Daniel L. RegerScott R. GoodeDavid W. Ball
www.cengage.com/chemistry/reger
Chapter 15Solutions of
Acids and Bases
• Acid: a substance that produces H3O+ when dissolved in water.
• Base: a substance that produces OH- when dissolved in water.
• Arrhenius acids and bases are limited to water solutions.
Arrhenius Acids and Bases
• Acid: proton donor.• Base: proton acceptor.• Bronsted-Lowry acid base
reaction: proton transfer from acid to base.
Bronsted-Lowry Acids and Bases style
• Conjugate Acid-Base Pairs: two species that differ by a proton.
• Acid : the species that contains the proton that is transferred.
• Conjugate base: the species formed by loss of the proton.HF(aq) + H2O(l) ⇌ F-(aq) + H3O
+(aq)
• HF and F- make up an acid-base conjugate pair. F- is the conjugate base of HF.
Conjugate Acid-Base Pairs
• HF(aq) + H2O(l) ⇌ F-(aq) + H3O+(aq)
HF is the acid, F- is its conjugate base(or F- is a base and HF is its conjugate acid).
• The reverse reaction is F-(aq) + H3O
+(aq) ⇌ HF(aq) + H2O(l) H3O+ is the acid, H2O is its conjugate base.
Acid-Base Conjugate Pairs
Acid Base
HCl Cl -
H2SO4 HSO4-
HSO4- SO4
2-
NH4+ NH3
H3O+ H2O
H2O OH-
H2O is amphoteric - it acts as both an acid and a base.
Acid-Base Conjugate Pairs
• An Arrhenius systemacid + base water + salt
is limited to reactions in water.
• A Bronsted-Lowry system
HA + B ⇌ A- + BH+
is more general - a proton is transferred from the acid (HA) to the base (B).
Acid-Base Reactions
acid + base ⇌ conj. base + conj. acid
HF + NH3 ⇌ F- + NH4+
HCl + H2O ⇌ Cl- + H3O+
H2O + NH2- ⇌ OH- + NH3
Bronsted-Lowry Acid-Base Reactions
HCN(aq) + H2O(l) ⇌ H3O+(aq) + CN-(aq) HCN is the acid, CN- is its conjugate base.
H2O is the base, H3O+ is its conjugate acid.
CH3COO-(aq)+H2O(l) ⇌ CH3COOH(aq)+OH-(aq) CH3COO- is the base, CH3COOH is its conjugate acid. H2O is the acid, OH- is its conjugate base.
Identifying Conjugate Pairs
Identify the acid-base conjugate pairs
HNO2(aq) + H2O(l) ⇌ H3O+(aq) + NO2-(aq)
CH3NH2(aq) + H2O(l) ⇌ CH3NH3+(aq) + OH-(aq)
Test Your Skill
H2O(l) + H2O(l) ⇌ H3O+(aq) + OH-(aq)
• H3O+ and H2O are a conjugate acid-base pair.
• H2O and OH - are a conjugate acid-base pair.
Autoionization of Water
H2O(l) + H2O(l) ⇌ H3O+(aq) + OH-(aq)
• The equilibrium constant for this reaction is called Kw.
• Kw = [H3O+][OH -]
• Kw changes with temperature and is equal to 1.0 × 10-14 at 25o C.
Autoionization of Water
H2O(l) + H2O(l) ⇌ H3O+(aq) + OH-(aq)
• In pure water, [H3O+] = [OH -].
Kw = [H3O+][OH -] = 1.0 × 10-14
Kw = [H3O+]2 = 1.0 × 10-14
• [H3O+] = [OH -] = 1.0 × 10-7 M
Calculating Hydrogen and Hydroxide Ion Concentrations
• Adding an acid or a base to water causes the H3O+ and OH- concentrations to change.
• Calculate the hydroxide ion concentration of a solution in which the hydrogen ion concentration is 3.6 × 10-3 M.
Acidic or Basic Solutions
• Calculate the hydrogen ion concentration in a solution in which the hydroxide ion concentration is 0.025 M.
Test Your Skill
• pH = -log10[H3O+]Calculate the pH of a 0.0034 M solution of [H3O+].
• pH = -log(0.0034) = 2.47• pH values are generally given to two
decimal places. A pH of 2.47 has two significant figures; the 2 serves to locate the decimal point of the original number.
pH Scale
• Calculate the hydrogen ion concentration in a solution that has a pH of 3.52.
Calculating Hydrogen Ion Concentration from pH
• The p-notation can be used for other quantities.
• pOH = -log[OH-]
• pKw = -log Kw = -log(1.0 × 10-14) = 14.00
p-notation
[H3O+][OH-] = Kw = 1.0 × 10-
14
log([H3O+][OH-]) = log Kw
log[H3O+] + log[OH-] = log Kw
-log[H3O+] - log[OH-] = -log Kw
pH + pOH = pKw
pH + pOH = 14.00
Relating pH and pOH
pH + pOH = 14.00
Acid Neutral Base
pH <7 =7 >7
pOH >7 =7 <7
Relating pH and pOH
• HA(aq) + H2O(l) H3O+(aq) +A-(aq)
• Strong acids ionize completely in solution.
