1. Equilibrium in Acid-Base Systems
Chapter 16

2. The Water Ionization Constant, Kw
Water is in a liquid state, so we eliminate it from the equilibrium expression.

3. H2O(l) + H2O(l) H3O+(aq) + OH-(aq)
Water Ionization constant (Kw)
Pure water has a slight conductivity. This is because water has the ability to self ionize; however, ionization only occurs 10-6 % of the time. This means that only about one molecule in a billion ionizes. Subsequently, the reaction greatly favors the reactants under SATP conditions.
As a result, water does not conduct a measurable current since there are so few ions in present. A current will only be detected if very sensitive instruments are used.
10-6 %
H2O(l) + H2O(l) H3O+(aq) + OH-(aq)

4. Kw is the ionization constant for water.
In a neutral solution, [H3O+(aq)] = [OH–(aq)], so:
[ H3O+(aq) ] = 1×10–7 mol/L
neutral solution:
[ H3O+(aq) ] > 1×10–7 mol/L
acidic solution:
[ H3O+(aq) ] < 1×10–7 mol/L
basic solution:

5. Relating ionization of water to modified Arrhenius theory
In chemistry 20 you learned that according to the modified Arrhenius theory:
An acid is a substance that reacts with water to form hydronium ions, thus increasing the hydronium ion concentration and making the solution more acidic
Example: H2SO4(aq) + H2O(l)  H3O+(aq) + HSO4-(aq)
A base is a substance that reacts with water to form hydroxide ions, thus increasing the hydroxide ion concentration and making the solution more basic.
Hydroxide ions are formed either by:
Dissociation of an ionic hydroxide (a strong base)
Example: NaOH(s)  Na+ (aq) + OH-(aq)
NOTE: There is no need to include water- it is indicated in the reaction by stating that the resulting ions are in an aqueous state.
A partial reaction of a weak basic entity with water to form the hydroxide ion.
Example: NH3(aq) + H2O(aq)  NH4 +(aq) + OH-(aq)

6. HCl(aq) + H2O(l)  H3O+(aq) + Cl-(aq)
0.15 mol/L mol/L
Kw = [H3O + (aq)] [OH- (aq)]
[OH-(aq)]= Kw = 1.0 x10 -14
[H3O+(aq)] mol/L
[OH-(aq)] = 6.7 x mol/L
The low concentration of hydroxide ions indicates an ACIDIC SOLUTION

7. Ba(OH)2(s)  Ba 2+(aq) + 2OH-(aq)
0.25 mol/L
0.25 mol/L Ba(OH)2(s) x 2 OH-(aq) = 0.50 mol/L OH-(aq)
1 Ba(OH)2(s)
Kw = [H3O + (aq)] [OH- (aq)]
[H3O+(aq)]= Kw = 1.0 x10 -14
[OH-(aq)] mol/L
[H3O+(aq)] = 2.0x mol/L
The low concentration of hydronium ions indicates a BASIC SOLUTION

8. NaOH(s)  Na +(aq) + OH-(aq)
n = m = g = mol c = n = 0.065mol = mol/L
M g/mol V L
NaOH(s)  Na +(aq) + OH-(aq)
0.13 mol/L
0.13 mol/L NaOH x 1 OH-(aq) = 0.13 mol/L OH-(aq)
1 NaOH
Kw = [H3O + (aq)] [OH- (aq)]
[H3O+(aq)] = Kw = 1.0 x10 -14
[OH-(aq)] mol/L
[H3O+(aq)] = 7.7 x mol/L

9. Communicating concentration in terms of pH
A simple system for communicating hydronium ion concentration is the pH scale.
pH refers to the power of hydrogen (hydronium) ions and is a measure of the activity of hydrogen (hydronium) ions in a solution and, therefore, its acidity.
A pH value is a number without units, ranging between 0 and 14. Note that pH values can, though not often, exceed this range.

10. # of SIG DIGS for the concentration = # decimal places of the pH
Communicating concentration in terms of pH
To convert a hydronium ion concentration to pH, use the following formula: 
pH= -log[H3O+(aq)]
To convert pH to the concentration of hydronium ions, use the following formula:
[H3O+(aq)] = antilog (-pH)
= 10 –pH
NOTE: antilog = second function log on your calculator 
SINGNIFICANT DIGITS
 To determine the number of significant digits, use the following rule.
# of SIG DIGS for the concentration = # decimal places of the pH

11. Measuring pH – the pH meter
A pH meter is a device that measures the concentration of the hydronium ion using an electrochemical cell. A pH meter does this by measuring the potential difference (voltage) between a pH probe placed in a solution containing hydronium ions and a reference half cell. The reduction potential difference is then converted into a pH reading which is displayed; making this method of determining pH much more specific than litmus paper. A pH meter gives an exact pH whereas litmus paper provides a range of pH’s for a solution.

12. Communicating concentration in terms of pOH
Sometimes it is more convenient to express alkalinity use pOH
pOH refers to the power of the hydroxide ion and is a measure of the activity of the hydroxide ion in a solution and therefore, its alkalinity.
The pOH value is also a number without units, between 0 and 14.

