# Chapter 16: Acid-Base Equilibria

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```◆
In the 1st half of this chapter we will focus on the
equilibria that exist in aqueous solutions
containing:
weak acids
polyprotic acids
weak bases
salts
Chapter 16:
Acid-Base Equilibria
◆
use equilibrium tables to determine:
equilibrium composition of solutions
pH
% ionization
Ka or Kb
◆
In the 2nd half of the chapter, our focus will shift to
understanding solutions in which there is some
combination of acidic and basic species:
buffer solutions
titration experiments
◆
◆
We will need to consider that neutralization
reactions can/will occur, as well as the equilibria that
exist.
use multiple steps:
determine the pH of solutions after
neutralization reactions are complete
construct and interpret titration curves
Steps for solving weak acid equilibrium problems:
1. Identify all major species in solution.
2. Identify all potential H+ transfer reactions that
could contribute to the [H3O+]total in the sol’n.
3. By considering K values, determine the dominant
source of H3O+ in the solution.
4. Set up the equilibrium calculation based on
equilibrium identified in step 3.
5. Solve!
+
◆ x = [H3O ]
◆ solve for pH, % ionization, or Ka
example:
Determine the pH of 0.10 M HCN (aq). For HCN,
Ka = 4.9 x 10–10.
1. Identify all major species in solution.
this is an aqueous solution of a weak acid, so the
major species are: HCN & H2O
◆
example:
Determine the pH of 0.10 M HCN (aq). For HCN, Ka = 4.9 x 10–10.
3. By considering K values, determine the dominant source
of H3O+ in the solution.
◆
there are 2 possible sources of H3O+ in this sol’n:
HCN (aq) + H2O (aq) ⇄ CN– (aq) + H3O+ (aq); Ka = 4.9 x 10–10
2 H2O (l) ⇄ H3O+ (aq) + OH– (aq); KW = 1 x 10–14
2. Identify all potential H+ transfer reactions that could
contribute to the [H3O+]total in the sol’n.
◆
Ka > KW, so the acid ionization of HCN will be the
dominant source of H3O+ in his solution.
there are 2 possible sources of H3O+ in this sol’n:
◆
OR
HCN (aq) + H2O (aq) ⇄ CN– (aq) + H3O+ (aq); Ka = 4.9 x 10–10
[H3O+]total = [H3O+]HCN-ionization + [H3O+]H2O-ionization
but we will assume that [H3O+]H2O-ionization is negligibly small
so [H3O+]total ≈ [H3O+]HCN-ionization
2 H2O (l) ⇄ H3O+ (aq) + OH– (aq); KW = 1 x 10–14
example:
Determine the pH of 0.10 M HCN (aq). For HCN, Ka = 4.9 x 10–10.
5. Solve!
4. Set up the equilibrium calculation based on
equilibrium identified in step 3.
HCN (aq) + H2O (l)
⇄ CN– (aq) + H3O+ (aq)
initial [ ]
0.10 M
---
0
0
∆[]
–x
---
+x
+x
---
xM
xM
equil [ ] (0.10–x)M
[H3O+][CN–]
Ka = ––––––––––– ;
[HCN]
4.9 x
10–10
example:
Determine the pH of 0.10 M HCN (aq). For HCN, Ka = 4.9 x 10–10.
x2
= –––––––––
0.10 – x
x = [H3O+]
[H3O+][CN–]
Ka = ––––––––––– ;
[HCN]
◆
4.9 x
10–10
x2
= –––––––––
0.10 – x
use a simplifying approximation
Because Ka is very small, the reaction does not
proceed very far forward (toward products) before
reaching equilibrium.
We will assume that “x” in the denominator will be
negligibly small relative to [HCN]0.
OR
0.10 – x ≈ 0.10
example:
Determine the pH of 0.10 M HCN (aq). For HCN, Ka = 4.9 x 10–10.
solution:
example:
Determine the pH of 0.10 M HCN (aq). For HCN, Ka = 4.9 x 10–10.
◆
x2
x2
4.9 x 10–10 = –––––––––
≈ –––––
0.10 – x
0.10
check the validity of the approximation:
x x 100 < 5%, the approximation is valid
if –––––
[HA]0
x = 7.0 x 10–6
so at equilibrium:
◆
[H3O+] = [CN–] = 7.0 x 10–6 M
7.0 x 10–6 x 100 = 0.007%
––––––––––
0.10
[HCN] = 0.10 M
pH = – log (7.0 x 10–6) = 5.15
∴ the approximation is valid: 0.10 – x ≈ 0.10
Percent Ionization
example:
Determine the pH and % ionization of 0.0100 M
CH3COOH (aq). For acetic acid, Ka = 1.8 x 10–5.
for our example:
◆
What percentage of a weak acid originally present
is in its ionized form at equilibrium?
[HA]ionized
percent ionization = –––––––––– x 100
[HA]0
◆
percent ionization is another way that we can
assess the acidity of a solution and strength of an
acid
greater % ionization ! higher [ion]
higher [ion] ! higher [H3O+]
higher [H3O+] ! lower pH ! more acidic solution
Percent Ionization and Acid Concentration
◆
◆
for a given acid, HA, % ionization will increase
as [HA] decreases
dilution effect - changing concentrations of
species in solution results in Q < K
◆
Some Comparisons
compare 2 solutions of different concentration of acetic
acid (HC2H3O2, Ka = 1.8 x 10–5)
◆
compare 2 solutions of different concentration of
hydrocyanic acid (HCN, Ka = 4.9 x 10–10)
◆
compare acetic acid and hydrocyanic acid solutions of the
same concentration
reaction proceed forward to re-establish
equilibrium
new equilibrium [H3O+] and [A–] are higher
relative to new [HA]0
∴ % ionization is greater
◆
Be careful when comparing solutions and making qualitative
◆
You can compare 2 different acids at the same concentration:
acid with larger Ka is the stronger acid
∴ acid solution with larger Ka will have:
higher [H3O+]
lower pH
higher % dissociation
◆
You can compare the same acid at 2 different concentrations:
Ka is the same, so acid strength is the same
solution with higher concentration will have:
higher [H3O+]
lower pH
lower % dissocation
0.010 M
HC2H3O2
0.025 M
HC2H3O2
0.025 M
HCN
0.10 M
HCN
[H3O+], M
4.2 x 10–4
6.7 x 10–4
3.5 x 10–6
7.0 x 10–6
pH
3.38
3.17
5.46
5.15
%
ionization
4.2%
2.7%
0.014%
0.0070%
Determination of Ka from Experimental Data:
Given [HA]0 and pH
example:
The pH of 0.250 M HF (aq) is 2.036. Determine the
Ka for HF.
Polyprotic Acids
Determination of Ka from Experimental Data:
Given [HA]0 and % Ionization
example:
◆
acid with more than one acidic proton
A 0.340 M solution of HNO2 (aq) is 3.65% dissociated
at equilibrium. Determine Ka for nitrous acid, and the
pH of the solution.
