will round the log to two decimal places.

Example 2

The pH of a solution is 3.25. Calculate the hydronium ion concentration in the solution.

Solution

[H3O+] = 10-pH

[H3O+] = 10-3.25

[H3O+] = 5.6 x 10-4 mol/L

pOH Recall, the ion product for water:

KW = [H3O+][OH¯]

If we take the negative log of each term, we get

-log(kW) = pH + pOH

According to the rules of logs, when multiplying terms is equivalent to adding their logs.

If we calculate the negative log kW, -log(kW) = -log(1.0 x 10-

14) = 14.00

pH + pOH = 14.00pOH Calculations  

Example 3

The pH of a solution is 10.30, what is the hydroxide ion concentration?

Solution

From the previous page,

pOH = 14.00 - pH

pOH = 14.00 - 10.30 = 3.70

[OH¯] = 10-pOH

[OH¯] = 10-3.70

[OH¯] = 2.0 x 10-4 mol/L

Just as we did with the pH, we can determine [OH¯].

 Example 4

What is the pH of a 5.0 x 10-5 mol/L Mg(OH)2 solution?

 Solution

Mg(OH)2 is a strong base, so it dissociates 100%.

Mg(OH)2(s) Mg2+(s) + 2 OH¯(s)

[OH¯] = 2 x [Mg(OH)2] = 1.0 x 10-4 mol/L

We can calculate the pOH, then subtract from 14 to get the pH.

pOH = -log[OH¯] = -log(1.0 x 10-4) = 4.00

pH = 14.00 - 4.00 = 10.00

Solubility and Solutions

Depending on the amount of solute dissolved in a solvent, differing solutions can result. A solution that has its maximum amount of solute dissolved in it is often referred to as saturated, whereas a solution that can dissolve more solute is unsaturated. Under special circumstances a solution can be made to hold more solute than usual at a specific temperature, this type of solution is known as being super-saturated.

Temperature and Solubility

Increased temperature generally increases the solubility of a substance in water, with the exception of gases.

When solids dissolve in liquids the process is endothermic.

I2 (s) I2 (aq) ∆H = + 1.6 kJ

For gases dissolving in liquids the dissolving process is exothermic.

O2 (g) O2 (aq) ∆H = - 3.0 kJ

Therefore, an increase in temperature results in less material being dissolved.

E.g. Carbon Dioxide in water (Soda pop)

Pressure and Solubility

Pressure has little effect on solutions, except if the solute is a gas. An increase in pressure will increase the solubility of a gas in a solvent.

E.g. Carbon Dioxide in water (Soda pop)

At low temperatures liquids can dissolve a greater mass of gas than at higher temperatures. Cold liquids have less collisions between the solvent and solute, that take place at higher temperatures.

At high temperatures the gas/liquid solution collide with increased frequency and energy. Energy transfers through collisions, may be enough to allow individual atoms to escape from the solution into the gas state.

Sealed containers containing a gas solution reach and equilibrium between the liquid and gas state.

Reading a Solubility Chart

1) The curve shows the # of grams of solute in a saturated solution containing 100 mL or 100 g of water at a certain temperature.

2) Any amount of solute below the line indicates the solution is unsaturated at a certain temperature

3) Any amount of solute above the line in which all of the solute has dissolved shows the solution is supersaturated.

4) If the amount of solute is above the line but has not all dissolved, the solution is saturated and the # grams of solute settled on the bottom of the container = total # g in solution – # g of a saturated solution at that temperature. (according to the curve)

5) Solutes whose curves move upward w/ increased temperature are typically solids b/c the solubility of solids increases w/ increased temperature.

6) Solutes whose curves move downward w/ increased temperature are typically gases b/c the solubility of gases decreases withincreased temperature.

0 10 20 30 40 50 60 70 80 90 100

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

Solubility Curves of Pure Substances

Temperature/Celsuis

gram

s so

lute

per

100

gra

ms

H2O

KI

NaNO3

KNO3

Ce2(SO4)3

NH3

KClO3

NH4Cl

KClNaCl

Assignment 2