13. # of SIG DIGS for the concentration = # decimal places of the pOH
Communicating concentration in terms of pOH
To convert a hydroxide ion concentration to pOH, use the following formula: 
pOH= -log[OH-(aq)]
To convert pOH to the concentration of hydroxide ions, use the following formula:
[OH- (aq)] = antilog (-pOH)
= 10 –pOH
NOTE: antilog = second function log on your calculator 
SINGNIFICANT DIGITS
 To determine the number of significant digits, use the following rule.
# of SIG DIGS for the concentration = # decimal places of the pOH

14. Relationship between pH and pOH
Since pH and pOH are based on scientific notation and logarithms, one is able to express pH and pOH using a simple mathematical relationship:
pH + pOH = (at SATP)
(see textbook for derivation of formula using the rules of logarithms – p.717)

15. Communicating Concentrations: pH and pOH
pH = −log [ H3O+(aq) ]
[ H3O+(aq) ] = 10−pH
pOH = −log [ OH−(aq) ]
[ OH−(aq) ] = 10−pOH
pOH + pH = 14
Kw = [H3O + (aq)] [OH- (aq)] = 1.0 x 10-14

16. Sample Problems
For each of the following determine the pH and the pOH of the solution.
1a. A hydrochloric acid solution has a hydronium ion concentration of 0.15 mol/L.
pH = 0.82
pOH = 14 – 0.82 = 13.18
1b. A barium hydroxide solution has a hydronium ion concentration of 2.0 x mol/L
pH = 13.70
pOH = = 0.30

17. Sample Diploma Question
Sour pickles have a pH of about The concentration of hydroxide ions is:
1.0 x mol/L
3.0 x mol/L
1.0 x mol/L
3.0 x mol/L
pOH = 14 – 3 = 11; [OH-] = antilog - pOH

18. (Record your three digit answer in the space provided)
Sample Diploma Question
The concentration of hydrogen(hydronium) ions in a bottle of wine is 3.2 x mol/L. The pH of the wine is
(Record your three digit answer in the space provided)

19. Sample Diploma Question
A cleaning agent has a pH of 1 and a carbonated beverage has a pH of 5. The cleaning agent is more acidic than the carbonated beverage by a factor of:
10 000
1 000
100 10

20. ClO-(aq) + H2O(l)  HClO(aq) + OH-(aq)
Sample Diploma Question
Hot tub owners can control disease causing bacteria and algae by adding solid sodium hypochlorite pellets (NaClO(s)) to the water. This results in the formation of HClO(aq) as represented by the equilibrium
ClO-(aq) + H2O(l)  HClO(aq) + OH-(aq)
Undissociated HClO(aq) effectively kills bacteria and algae. A pH of 7.40 is considered ideal for a hot tub.  
Ideally the water in a hot tub should have a hydrogen ion (hydronium) concentration of:
4.0 x 10-8 mol/L and is basic
2.5 x 10-7 mol/L and is basic
4.0 x 10-8 mol/L and is acidic
2.5 x 10-7 mol/L and is acidic

21. Strong Acid  H3O+(aq) + conjugate base
Acid strength as an equilibrium position- defining strong vs. weak
Strong and weak acids are NOT defined by their concentration; they are defined by their ability to ionize.
Theoretically:
A strong acid ionizes quantitatively with water to form a hydronium ion and its conjugate base.
Strong Acid  H3O+(aq) + conjugate base
A weak acid ionizes only partially with water (<50%) to form a hydronium ion and its conjugate base.
<50%
Weak Acid  H3O+(aq) + conjugate base

22. Acid Strength as an Equilibrium Position
A strong acid is explained as an acid that reacts quantitatively with water to form hydronium ions.
e.g. hydrochloric acid
HCl(aq) + H2O(l) → H3O+(aq) + Cl–(aq)
>99% 
A single arrow is used instead of:
A weak acid is explained as an acid that reacts partially with water to form hydronium ions (most less than 50%).
e.g. acetic acid
1.3%
CH3COOH(aq) + H2O(l)  CH3COO-(aq) + H3O+(aq)

23. [strong acid] = [H3O+(aq)]
Strong acids
Strong acids are acids that ionize quantitatively (99-100%) in water to form hydronium ions. As a result:
[strong acid] = [H3O+(aq)]
There are 6 acids that are ordinarily classified as strong. These acids are the first six listed on the relative strengths of acids and bases table in your data booklet.
Example: HCl(aq) + H2O(l)  H30+(aq) + Cl-(aq)
This means that if the concentration of hydrochloric acid is mol/L, the hydronium ion concentration would also be about mol/L due to the percent ionization. As a result, the volume of solution is assumed to be equal to the volume of H2O(l) present.
Since strong acids have more hydronium ions in solution, they exhibit a lower pH and as a result are more acidic.

24. HA(aq) + H2O(l) → H3O+(aq) + A–(aq)
Percent Ionization:
Percent ionization is a way to express acid strength quantitatively.
HA(aq) + H2O(l) → H3O+(aq) + A–(aq)
It relates the concentration of hydronium ions at equilibrium to the original concentration of the acid.

27. Strong vs. Weak Acids- Empirical properties
When comparing strong vs. weak acids of equal concentration, the following differences can be observed.
Strong Acid
Weak Acid
High conductivity (strong electrolyte)
Low conductivity (weak electrolyte)
Fast reaction rate with active metals to produce hydrogen gas
Slow reaction rate with active metals to produce hydrogen gas
Fast reaction rate with carbonates to produce carbon dioxide
Slow reaction rate with carbonates to produce carbon dioxide
pH closer to 0
pH closer to 7

28. Homework: Read pgs. 712 – 720 pgs. 716, 718 Practice #’s 1 – 9
pg. 721 Section 16.1 Questions #’s 1 – 14
Pg. 712 Do lab exercise 16.A