◆
polyprotic acids dissociate in a step-wise manner
each step corresponds to the dissociation
of one H+
each step has a unique Ka value
Polyprotic Acids
◆
consider oxalic acid, H2C2O4:
1st dissociation step:
H2C2O4 (aq) + H2O (l) ⇄ HC2O4– (aq) + H3O+ (aq); Ka1 = 5.9 x 10–2
2nd dissociation step:
HC2O4– (aq) + H2O (l) ⇄ C2O42– (aq) + H3O+ (aq); Ka2 = 6.4 x 10–5
◆
◆
Ka1 > Ka2 this is always true for polyprotic acids
the acids become weaker with each successive
dissociation step
H2C2O4 is a stronger acid than HC2O4–
Why?
example:
Consider a 0.040 M solution of carbonic acid.
Determine the pH of this solution as well as the
equilibrium concentrations of: [H2CO3], [HCO3–],
[H3O+], [CO32–], and [OH–].
For H2CO3, Ka1 = 4.3 x 10–7 and Ka2 = 5.6 x 10–11.
1st ionization equation:
H2CO3 (aq) + H2O (l) ⇄ HCO3– (aq) + H3O+ (aq)
2nd ionization equation:
HCO3– (aq) + H2O (l) ⇄ CO32– (aq) + H3O+ (aq)
solution:
◆ because Ka1 > Ka2 & Ka1 >> Kw, the primary source
of H3O+ in the solution will be the 1st ionization
step for H2CO3:
H2CO3 (aq) + H2O (l)
⇄
HCO3–
(aq) +
H3O+
solution:
2–
◆ to determine [CO3 ] we will have to consider the
2nd ionization step:
HCO3– (aq) + H2O (l) ⇄ CO32– (aq) +
(aq)
initial [ ] 1.3 x 10–4 M
initial [ ]
0.040 M
---
0
0
∆[]
–x
---
+x
+x
---
xM
xM
equil [ ] (0.040–x)M
◆
use Ka1; solve for x:
x = 1.3 x 10–4
so: [H2CO3] ≈ 0.040 M
[HCO3–] = [H3O+] = 1.3 x 10–4 M
pH = 3.89
Steps for solving weak base equilibrium problems:
1. Identify all major species in solution.
4. Set up the equilibrium calculation based on
equilibrium identified in step 3.
5. Solve!
◆ x = [OH-]
◆ solve for pH, % ionization, or Kb
---
0
1.3 x 10–4 M
∆[]
–x
---
+x
+x
equil [ ]
(1.3 x 10–4 –x)M
---
xM
(1.3 x 10–4 + x)M
◆
◆
use Ka2; solve for x:
x = 5.6 x 10–11
so: [CO32–] = 5.6 x 10–11 M
[OH–]?
[OH–] = KW/[H3O+] = 7.7 x 10–11 M
example:
Calculate pH and % dissociation of 0.40 M NH3 (aq).
For NH3, Kb = 1.8 x 10–5.
2. Identify all potential H+ transfer reactions that
could contribute to the [OH-]total in the sol’n.
3. By considering K values, determine the dominant
source of OH- in the solution.
H3O+ (aq)
NH3 (aq) + H2O (l)
⇄ NH4+ (aq) + OH– (aq)
initial [ ]
0.40 M
---
0
0
∆[]
–x
---
+x
+x
---
xM
xM
equil [ ] (0.40–x)M
◆
Some Comparisons
compare 2 solutions of different concentration of ammonia
(NH3, Kb = 1.8 x 10–5)
◆
compare 2 solutions of different concentration of pyridine
(C5H5N, Kb = 1.4 x 10–9)
◆
compare ammonia and pyridine solutions of the same
concentration
0.15 M NH3
0.40 M NH3
0.40 M
C5H5N
2.4 x
10–5
◆
Be careful when comparing solutions and making qualitative
◆
You can compare 2 different bases at the same concentration:
base with larger Kb is the stronger base
∴ base solution with larger Kb will have:
higher [OH–]
higher pH
higher % dissociation
◆
You can compare the same base at 2 different concentrations:
Kb is the same, so base strength is the same
solution with higher concentration will have:
higher [OH–]
higher pH
lower % dissocation
0.80 M
C5H5N
[OH–], M
3.3 x
10–5
0.0016
0.0027
pH
11.20
11.43
9.38
9.52
%
ionization
1.1%
0.68%
0.0060%
0.0041%
example:
Codeine (C18H21NO3) is a naturally occurring amine.
The pH of a 0.012 M solution of codeine is
determined to be 10.14.
Determine the base ionization constant for codeine,
and the % ionization of the solution.
Relationship Between Ka & Kb for Conjugate Acid/Base Pair
◆
consider the conjugate acid/base pair of NH3 & NH4+
NH3 (aq) + H2O (l) ⇄ NH4+ (aq) + OH– (aq)
[NH4+][OH–]
Kb = ––––––––––––
[NH3]
NH4+ (aq) + H2O (l) ⇄ NH3 (aq) + H3O+ (aq)
[NH3][H3O+]
Ka = ––––––––––––
[NH4+]
so:
[NH3][H3O+] [NH4+][OH–]
Ka x Kb = ––––––––––––
x –––––––––––
[NH3]
[NH4+]
Ka x Kb = [H3O+][OH–]
Ka x Kb = KW
Salt Solutions and pH Considerations
◆
◆
◆
Steps for solving salt solution pH problems:
salt - an ionic compound
1. Identify all major species in solution.
soluble salts dissolve in water to produce solutions
that may be acidic, basic, or neutral
2. Identify all potential H+ transfer reactions that
could contribute to the [H3O+]total OR [OH-]total
in the sol’n.
consider the cation and anion separately
assess the potential acidic or basic nature of each
recall the inverse nature between strengths in a
conjugate acid/base pair:
the stronger an acid or base, the weaker its
conjugate
the weaker an acid or base, the stronger its
conjugate
a closer look at a weak acid/conjugate base pair: HA & AHA (aq) + H2O (l) ! A– (aq) + H3O+ (aq)
3. By considering K values, determine the dominant
source of H3O+ OR OH- in the solution.
4. Set up the equilibrium calculation based on
equilibrium identified in step 3.
