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Tadeusz Górecki Ionic Equilibria
Page 20
Acid-Base Equilibria
Brønsted-Lowry: an acid is a proton _______, a base is a ______________.++↔ HBaseAcid
________________ (H3PO4, H2O), ______ ( +4NH ) and _____ (H2PO4
-) can allbehave as acids.
Example:++ +↔ HNHNH 34
Substances which can behave both as acids and as bases: ____________, or______________ substances (e.g. H2O, SH-).
baseacidSHSH −+− +↔ 2
acidbaseSHSHH 2↔+ −+
Free protons _________ in any solvent, thus the above reactions are______________. In reality:
++ +↔+ OHNHOHNH 3324
Energy required to dissociate _____ to ____ and __: _____ kcal/mol
Tadeusz Górecki Ionic Equilibria
Page 21
Equilibrium constant for _______________:−+ +↔+ AOHOHHA 32
][]][[
HAAHKa
−+
=
________________:−+ +↔+ OHBHOHB 2
][]][[
BOHBHKb
−+
=
Relationship between Ka and Kb:
wba KKK =⋅
b
wa K
KK =a
wb K
KK =
Lewis: an acid is an ___________________; a base is an _________________.
________________________________________________________________
Strength of acids and bases−+− +↔+ 2
4324 SOOHOHHSO
−+ +↔+ 33232 HCOOHOHCOH
−+ +↔+ CNOHOHHCN 32
1221 baseacidbaseacid +↔+
_______][
]][[
4
243 == −
−+
HSOSOOHKa
_______][
]][[
32
33 ==−+
COHHCOOHKa
Tadeusz Górecki Ionic Equilibria
Page 22
______][
]][[ 3 ==−+
HCNCNOHKa
_______ value of __ means that the acid is ________, thus:
______________________
____________ of water:−+ +↔ OHHOH2
Equilibrium constant using __________:
OH
OHH
aaa
K2
0 −+=
Activity of water is by thermodynamic convention proportional to the _____________ of water in the solution. In dilute solutions it is close to __.
Activity of water can be _____________________:
___][][ == −−
++
−+ γγ OHHaa OHH
"________________" constant:
wKOHH =−+ ]][[
−+−+
== γγγγ
/00 2w
OHw K
aKK
Tadeusz Górecki Ionic Equilibria
Page 23
At 50°C, pKw = ______, and the neutral point is pH = ____. At 25°C in 3 MNaClO4 pKw = _____, and the neutral point is pH = ____.
Tadeusz Górecki Ionic Equilibria
Page 24
____________ solvents:−+ +↔+ 2433 NHNHNHNH
At -60°C, the equilibrium constant is:32
24 10]][[ −−+ == NHNHK
Thus, the pH scale (defined as -log[NH4+]) in liquid ammonia ranges from _ to
__.
pH of a strong acid
Initially PH, or "_________________", defined as
PH = -log CH
Today's definition of pH:
)]log([log ++−=−== γHapapH HH
General approach
Example: HCl
Mass balance: ____][ =−ClIon product of water: ____]][[ ==−+
wKOHHCharge balance: ][][][ −−+ += ClOHH
Solution: HAw C
HKH += +
+
][][
This is a quadratic equation, which applies ________.
When ____________, [H+] = ___ ([OH-] is _______________)
At higher ionic strength, activity coefficient should be used.
Tadeusz Górecki Ionic Equilibria
Page 25
Strong base:
Example: NaOH
Mass balance: ___][ =+NaIon product of water: 1410]][[ −−+ == wKOHHCharge balance: _____________________
Solution:][
][ ++ =+
HKCH w
b
Basic solution, thus ______________, and in general
b
w
CKH =+ ][
___________________
____________________________________
Example: pH of 7102 −⋅ M solution of NaOH
0][][ 2 =−+ ++wb KHCH
24
][2
wbb KCCH
++−=+
LmolH /1014.4][ 8−+ ⋅= pH = _____
Simplified equation: pH = _____
____________________________________
Tadeusz Górecki Ionic Equilibria
Page 26
pH of strong acid/base as a function of concentration:
-10-9-8-7-6-5-4-3-2-10
0 2 4 6 8 10 12 14
pH
log
Clog C(acid) log C(base)
Mixture of a strong acid and a strong base
Example: HCl and NaOH
Mass balance: ___][ =−ClMass balance: ___][ =+NaIon product of water: 1410]][[ −−+ == wKOHHCharge balance: ][][][][ −−++ +=+ OHClNaH
][][ +
+ −=−HKHCC w
ba
When the acid and the base are ____________:
LmolKOHH w /10][][ 7−−+ ===
Tadeusz Górecki Ionic Equilibria
Page 27
Titration of Strong Acids and Bases
Volume of the system changes, thus _______ must be taken into mass balancesrather than _______________.