• Memorize the six common strong acids: HCl, HBr, HI, HNO3, HClO4, and H2SO4.
100%
Strong Acids and Bases
• Calculate the pH of a 0.050 M HCl solution.
pH of a Strong Acid Solution
• Strong bases quantitatively produce hydroxide ions in water.
• The most common strong bases are the group IA and soluble IIA oxides and hydroxides.
Strong Bases
NaOH(s) Na+(aq) + OH-(aq)
Li2O(s) + H2O(l) 2Li+(aq) + 2OH-(aq)
Strong Bases
• Calculate the pH of a 0.035 M Ba(OH)2 solution.
pH of a Strong Base Solution
What is the concentration of a solution of HCl if the pH is 3.75?
What is the concentration of a solution of KOH if the pH is 11.60?
Test Your Skill
• Weak acids and weak bases are those that do not ionize completely in water.
• A weak acid exists in equilibrium with its conjugate base.HCN(aq) + H2O(l) ⇌ H3O+(aq) + CN-(aq)
• A weak base exists in equilibrium with its conjugate acid.
CH3NH2 (aq) + H2O(l) ⇌ CH3NH3
+(aq) + OH-(aq)
Weak Acids and Bases
• HA(aq) + H2O(l) ⇌ H3O+(aq) + A-(aq)
• B(aq) + H2O ⇌ BH+(aq) + OH-(aq)
[HA]
]][AO[H3
aK
[B]
]][OH[BH bK
Weak Acids and Bases
HA(aq) + H2O(l) ⇌ H3O+(aq) + A-(aq)
• Both H2O and A- are bases and compete for the proton.
• If HA is a strong acid, A- is an extremely poor proton acceptor.
HCl(aq) + H2O(l) → H3O+(aq) + Cl-(aq)
Proton bonded to Cl-
Proton bonded to H3O+
Competition for Protons
HA(aq) + H2O(l) ⇌ H3O+(aq) + A-(aq)
• If HA is a weak acid, A- is a weak base.• The stronger the weak acid, the weaker
the conjugate base.
HF(aq) + H2O ⇌ H3O+(aq) + F-(aq)
Proton bonded to F-
Proton bonded to H3O+
Competition for Protons
• Leveling Effect: In water, all acids stronger than H3O+ appear to be equally strong. By using a weaker base than water as the solvent, we can differentiate between the strong acids.
weakest strongest | |HNO3 < H2SO4 < HCl < HBr < HI < HClO4
The Influence of the Solvent
• Analytical Concentration: the total concentration of all forms of an acid; both the protonated form (the acid) and the unprotonated form (the conjugate base).
The Concentration of an Acid
• You will likely see two kinds of equilibrium calculations:
1. You measure equilibrium concentrations and calculate K or
2. you are given starting concentrations and K and calculate equilibrium concentrations.
• The approach is the same.
1. Write the balanced chemical equation.
2. Calculate equilibrium concentrations/iCe table.
3. Write the algebraic expression for K.
4. Substitute concentrations into expression.
5. Solve.
Equilibrium Calculations
• A 0.250 M solution of HF is determined to be 3.7% ionized. Determine Ka for HF.
Calculating Ka for a Weak Acid
• The pH of a 0.100 M solution of HOCl is 4.26. Calculate Ka for the acid.
HOCl + H2O ⇌ H3O+ + OCl-
Determining Ka from pH
• Calculate the pH of a 0.50 M
CH3COOH solution. Ka = 1.8 × 10-5
CH3COOH + H2O ⇌ H3O+ + CH3COO-
Determining Concentrations of Species in Weak Acid Solution
• Determine the pH of a 0.025 M solution of HCN, Ka = 7.2 × 10-10.
Test Your Skill
• Calculate the equilibrium concentrations and pH of a 0.100 M HF solution, Ka = 6.3 × 10-4. Use approximation.
Calculating pH of a Weak Acid Solution
• Is 7.9 10-3 << 0.050?• No, it is not. 5% of 0.050 is 2.5 10-3
and the calculated value is larger. The approximation fails.
• We need another method to compute the root.
Check Approximation
3-2
5-22
3-
224
1
224
2.
-31
106.7
1080.5
109.7100.0
)(103.6
100.0
))((103.6
. value,new a
calculate to ionapproximat an as it use and
107.9 value first the Call
y
y
y
y
yy
y
y
Successive Approximation
• Is y2 sufficiently close to y1?
• Restating the question, is 7.6 10-3 within 5% of 7.9 10-3?
• By within 5%, we mean is 7.6 10-3 within a range varying from 95% to 105% of 7.9 10-3?
• The answer is yes. Since the second approximation was quite close to the first, we can accept it.
Check Second Approximation
HA(aq) + H2O(l) ⇌ H3O+(aq) + A-(aq)
HA of ionconcentrat nalytical
]O[H
][A [HA]
][A ionized fraction
3
-
-
a
Fraction Ionized in Solution
• Calculate fraction ionized for 0.500 M HOCl, Ka = 4.0 × 10-8.