5. Solve!
-- x = [H3O+] OR [OH-]
-- solve for pH
a closer look at a weak base/conjugate acid pair: B & BH+
B (aq) + H2O (l) ! BH+ (aq) + OH- (aq)
the stronger the acid (HA), the weaker its conjugate base (A-):
strong monoprotic acids produce conjugate bases that are not
effective bases in solution - they are neutral anions
the stronger the base (B), the weaker its cation:
strong bases produce cations that are not effective acids in
solution - they are neutral cations
neutral anions are: Cl–, Br–, I–, NO3– , ClO4–
neutral cations are: Li+, Na+, K+, Rb+, Cs+, Ca2+, Sr2+, Ba2+
the weaker the acid (HA), the stronger its conjugate base (A-):
weak acids produce conjugate bases that can function as bases
in solution - they are basic anions
the weaker the base (B), the stronger its conjugate acid (BH+):
weak bases produce conjugate acids that can function as acids
in solution - they are acidic cations
base ionization equilibrium for A-:
A- (aq) + H2O (l) ! HA (aq) + OH- (aq); Kb
acid ionization equilibrium for BH+:
BH+ (aq) + H2O (l) ! B (aq) + H3O+ (aq); Ka
examples of basic anions include:
F-, CO32-, ClO2-, SO32-, PO43-, NO2-, BrO4-
examples of acidic cations include:
NH4+, CH3NH3+, C2H5NH3+, C5H5NH+, C6H5NH3+
salts that produce neutral solutions:
recall the relationship between Ka and Kb for a
conjugate acid/base pair:
◆
pH = 7.00 at 25oC
◆
neutral cation with a neutral anion
Ka x Kb = Kw
OR
examples: KNO3, NaCl, Ca(ClO4)2, SrBr2, CsI
pKa + pKb = pKw
and:
at 25oC, pKw = -log(1 x 10-14) = 14.00
so:
pKa + pKb = 14.00
salts that produce acidic solutions:
◆
pH < 7.00 at 25oC
◆
type 1: acidic cation with neutral anion
◆
type 3: hydrated metal cation of high positive chargedensity with neutral anion
recall:
examples: NH4Cl, CH3NH3NO3, C5H5NHBr
example problem: calculate the pH of 0.10 M NH4Cl (aq)
NH4+ (aq) + H2O (l) ! NH3 (aq) + H3O+ (aq);
Ka = Kw/Kb for NH3 = 5.6 x 10-10
◆
type 2: neutral cation with anion from a polyprotic acid
hydrated metal ion can behave as a Bronsted-Lowry acid:
[Al(H2O)6]3+(aq) + H2O(l) ! Al[(H2O)5(OH)]2+(aq) + H3O+(aq)
examples: KHSO4, NaHCO3, Ca(HC2O4)2
examples: MgCl2, AlBr3, Zn(NO3)2, Cr(NO3)3
example problem: calculate the pH of .20 M Ca(HC2O4)2 (aq)
example problem: calculate the pH of 0.097 M AlCl3 (aq);
for [Al(H2O)6]3+, Ka = 1.4 x 10-5
HC2O4- (aq) + H2O (l) ! C2O42- (aq) + H3O+ (aq);
Ka = Ka2 for H2C2O4 = 5.1 x 10-5
salts that produce basic solutions:
◆
pH > 7.00 at 25oC
◆
neutral cation with basic anion
The Common Ion Effect
examples: KF, CaSO4, Na2CO3, K3PO4, Na2C2O4, NaNO2
example problem: calculate the pH of 0.20 M NaNO2 (aq)
What happens to the pH of a weak acid (HA) or
weak base (B) solution when a salt containing its
◆
NO2- (aq) + H2O (l) ! HNO2 (aq) + OH- (aq);
Kb = Kw/Ka for HNO2 = 2.2 x 10-11
◆
◆
example:
0.10 mol HC2H3O2 and 0.10 mol NaC2H3O2 are
combined in a solution with a total volume of 1.0 L.
resulting solution contains a conjugate acid
base pair
calculate and compare [H3O+] or [OH-],
pH, % ionization
demonstration of LeChatelier’s Principle
for comparison:
0.10 M HC2H3O2 (aq)
0.10 M HC2H3O2 (aq)
+
0.10 M NaC2H3O2 (aq)
[H3O+]
1.3 x 10 -3 M
1.8 x 10-5 M
pH
2.89
4.74
% ionization
1.3%
0.018%
Determine the [H3O+], pH, and % ionization in this
solution. For HC2H3O2, Ka = 1.8 x 10–5.
the equilibrium that controls the pH of this sol’n:
HC2H3O2(aq) + H2O (l) ⇄ C2H3O2– (aq) + H3O+(aq)
initial [ ]
0.10 M
---
0.10 M
0
∆[]
–x
---
+x
+x
equil [ ]
(0.10–x)M
---
(0.10+x)M
xM
for comparison:
Buffer Solutions
0.15 M NH3 (aq)
0.15 M NH3 (aq)
+
0.45 M NH4Cl (aq)
[OH–]
1.6 x 10–3 M
6.0 x 10-6 M
pH
11.20
8.78
% ionization
1.1%
0.0040%
Consider, again, 0.10 M HC2H3O2 & 0.10 M NaC2H3O2
common ion solution; starting pH = 4.74.
◆
How does the pH change after the addition of 0.010 mol
HCl to 1.00 L of this solution?
◆
1st: addition of strong acid (H+) results in a neutralization
reaction (note: Cl- is a spectator ion; this is the net
ionic equation):
◆
common ion solutions
sol’ns that contain a conjugate acid/base pair
HA & A- or B & BH+
◆
solution resists change in pH when small amounts
of strong acid (H+) or strong base (OH-) are added
How does the pH change after the addition of 0.010 mol HCl to
1.00 L of a solution composed of 0.10 M HC2H3O2 & 0.10 M
NaC2H3O2 (initial pH = 4.74).
1st: addition of strong acid (H+) results in a neutralization
reaction (note: Cl- is a spectator ion; this is the net
ionic equation):
◆
the added strong acid (H+) will react with the base
(C2H3O2-) in the buffer solution
C2H3O2- (aq) + H+ (aq) " HC2H3O2 (aq)
◆ 2nd:
◆
C2H3O2– (aq) +
H+ (aq)
→ HC2H3O2 (aq)
after the strong acid is consumed, equilibrium is
established that determines the pH of the solution:
before rxn
0.10 mol
0.010 mol
0.10 mol
HC2H3O2 (aq) ! C2H3O2- (aq) + H+ (aq)
∆
–0.010 mol
–0.010 mol
+0.010 mol
after rxn
0.090 mol
0
0.11 mol
resulting solution pH = 4.66;
∆pH = -.08
How does the pH change after the addition of 0.010 mol HCl
to 1.00 L of a solution composed of 0.10 M HC2H3O2 & 0.10 M
NaC2H3O2 (initial pH = 4.74).
2nd: after the strong acid is consumed, equilibrium is
established that determines the pH of the solution:
HC2H3O2 (aq) + H2O (l) ! C2H3O2- (aq) + H3O+ (aq)
◆
initial [HC2H3O2] and [C2H3O2–] in equilibrium problem
determined by consideration of what is in solution after
the neutralization reaction is complete
HC2H3O2 (aq) + H2O (l) ⇄ C2H3O2– (aq) + H3O+ (aq)
initial [ ]
0.11 M
---
0.090 M
0
∆[]
–x
---
+x
+x
equil [ ]
(0.11–x)M
---
(0.090+x)M
xM
Consider, again, 0.10 M HC2H3O2 & 0.10 M NaC2H3O2
common ion solution; pH = 4.74.
How does the pH change after the addition of 0.010 mol
NaOH to 1.00 L of this solution?