Example: titration of HCl with NaOH:
Mass balance: ________)]([ =+−ba VVCl
Mass balance: ________)]([ =++ba VVNa
Ion product of water: 1410]][[ −−+ == wKOHHCharge balance: ][][][][ −−++ +=+ OHClNaH
][][ +
+ ++
=+
+HK
VVVC
VVVCH w
ba
aa
ba
bb
At the equivalence point, __________ (1:1 stoichiometry) and ___________
Before the equivalence point, _______________:
ba
bbaa
VVVCVCH
+−
=+ ][
After the equivalence point, _______________:
ba
aabbw
VVVCVC
HK
+−
=+ ][
aabb
baw
VCVCVVKH
−+
=+ )(][
Tadeusz Górecki Ionic Equilibria
Page 28
In the vicinity of the equivalence point (Ca = 0.1 M, Va = 50 mL, Cb = 0.2 M):
5
6
7
8
9
24.999 24.9995 25 25.0005 25.001
Vb
pH
OH- neglectedFull equationH+ neglected
Plotting the titration curve
__________ titrated with _________:
−++−
= ++
++
]/[][]/[][
HKHCHKHCVV
wb
waab
Titration of ___________ with ___________:
+−−+
= ++
++
]/[][]/[][
HKHCHKHCVV
wa
wbba
Tadeusz Górecki Ionic Equilibria
Page 29
Example:
Titration curve
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Vb
pH
_______________ titration:
HCl titrated with NaOH
][][][][ −−++ +++=Λ ClOHNaH ClOHNaH λλλλ
Λ - _______ conductance ( ][ 11 −−Ω cmk )Xλ - __________ conductance.
At 25°C, ________ conductances 0λ are:
_____0 =+ λH_____0 =+ λNa_____0 =− λOH_____0 =− λCl
Procedure:
• ______ the values of pH;
Tadeusz Górecki Ionic Equilibria
Page 30
• ________ [H+] and [OH-];• calculate V from the ____________ equation;• calculate )/(][ 0VVVCNa b +=+ (from ___________);
• calculate )/(][ 00 VVVCCl a +=− (from ___________).
50 mL 0.1 M HCl titrated with 0.2 M NaOH:
0
5
10
15
20
25
30
35
0 10 20 30 40 50
Vb
Con
duct
ance
50 mL 0.0001 M HCl titrated with 0.0001 M NaOH:
0.006
0.0065
0.007
0.0075
0.008
0.0085
0.009
0.0095
0.01
0.0105
0.011
40 50 60
Vb
Con
duct
ance
Tadeusz Górecki Ionic Equilibria
Page 31
Titration error
''
VVV
errorTitration ep −=
Vep - V at ________V' - V at _______________Titration of 50 mL 0.1 M HCl with 0.2 M NaOH:
Enlarged section (end point detected with __________ at pH = 5):
Tadeusz Górecki Ionic Equilibria
Page 32
Titration error:
_________25
259963.24100 =−
⋅
________________50 mL 0.0001 M HCl titrated with 0.0001 M NaOH:
Titration error:
______50
5040100 =−
⋅
Gran plotsTitration of a ___________ with a __________:
][][ +
+ ++
=+
+HK
VVVC
VVVCH w
ba
aa
ba
bb
Before the equivalence point, ______ is negligibly small, thus:
bbaaba VCVCHVV −=+ + ])[(
Tadeusz Górecki Ionic Equilibria
Page 33
or bbaapH
ba VCVCVVf −=+= −10)(1
__ , ___ and __ are _________, thus a plot of f1 as a function of Vb should be a____________ with a slope of _____ intersecting the X axis at the _______________, _____________.Example: 50 mL 0.0001 M HCl titrated with 0.0002 M NaOH:
0
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
0.00035
0.0004
0.00045
0.0005
22 23 24 25 26 27
Vb [mL]
f1
In the vicinity of the equivalence point:
0
0.00001
0.00002
0.00003
0.00004
0.00005
0.00006
0.00007
0.00008
0.00009
0.0001
24.5 24.6 24.7 24.8 24.9 25 25.1 25.2 25.3
Vb
f1
Tadeusz Górecki Ionic Equilibria
Page 34
Weak monoprotic acids and bases
−+ +↔ AHHA
][]][[
HAAHKa
−+
=
−+ +↔+ OHBHOHB 2
][]][[
BOHBHK b
−+
=
wba KKK =⋅
wba pKpKpK =+
Tadeusz Górecki Ionic Equilibria
Page 35
NH4+: __________
NH3: __________Dependence of ___ on ___________:
00
0
][ ]][[
γγγ
γγγ −+−+
−+
== aa KHA
AHK
00 logloglog γγγ −++= −+aa pKpK
Using _______________ and setting bI=0logγ (activity coefficient for an______________________):
bIIbI
IpKa −
−
+⋅−= '
151.02757.4
where b' is the ________________ (usually 0.2).