• HOCl + H2O ⇌ H3O+ + OCl-
Fraction Ionized in Solution
• A weak base reacts with water to form hydroxide ions.
B(aq) + H2O(l) ⇌ BH+(aq) + OH-(aq)
[B]
]][OH[BH bK
Solutions of Weak Bases
CH3NH2 + H2O ⇌ CH3NH3+ + OH-
Calculate the pH of a solution of 0.150 M methylamine, CH3NH2, Kb = 4.4 × 10-4.
pH of a Solution of a Weak Base
• Calculate the pH of a 0.35 M solution of hydroxylamine, NH2OH, Kb = 1.1 × 10-8.
Test Your Skill
HA(aq) + H2O(l) ⇌ H3O+(aq) + A-(aq)
A-(aq) + H2O(l) ⇌ HA(aq) + OH-(aq)
[HA]
]][AO[H3a
K
][A
][HA][OH-b
K
Relating Ka and Kb
wKKK
KK
KK
ba
3ba
-3
ba
]][OHO[H
][A
][HA][OH
[HA]
]][AO[H
Relating Ka and Kb
• The conjugate base of a weak acid is a weak base:
CH3COOH + H2O ⇌ H3O+ + CH3COO- Ka = 1.8 × 10-5
CH3COO- + H2O ⇌ CH3COOH + OH- Kb = 5.6 × 10-10
HCN + H2O ⇌ H3O+ + CN- Ka = 6.2 × 10-10
CN- + H2O ⇌ HCN + OH- Kb = 1.6 × 10-5
Strengths of Weak Acid-Base Conjugate Pairs
• Ka for HNO2 is 4.6 x 10-4. Calculate Kb for the NO2
- ion. NO2
-(aq) + H2O(l) ⇌ HNO2(aq) + OH-(aq)
Calculating Ka and Kb for Acid-Base Conjugate Pairs
• Kb for pyridine is 1.8 × 10-9. Calculate Ka for the pyridinium ion.
Test Your Skill
Kb = 2.8 x 10-11 Kb = 1.4 x 10-5
Ka = 7.2 x 10-10 Ka = 3.5 x 10-4
acidStronger
acid
HCN HF
Weaker
baseStrongerWeaker
CN-F-
base
Ranking Acid-Base Strength
• The stronger the acid, the weaker the conjugate base.
• strong acid very weak conjugate base
• strong base very weak conjugate acid
• weak acid weak conjugate base
Conjugate Partners of Strong Acids and Bases
• The pH of a salt solution is =7 (neutral) if it contains the cation of a strong
base (Na+) and the anion of a strong acid (Cl-) >7 (basic) if it contains the cation of a strong
base (K+) and the anion of a weak acid (F-) <7 (acidic) if it contains the cation of a weak
base (NH4+) and the anion of a strong acid
(NO3-).
pH of Salt Solutions
• Determine the pH of a 0.59 M solution of CH3OONa. Ka of CH3OOH = 1.8 × 10-5.
CH3OO-(aq) + H2O(l) ⇌ CH3OOH(aq) + OH-(aq)
• The acetate ion is a base. Calculate Kb for the acetate ion:
The pH of a Salt Solution
• When two or more acids are present in solution, the effects of the weaker acids may be ignored if Ka is smaller by a factor of 100 or more.
Mixtures of Acids
• To calculate the pH of a mixture of HCl (strong acid) and HOCl (Ka = 3.0 × 10-8), ignore the HOCl; treat the solution as a solution of HCl.
• To calculate the pH of a mixture of HCOOH (Ka = 1.8 × 10-4) and HCN (Ka = 7.2 × 10-10), ignore the HCN; treat the solution as a solution of HCOOH.
Mixtures of Acids
• Binary hydrides contain hydrogen and one other element.
• Acidity depends on the HA bond strength and the stability of A-.
Binary Hydrides
• Acidity increases with decreasing H-A bond dissociation energy
HF << HCl < HBr < HI
568.2 431.9 366.1 298.3 kJ/mol
Binary Hydrides
• Acidity increases with increasing electronegativity of A.
CH4 < NH3 < H2O < HF
2.5 3.0 3.5 4.0
Binary Hydrides
• Oxyacids contain H, O, and a third element X.
X–O–H• X is usually a non-metal or a
transition metal in a high oxidation state.
Oxyacids
• As the electronegativity of X increases, the X-O bond becomes more covalent and the O-H bond becomes more polar.
X–O–H X–O- + H+
Oxyacids
• Two factors increase acidity of the oxyacid: Greater electronegativity of central
atom.
HClO4 > HBrO4
Greater oxidation number of central atom (more oxygen atoms).
HClO4 > HClO3 > HClO2 > HClO
Oxyacids
• Lewis acid: electron pair acceptor.• Lewis base: electron pair donor.• Lewis acid-base reaction: formation
of a coordinate-covalent bond.
AlCl3 + Cl- AlCl4-
• Coordinate-covalent bond: covalent bond in which both electrons come from one atom.
Lewis Acids and Bases