1st: addition of strong base (OH-) results in a neutralization
reaction (note: Na+ is a spectator ion; this is the net
ionic equation):
the result of the neutralization reaction:
C2H3O2– (aq) + H+ (aq) → HC2H3O2 (aq)
◆
◆
◆
C2H3O2– is consumed
[C2H3O2–] decreases
HC2H3O2 (aq) ! C2H3O2- (aq) + H+ (aq)
resulting solution pH = 4.82;
∆pH = +.08
HC2H3O2 is formed
[HC2H3O2] increases
strong acid, H+, is the limiting reactant
H+ is completely consumed
pH of solution decreases slightly
solution becomes slightly more acidic
How does the pH change after the addition of 0.010 mol NaOH
to 1.00 L of a solution composed of 0.10 M HC2H3O2 & 0.10 M
NaC2H3O2 (initial pH = 4.74).
1st: addition of strong base (OH–) results in a neutralization
reaction (note: Na+ is a spectator ion; this is the net
ionic equation):
◆
the added strong base (OH–) will react with the acid
(HC2H3O2) in the buffer solution
HC2H3O2 (aq) + OH- (aq) " C2H3O2- (aq) + H2O (l)
2nd: after the strong base is consumed, equilibrium is
established that determines the pH of the solution:
◆
HC2H3O2 (aq) + OH– (aq) → C2H3O2– (aq) + H2O (l)
before rxn
0.10 mol
0.010 mol
0.10 mol
---
∆
–0.010 mol
–0.010 mol
+0.010 mol
---
after rxn
0.090 mol
0
0.11 mol
---
How does the pH change after the addition of 0.010 mol NaOH
to 1.00 L of a solution composed of 0.10 M HC2H3O2 & 0.10 M
NaC2H3O2 (initial pH = 4.74).
2nd:
after the strong base is consumed, equilibrium is
established that determines the pH of the solution:
HC2H3O2 (aq) + H2O (l) ! C2H3O2- (aq) + H3
O+
◆
(aq)
initial [HC2H3O2] and [C2H3O2–] in equilibrium problem
determined by consideration of what is in solution after
the neutralization reaction is complete
HC2H3O2 (aq) + H2O (l) ⇄ C2H3O2– (aq) + H3O+ (aq)
initial [ ]
0.090 M
---
0.11 M
0
∆[]
–x
---
+x
+x
equil [ ]
(0.090–x)M
---
(0.11+x)M
xM
the result of the neutralization reaction:
HC2H3O2 (aq) + OH– (aq) → C2H3O2– (aq) + H2O (l)
◆
◆
◆
HC2H3O2 is consumed
[HC2H3O2] decreases
◆
C2H3O2– is formed
[C2H3O2–] increases
strong base, OH–, is the limiting reactant
OH– is completely consumed
pH of solution increases slightly
solution becomes slightly more basic
How Does a Buffer Work?
Change of pH of a Buffer Solution With H+ or OH– Added
◆
◆
pH is controlled by [H+]
in an HA/A– buffer solution:
HA (aq) ⇄ H+ (aq) + A– (aq)
[H+][A–]
Ka = ––––––––
[HA]
◆
OR
[HA]
[H+] = Ka –––––
[A–]
to keep [H+] (and therefore pH) relatively constant,
[HA]/[A–] must also remain relatively constant
[HA]
[H+] = Ka –––––
[A–]
in buffer solution with HA & A–:
◆
neutralization:
OH– + HA → A– + H2O
[HA] increases slightly
◆
◆
neutralization:
◆
H+ + A– → HA
◆
Buffer Capacity and Buffer Failure
◆
[HA] decreases slightly
[A–] decreases slightly
[A–] increases slightly
[HA]/[A–] increases
[H+] increases
pH decreases
[HA]/[A–] decreases
[H+] decreases
pH increases
◆
◆
Buffer Capacity
◆
compare 2 HF + NaF buffer solutions:
0.25 M HF & 0.50 M NaF
[HF]/[F–] = 0.50
pH = 3.76
◆
H+ to 100 mL solution
[HF]/[F–] = 0.56
pH = 3.71
∆pH = 0.05
better buffer capacity
0.050 M HF & 0.10 M NaF
[HF]/[F–] = 0.50
pH = 3.76
◆
H+ to 100 mL solution
[HF]/[F–] = 0.88
pH = 3.51
∆pH = 0.25
◆
buffer capacity is the amount of strong acid or
strong base that can be added to a buffer solution
before it fails
a buffer fails when enough strong acid or strong
base is added to cause a ∆pH > 1 unit
pH of buffer solution depends on the [HA]/[A–]
ratio
capacity of a buffer solution depends on magnitude
of [HA] and [A–]
Henderson-Hasselbalch Equation
[HA]
[H+] = Ka –––––
[A–]
take –log of both sides of equation
[A–]
pH = pKa + log –––––
[HA]
OR
[base]
pH = pKa + log –––––
[acid]
◆
◆
buffer solutions work best when [base]/[acid] is
close to 1
when [base] = [acid]:
[base]/[acid] = 1
pH = pKa
example:
example:
Consider the following acids and their pKa values:
H2PO4– pKa = 7.21
HF pKa = 3.14
+
NH4
pKa = 9.25
HC7H5O2 pKa = 4.19
What is the pH of a buffer solution prepared by
mixing 100 mL of 0.104 M NaF with 200 mL of
0.275 M HF? For HF, pKa = 3.14.
What would be the best acid/conjugate base to
prepare a buffer solution with pH = 7.00?
What would be the best acid/conjugate base to
prepare a buffer solution with pH = 9.00?
◆
Since buffer solutions work best when [base]/[acid]
is close to 1, the best acid to pick for a buffer is
one with pKa close to the desired pH.
example:
What concentration of NaC7H5O2 is required to
prepare a buffer solution with pH = 4.10 with 0.249
M HC7H5O2 (aq)? For HC7H5O2, pKa = 4.19.
ideally: pKa of acid = sol’n pH + 1
◆
Acid-Base Titrations: A Quick Review
titration is an analytical technique in which one
reactant is added to another in a very controlled way
◆
stop when the reaction is just complete
at this point there is no limiting reactant, and no
excess reactants
reactants are completely converted to products
◆
strong acid + strong base
weak acid + strong base
strong acid + weak base
◆
this point is called the:
stoichiometric point
equivalence point
end point
usually some visible indication that you are at the
stoichiometric point (use of indicators)
for each we will:
calculate the pH at points before, at, and
beyond the stoichiometric point
stoichiometrically correct mol ratio of reactants
◆
Acid-Base Titrations
we will look in detail at the following titrations:
discuss characteristics of each type of
titration
create and interpret titration curves
◆
end with a discussion of acid-base indicators
Strong Acid + Strong Base Titrations
Strong Acid + Strong Base Titrations
basic strategy:
example:
1. write the net ionic equation for the neutralization
reaction that will occur
40.0 mL of 0.110 M HCl (aq) is titrated with
0.095 M NaOH (aq).
2. using V and M, calculate mol of each reactant
present
Determine the following:
initial pH of the solution
pH after the addition of 30.0 mL of NaOH
pH at the stoichiometric point
pH after the addition of 60.0 mL NaOH
3. set up a reaction table; identify the limiting and
excess reactant
4. determine [H+] or [OH–] after neutralization
reaction is complete
remember to use the total solution volume!
5. calculate pH of solution
example:
example:
40.0 mL of 0.110 M HCl (aq) is titrated with 0.095 M
NaOH (aq).
◆
◆
◆
neutralization reaction (Na+ and Cl– spectator ions):
H+ (aq) + OH– (aq) → H2O (l)
calculate mol H+ (aq):
mol H+ = (0.0400 L)(0.110 mol/L)
= 0.00440 mol H+
calculate volume NaOH (aq) required to reach the
stoichiometric point:
mol OH– x –––––––––––
1 L sol’n
0.00440 mol H+ x 1––––––––––
= 0.0463 L
+
1 mol H
.095 mol OH–
or 46.3 mL
40.0 mL of 0.110 M HCl (aq) is titrated with 0.095 M NaOH (aq).
◆
Determine the initial pH; pH of the solution before
another way to say this . . .
What is the pH of 0.110 M HCl (aq)?
[H+] = 0.110 M
pH = – log (0.110) = 0.96
example:
example:
40.0 mL of 0.110 M HCl (aq) is titrated with 0.095 M NaOH (aq).
40.0 mL of 0.110 M HCl (aq) is titrated with 0.095 M NaOH (aq).
◆
Determine [excess reactant] after neutralization
reaction is complete:
◆
Determine the pH after the addition of 30.0 mL
NaOH (aq).
mol H+ after rxn
[H+] = ––––––––––––––––
total sol’n volume
mol OH– added = (0.0300 L)(0.095 mol/L)
= 0.0029 mol OH–
set up a reaction table to identify limiting and excess reactant:
◆
H+ (aq)
+
before rxn: 0.00440 mol
OH– (aq)
→
0.0015 mol H+
[H+] = –––––––––––––––––
(0.0400 + 0.0300) L
H2O (l)
0.0029 mol
---
change:
–0 .0029 mol
– 0.0029 mol
---
after rxn:
0.0015 mol
0
---
[H+] = 0.021 M
pH = 1.68
example:
example:
40.0 mL of 0.110 M HCl (aq) is titrated with 0.095 M NaOH (aq).
40.0 mL of 0.110 M HCl (aq) is titrated with 0.095 M NaOH (aq).
◆
Determine the pH at the stoichiometric point.
◆
46.3 mL NaOH (aq) added to reach stoichiometric pt
at stoichiometric point:
Determine the pH after the addition of 60.0 mL
NaOH (aq).
mol OH– added = (0.0600 L)(0.095 mol/L)
= 0.0057 mol OH–
mol OH– added = mol H+ present = 0.00440 mol
◆
set up reaction table:
H+
(aq)
before rxn: 0.00440 mol
◆
+
OH–
(aq)
→
H2O (l)
0.0044 mol
---
change:
–0 .0044 mol
– 0.0044 mol
---
after rxn:
0
0
---
◆
after reaction the solution is neutral; pH = 7.00
set up a reaction table to identify limiting and excess reactant:
H+ (aq)
before rxn: 0.00440 mol
+
OH– (aq)
→
H2O (l)
0.0057 mol
---
change:
–0 .0044 mol
– 0.0044 mol
---
after rxn:
0
0.0013 mol
---
example:
40.0 mL of 0.110 M HCl (aq) is titrated with 0.095 M NaOH (aq).
◆
Determine [excess reactant] after neutralization
reaction is complete:
mol OH–
[OH–] = ––––––––––––––––
total sol’n volume
Some Titration Data/Titration Curves
Strong Acid/Strong Base Titrations:
• Consider the titration of 40.0 mL of 0.110 M HCl (aq) with 0.095 M NaOH (aq).
total sol’n vol.
[H3O+] after rxn
before
0
40
0.110 M
stoichiometric
5
45
0.087 M
point:
10
50
0.070 M
30
70
0.021 M
45
85
0.012 M
46
86
3.5 x 10 4 M
at stoich. point:
46.3
86.3
1.0 x 10 7 M
pH
0.96
1.07
1.15
1.68
1.92
3.46
!
7.00
!
0.0013 mol
[OH–] = –––––––––––––––––
(0.0400 + 0.0600) L
Some Titration Data/Titration Curves
Strong Acid/Strong Base Titrations:
• Consider the titration of 40.0 mL of 0.110 M HCl (aq) with 0.095 M NaOH (aq).
total sol’n vol.
[H3O+] after rxn
before
0
40
0.110 M
stoichiometric
5
45
0.087 M
point:
10
50
0.070 M
30
70
0.021 M
45
85
0.012 M
46
86
3.5 x 10 4 M
at stoich. point:
46.3
86.3
1.0 x 10 7 M
beyond
stoichiometric
point:
47
50
60
70
80
pH
0.96
1.07
1.15
1.68
1.92
3.46
[OH–] = 0.013 M
pOH = 1.89; pH = 12.11
!
87
90
100
110
120
[OH–] after rxn
0.00115 M
0.0044 M
0.013 M
0.020 M
0.027 M
11.06
11.64
12.11
12.31
12.43
7.00
!
–
beyond
stoichiometric
point:
47
50
60
70
80
87
90
100
110
120
[OH ] after rxn
0.00115 M
0.0044 M
0.013 M
0.020 M
0.027 M
11.06
11.64
12.11
12.31
12.43
Titration of 40.0 mL of 0.110 M HCl (aq) with 0.095 M NaOH (aq)
14
12
Titration Curve for Strong Acid + Strong Base
Titration of 40.0 mL of 0.110 M HCl (aq) with 0.095 M NaOH (aq)
Weak Acid + Strong Base Titrations
strategy:
10
1. write the net ionic equation for the neutralization
reaction that will occur
◆ strong base is completely ionized
◆ weak acid is only partially ionized
pH
14
12
8
10
pH
6
8
stoichiometric pt
4
6
2. using V and M, calculate mol of each reactant
present
4
2
2
3. set up a reaction table; identify the limiting and
excess reactant
0
0
notes:
start at low (acidic) pH
pH < 7 before stoichiometric point (OH– limiting reactant)
pH = 7 at stoichiometric point (neutral solution)
pH > 7 beyond stoichiometric point (H+ limiting reactant)
end at high (basic) pH
0
20
40
60
80
0
20
40
60
80
Weak Acid + Strong Base Titrations
Weak Acid + Strong Base Titrations
example:
4. identify the species present when the neutralization
reaction is complete, and determine which of them are
key to determining the pH of the solution
◆
before the stoichiometric point, the neutralization
reaction results in a HA/A– buffer solution
◆
at the stoichiometric point, the base ionization of A–
will determine the pH
◆
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with
0.100 M NaOH (aq).
Determine the following:
◆
◆
◆
beyond the stoichiometric point excess OH–
determines the pH
◆
initial pH of the solution
pH after the addition of 20.0 mL of NaOH
pH at the stoichiometric point
pH after the addition of 50.0 mL NaOH
5. using post-neutralization concentrations of species, set up
the appropriate calculation and determine pH of solution
example:
example:
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
neutralization reaction (Na+ spectator ion):
HC2H3O2 (aq) + OH– (aq) → C2H3O2– (aq) + H2O (l)
◆
◆
◆
calculate mol HC2H3O2 (aq):
mol HC2H3O2 = (0.0300 L)(0.125 mol/L)
= 0.00375 mol HC2H3O2
calculate volume NaOH (aq) required to reach the
stoichiometric point:
1 mol OH–
1 L sol’n = 0.0375 L
.003750 mol HC2H3O2 x ––––––––––––
x –––––––––––
1 mol HC2H3O2 .100 mol OH–
or 37.5 mL
◆
Determine the initial pH; pH of the solution before
another way to say this . . .
What is the pH of 0.125 M HC2H3O2 (aq)?
weak acid calculation; Ka for HC2H3O2 = 1.8 x 10–5
x = [H+] = 0.0015 M
pH = – log (0.0015) = 2.82
example:
example:
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
◆
Determine the pH after the addition of 20.0 mL
NaOH (aq).
◆
mol OH– added = (0.0200 L)(0.100 mol/L)
= 0.00200 mol OH–
HC2H3O2 +
→
OH–
C2H3O2–
+ H2O
before rxn: .00375 mol
.00200 mol
0
---
change:
–.00200 mol
–.00200 mol
+.00200 mol
---
after rxn:
.00175 mol
0
.00200 mol
---
example:
.00200 mol
[C2H3O2–] = ––––––––––––
[HC2H3O2] = 0.0350 M
[C2H3O2–] = 0.0400 M
◆
using an equilibrium table (Ka = 1.8 x
HC2H3O2
⇄
10–5):
C2H3O2
–
this is a buffer solution
determine [H+] and pH by using an equilibrium
table
OR
the Henderson-Hasselbalch equation
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
◆
+
H+
initial [ ]:
.0350 M
.0400 M
0
change [ ]:
–x
+x
+x
equil [ ]:
(.0350 – x) M
(.0400 + x) M
xM
x=
[H+]
= 1.6 x
10–5
M;
Determine the pH at the stoichiometric point.
37.5 mL NaOH (aq) added to reach stoichiometric pt
at stoichiometric point:
mol OH– added = mol HC2H3O2 present = 0.00375 mol
◆
◆
(.0300 + .0200)L
example:
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
◆
.00175 mol
[HC2H3O2] = ––––––––––––––
(.0300 + .0200)L
set up a reaction table to identify limiting and excess reactant:
◆
Determine [HC2H3O2] and [C2H3O2–] after
neutralization reaction is complete:
set up reaction table:
pH = 4.80
using Henderson-Hasselbalch (pKa = 4.74):
.0400
pH = 4.74 + log ––––––
.0350
pH = 4.80
HC2H3O2 +
OH–
→
C2H3O2–
+ H2O
before rxn: .00375 mol
.00375 mol
0
---
change:
–.00375 mol
–.00375 mol
+.00375 mol
---
after rxn:
0
0
.00375 mol
---
example:
example:
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
the equilibrium table and calculation:
◆
⇄
◆
after the neutralization reaction, HC2H3O2 and OH–
are completely consumed
initial [ ]:
.0556 M
---
0
0
◆
base ionization of C2H3O2 controls the pH of sol’n:
∆ [ ]:
–x
---
+x
+x
equil [ ]:
(.0556 –x)M
---
xM
xM
C2H3O2–
–
C2H3O2– (aq) + H2O (l) ⇄ HC2H3O2 (aq) + OH– (aq)
H2O
HC2H3O2
+ OH–
x2
Kb = KW÷(Ka for HC2H3O2) = 5.6 x 10–10
◆
+
Kb = 5.6 x 10–10 = ––––––––––
.0556 – x
determine [C2H3O2–] after neutralization reaction:
◆
.00375 mol
[C2H3O2–] = ––––––––––– = 0.0556 M
.0675 L
◆
solve for x:
x = [OH–] = 5.6 x 10–6 M
pOH = 5.25
pH = 8.75
for a weak acid titrated with a strong base, the pH > 7 at
the stoichiometric point
example:
example:
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
◆
◆
Determine the pH after the addition of 50.0 mL
NaOH (aq).
mol
◆
OH–
mol OH–
[OH–] = ––––––––––––––––
total sol’n volume
= 0.00500 mol OH–
set up a reaction table to identify limiting and excess reactant:
HC2H3O2 +
OH–
→
C2H3O2–
determine [excess reactant] after neutralization
reaction is complete:
0.00125 mol
[OH–] = –––––––––––––––––
(0.0300 + 0.0500) L
+ H2O
before rxn: .00375 mol
.00500 mol
0
---
change:
–.00375 mol
–.00375 mol
+.00375 mol
---
after rxn:
0
.00125 mol
.00375 mol
---
[OH–] = 0.0156 M
pOH = 1.81; pH = 12.19
point:
60
75
90
105
0.025 M
0.0357 M
12.40
12.55
Titration Curve for Weak Acid + Strong Base
Titration of 0.125 M HCH O (aq) with 0.100 M NaOH (aq)
2
3
2
14
!
!
!
!
!
!
!
!
12
pH
2.82
3.93
4.30
4.80
5.34
5.89
6.61
10
8
6
buffer zone
8.75
11.56
12.19
12.40
12.55
stoichiometric pt
pH
Weak Acid/Strong Base Titrations:
• Consider the titration of 30.0 mL of 0.125 M HC2H3O2 (aq) with 0.100 M NaOH (aq).
total sol’n vol.
[H3O+] after rxn
before
0
30
1.5 x 10 3 M
stoichiometric
5
35
1.2 x 10 4 M
point:
10
40
5.0 x 10 5 M
20
50
1.6 x 10 5 M
30
60
4.6 x 10 5 M
35
65
1.3 x 10 6 M
37
67
2.5 x 10 7 M
[OH–] after rxn
at stoich. point:
37.5
67.5
5.6 x 10 6 M
beyond
40
70
0.0036 M
stoichiometric
50
80
0.0156 M
point:
60
90
0.025 M
75
105
0.0357 M
4
2
notes:
start at low (acidic) pH
pH < 7 before stoichiometric point (OH– limiting reactant)
pH > 7 at stoichiometric point (basic solution)
pH > 7 beyond stoichiometric point (H+ limiting reactant)
end at high (basic) pH
0
10
20
30
40
50
60
70
80
Titration of 0.125 M HCH O (aq) with 0.100 M NaOH (aq)
2
3
2
14
example:
12
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
example:
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
10
an important point in a weak acid + strong base
titration is the half-way point
◆
pH
◆
8
Determine the pH after the addition of 18.75 mL
NaOH (aq).
half-way to the stoichiometric point
vol required = !(vol to reach stoich.pt.)
mol OH– added = (0.01875 L)(0.100 mol/L)
= 0.001875 mol OH–
6
◆
◆
for this titration:
vol required = !(37.5 mL)
set up a reaction table to identify limiting and excess reactant:
4
HC2H3O2 +
∴ half-way to the stoichiometric point is after
the addition of 18.75 mL NaOH
2
0
10
20
30
40
50
60
70
80
before rxn: .00375 mol
change:
OH–
.001875 mol
–.001875 mol –.001875 mol
after rxn: .001875 mol
0
→
C2H3O2–
+ H2O
0
---
+.001875 mol
---
.001875 mol
---
example:
30.0 mL of 0.125 M HC2H3O2 (aq) is titrated with 0.100 M NaOH.
◆
determine [HC2H3O2] and [C2H3O2–] after
neutralization reaction is complete:
.001875 mol
.04875 L
.001875 mol
.04875 L
[HC2H3O2] = ––––––––––––––
[C2H3O2–] = ––––––––––––
[HC2H3O2] = 0.0385 M
[C2H3O2–] = 0.0385 M
◆
◆
this is a buffer solution with [acid] = [base]
using Henderson-Hasselbalch (pKa = 4.74):
.0385
pH = 4.74 + log ––––––
.0385
pH = pKa = 4.74
◆
Strong Acid + Weak Base Titrations
strategy:
1. write the net ionic equation for the neutralization
reaction that will occur
◆ strong acid is completely ionized
◆ weak base is only partially ionized
2. using V and M, calculate mol of each reactant
present
3. set up a reaction table; identify the limiting and
excess reactant
at the half-way point in a weak + strong titration, the
pH of the solution equals the pKa of the acid
Strong Acid + Weak Base Titrations
4. identify the species present when the neutralization
reaction is complete, and determine which of them are
key to determining the pH of the solution
◆
before the stoichiometric point, the neutralization
reaction results in a B/BH+ buffer solution
◆
at the stoichiometric point, the acid ionization of
BH+ will determine the pH
◆
beyond the stoichiometric point excess H+
determines the pH
5. using post-neutralization concentrations of species, set up
the appropriate calculation and determine pH of solution
Strong Acid + Weak Base Titrations
example:
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with
0.750 M HNO3 (aq).
Determine the following:
◆
◆
◆
◆
initial pH of the solution
pH after the addition of 10.0 mL of HNO3
pH at the stoichiometric point
pH after the addition of 50.0 mL HNO3
example:
example:
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with 0.750 M HNO3.
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with 0.750 M HNO3.
◆
◆
◆
neutralization reaction (NO3– spectator ion):
CH3NH2 (aq) + H+ (aq) → CH3NH3+ (aq)
◆
calculate mol CH3NH2 (aq):
mol CH3NH2 = (0.0200 L)(1.20 mol/L)
= 0.0240 mol CH3NH2
Determine the initial pH; pH of the solution before
another way to say this . . .
What is the pH of 1.20 M CH3NH2 (aq)?
weak base calculation; Kb for CH3NH2 = 3.7 x 10–4
calculate volume HNO3 (aq) required to reach the
stoichiometric point:
x = [OH–] = 0.021 M
pOH = – log (0.021) = 1.68
1 mol H+ x –––––––––––
1 L sol’n = 0.0320 L
0.0240 mol CH3NH2 x ––––––––––––
1 mol CH3NH2
.750 mol H+
or 32.0 mL
pH = 12.32
example:
example:
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with 0.750 M HNO3.
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with 0.750 M HNO3.
◆
Determine the pH after the addition of 10.0 mL
HNO3 (aq).
◆
mol H+ added = (0.0100 L)(0.750 mol/L)
= 0.00750 mol H+
◆
+
H+
→
.0165 mol
[CH3NH2] = ––––––––––––––
.00750 mol
[CH3NH3+] = ––––––––––––
[CH3NH2] = 0.550 M
[CH3NH3+] = 0.250 M
(.0200 + .0100)L
set up a reaction table to identify limiting and excess reactant:
CH3NH2
determine [CH3NH2] and [CH3NH3+] after
neutralization reaction is complete:
CH3NH3+
before rxn:
.0240 mol
.00750 mol
0
change:
–.00750 mol
–.00750 mol
+.00750 mol
after rxn:
.0165 mol
0
.00750 mol
◆
(.0200 + .0100)L
this is a buffer solution
determine [OH–] and pH by using an equilibrium
table
OR
the Henderson-Hasselbalch equation
example:
example:
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with 0.750 M HNO3.
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with 0.750 M HNO3.
◆
using an equilibrium table (Kb = 3.7 x 10–4):
CH3NH2
+
H2O
⇄
CH3NH3+
initial [ ]:
.550 M
---
.250 M
0
∆ [ ]:
–x
---
+x
+x
equil [ ]:
(.550 –x)M
---
(.250+x) M
xM
x = [OH–] = 8.1 x 10–4 M;
pH = 10.91
◆
◆
+ OH–
Determine the pH at the stoichiometric point.
32.0 mL HNO3 (aq) added to reach stoichiometric pt
at stoichiometric point:
mol H+ added = mol CH3NH2 present = 0.0240 mol
◆
pOH = 3.89
set up reaction table:
CH3NH2
using Henderson-Hasselbalch (pKa of CH3NH3+= 10.57):
+
→
H+
CH3NH3+
before rxn:
.0240 mol
.0240 mol
0
change:
–.0240 mol
–.0240 mol
+.0240 mol
after rxn:
0
0
.0240 mol
.550
pH = 10.57 + log ––––––
.250
pH = 10.91
example:
example:
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with 0.750 M HNO3.
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with 0.750 M HNO3.
◆
after the neutralization reaction, CH3NH2 and H+
are completely consumed
◆
acid ionization of CH3NH3+ controls the pH of sol’n:
◆
CH3NH3+
CH3NH3+ (aq) ⇄ CH3NH2 (aq) + H+ (aq)
Ka = KW÷(Kb for CH3NH2) = 2.7 x 10–11
◆
[CH3NH3
.0240 mol
= ––––––––––– = 0.462 M
.0520 L
⇄
CH3NH2
+
H+
initial [ ]:
0.462 M
0
0
∆ [ ]:
–x
+x
+x
equil [ ]:
(0.462 – x) M
xM
xM
x2
determine [CH3NH3+] after neutralization reaction:
+]
the equilibrium table and calculation:
◆
◆
Ka = 2.7 x 10–11 = ––––––––––
.462 – x
+
solve for x:
x = [H ] = 3.5 x 10–6 M
pH = 5.46
for a weak base titrated with a strong acid, the pH < 7 at
the stoichiometric point
example:
example:
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with 0.750 M HNO3.
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with 0.750 M HNO3.
Determine the pH after the addition of 50.0 mL HNO3 (aq).
◆
◆
mol H+ added = (0.0500 L)(0.750 mol/L)
= 0.0375 mol H+
◆
determine [excess reactant] after neutralization
reaction is complete:
mol H+
[H+] = ––––––––––––––––
total sol’n volume
set up a reaction table to identify limiting and excess reactant:
CH3NH2
+
H+
→
0.0135 mol
[H+] = –––––––––––––––––
(0.0200 + 0.0500) L
CH3NH3+
before rxn:
.0240 mol
.0375 mol
0
change:
–.0240 mol
–.0240 mol
+.0240 mol
after rxn:
0
.0135 mol
.0240 mol
[H+] = 0.193 M
pH = 0.741
example:
example:
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with 0.750 M HNO3.
20.0 mL of 1.20 M CH3NH2 (aq) is titrated with 0.750 M HNO3.
◆
Determine the pH after the add’n of 16.0 mL HNO3 (aq).
mol H+ added = (0.0160 L)(0.750 mol/L)
= 0.0120 mol H+
◆
+
H+
→
determine [CH3NH2] & [CH3NH3+] after neutralization
reaction is complete:
.0120 mol
[CH3NH2] = –––––––––––––
.0120 mol
[C2H3O2–] = ––––––––––––
[HC2H3O2] = 0.330 M
[C2H3O2–] = 0.330 M
.0360 L
set up a reaction table to identify limiting and excess reactant:
CH3NH2
◆
CH3NH3+
◆
◆
before rxn:
.0240 mol
.0120 mol
0
change:
–.0120 mol
–.0120 mol
+.0120 mol
after rxn:
.0120 mol
0
.0120 mol
.0360 L
this is a buffer solution with [acid] = [base]
using Henderson-Hasselbalch (pKa = 10.57):
.330
pH = 10.57 + log ––––––
.330
pH = pKa = 10.57
◆
at the half-way point in a weak + strong titration, the
pH of the solution equals the pKa of the acid
50
60
70
80
0.193 M
0.263 M
0.714
0.580
Titration Curve for Strong Acid + Weak Base
Titration of 20.0 mL of 1.20 M CH
NH (aq) with 0.75 M HNO (aq)
3
2
3
14
Weak Base/Strong Acid Titrations:
• Consider the titration of 20.0 mL of 1.20 M CH3NH2 (aq) with 0.75 M HNO3 (aq).
total sol’n vol.
[OH–] after rxn
before
0
20
0.021 M
stoichiometric
5
25
0.0020 M
point:
10
30
8.1 x 10 4 M
16
36
3.7 x 10 4 M
20
40
2.2 x 10 4 M
25
45
1.0 x 10 4 M
30
50
2.5 x 10 5 M
[H3O+] after rxn
at stoich. point:
32
52
3.5 x 10 6 M
beyond
35
55
0.042 M
stoichiometric
40
60
0.100 M
point:
45
65
0.151 M
50
70
0.193 M
60
80
0.263 M
12
pH
12.32
11.30
10.91
10.57
10.35
10.01
9.40
!
!
!
!
10
8
pH
!
1.38
1.00
0.821
0.714
0.580
stoichiometric pt
6
4
5.46
!
buffer zone
2
0
notes:
start at high (basic) pH
pH > 7 before stoichiometric point (H+ limiting reactant)
pH < 7 at stoichiometric point (acidic solution)
pH < 7 beyond stoichiometric point (OH– limiting reactant)
end at low (acidic) pH
0
10
20
30
40
50
60
70
Titration of 20.0 mL of 1.20 M CH
NH (aq) with 0.75 M HNO (aq)
3
2
3
14
Acid-Base Indicators
an indicator is used to indicate the stoichiometric
point in a titration - typically by change in color
Acid-Base Indicators
12
◆
◆
10
you want to choose an indicator that will change
color very close to the stoichiometric point in your
titration
results in minimal experimental error
8
pH
◆
a few examples of indicators:
6
4
2
◆
pH of indicator color change should be close
(+1) to pH at stoichiometric point
acid-base indicators tend to be large organic
molecules that are weak acids:
0
0
10
20
30
40
50
60
HIn (aq) + H2O (l) ⇄
acid form
In–
(aq) + H3
base form
O+
(aq)
70
phenolphthalein
acid form:
colorless
bromocresol green
acid form:
yellow
methyl red
acid form:
orange
base form:
pink
base form:
blue
base form:
yellow
pH range of
color change:
8 – 10
pH range of
color change:
3.8 – 5.3
pH range of
color change:
4.2 – 6.2
Acid-Base Indicators
◆
the color of an indicator solution depends on the
pH (and [H3O+]) and the relative amounts of HIn
and In– present
Acid-Base Indicators
2 extremes:
◆
HIn (aq) + H2O (l) ⇄ In– (aq) + H3O+ (aq)
acid form
[In–][H3O+]
KIn = ––––––––– ;
[HIn]
◆
base form
[HIn]
[H3O+] = KIn –––––
[In–]
pH affects the equilibrium position, and therefore
the ratio of acid form : base form of indicator in
sol’n
◆
in acidic solution
low pH
high [H3O+]
equilibrium position far to the left
[HIn] high
[In–] low
∴ indicator is in its acid form and color
in basic solution
high pH
low [H3O+]
equilibrium position far to the right
[HIn] low
[In–] high
∴ indicator is in its base form and color
Choosing an Indicator for a Titration
◆
◆
In general, an indicator will change color at a
solution pH = pKIn + 1.
Strong Acid + Strong Base Titration:
pH at stoichiometric point = 7
You should choose an indicator with pKIn value that
is close to the pH of the solution at the
Weak Acid + Strong Base Titration:
pH at stoichiometric point > 7
Strong Acid + Weak Base Titration:
pH at stoichiometric point < 7
Final Thoughts on Acid-Base Titrations
◆
◆
◆
◆
Final Thoughts on Acid-Base Titrations
◆
neutralization reactions happen 1st
fast
go to completion
set up reaction table (with mol of species) for the
neutralization reaction
at any point in a strong acid + strong base titration
beyond the stoichiometric point in weak + strong titration
◆
assess what is in solution when the neutralization
reaction is complete
calculate post-neutralization [ ] of important species
[ ] = mol ÷ total sol’n volume
if H3O+ or OH– is present after the neutralization reaction,
go straight to pH calculation
if HA & A– or B & BH+ are present after the neutralization
reaction:
buffer solution – use equilibrium calculation or
Henderson-Hasselbalch equation
before the stoichiometric point in weak + strong titration
◆
if A– or BH+ are present after the neutralization reaction:
equilibrium calculation based on ionization:
A– (aq) + H2O (l) ⇄ HA (aq) + OH– (aq)
BH+ (aq) ⇄ B (aq) + H+ (aq)
at the stoichiometric point in weak + strong titration
Final Thoughts on Acid-Base Titrations
◆
pH titration curves:
know the characteristic profiles for the 3 categories of
titrations
know the important points on the curve:
stoichiometric point
half-way point
buffer zone
◆
calculations for titrations:
volume of acid or base req’d to reach stoichiometric pt
initial pH of solution
pH before, at, beyond & half-way to the stoichiometric pt
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