Tadeusz Górecki Ionic Equilibria
Page 36
Best fit: _______________
Temperature dependence of apK 0 :
Tadeusz Górecki Ionic Equilibria
Page 37
Calculating the pH of weak acidKnown: ___________Unknown: ______________________
][]][[
HAAHKa
−+
=
]][[ −+= OHHK w
Mass balance: ][][ HAACHA += −
Charge balance: ][][][ −−+ += OHAH
+=
+=+=
+−
+−
−+−
a
a
aaHA K
KHA
KHA
KAHAC
][][][1][]][[][
a
aHA
KHKC
A+
=+
−
][][
From ______________:
a
HA
KHHCHA+
= +
+
][][][
From ____:
][][ +
− =HKOH w
Substituting ____ and _____ into __________________:
][][][ ++
+ ++
=HK
KHKCH w
a
aHA
Thus:
0)]([][][ 23 =⋅−+−+ +++wawaHAa KKKKCHKHH
Tadeusz Górecki Ionic Equilibria
Page 38
Simplifying assumption: _____ is negligibly small
a
aHA
KHKCH+
= ++
][][
0][][ 2 =−+ ++aHAa KCKHH
When ____________:
][][ +
+ =H
KCH aHA aHAKCH =+ 2][ aHAKCH =+ ][
Flood's diagramFrom ____ and _______________:
−
+= +
++
][][][
HKH
KKHC w
a
aHA
Flood's diagram
-8
-6
-4
-2
00 2 4 6 8
pH
log C
Strong acidpKa=4.75pKa=7.53pKa=10.72
Tadeusz Górecki Ionic Equilibria
Page 39
Degree of dissociation
a
aHA
KHKCA+
= +−
][][
a
HA
KHHCHA+
= +
+
][][][
Degree of _____________:
=+
== −
−−
][][][][AHA
ACA
HA
α
Degree of ____________:
=+
==− − ][][][][1AHA
HACHA
HA
α
Degree of dissociation and formation
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14
pH
degree of dissociationdegree of formation
Tadeusz Górecki Ionic Equilibria
Page 40
Sillén's diagram (______________, ____________________)Acetic acid, 0.01 M, pKa = 4.75
-14
-12
-10
-8
-6
-4
-2
00 2 4 6 8 10 12 14
pH
log
C
[OH-] [H+]
[A-]
[HA]
1. [H+] is determined from the _______________:
pHH −=+ ]log[
2. [OH-] is determined from _________________:
ww pKpH
HKOH −== +
−
][log]log[
3. [A-] is determined from ____________ and ___:
a
aHA
KHKCA+
= +−
][][
4. [HA] is determined from ____________ and ___:
a
HA
KHHCHA+
= +
+
][][][
Tadeusz Górecki Ionic Equilibria
Page 41
pH of a given system can be determined from the _______________:
][][][ −−+ += OHAH
Acidic solution, thus _____ can be neglected
][][ −+ = AH
Solution for the proton condition can be easily found on equilibrium diagramsusing the _______________:
( )][][][log −−+ −− OHAH
Acetic acid, _____ M, pKa = _____
3.4
-14
-12
-10
-8
-6
-4
-2
00 2 4 6 8 10 12 14
pH
log
C
[OH-] [H+]
[A-]
[HA]
Pointer
Tadeusz Górecki Ionic Equilibria
Page 42
Acetic acid, ____ M, pKa = ____
6.8
-14
-12
-10
-8
-6
-4
-2
00 2 4 6 8 10 12 14
Pointer
[OH-][H+]
[A-][HA]
Plotting equilibrium diagrams
1. [H+] and [OH-]: _______ lines at ________ (slopes of __ and __,respectively)
2. [A-]:
a
aHA
KHKCA+
= +−
][][
for ____________________
][][ +
− ≅H
KCA aHA
pHpKCA aHA +−=− log]log[
1]log[=
−
dpHAd
for ___________________ HACA ≅− ][
Tadeusz Górecki Ionic Equilibria
Page 43
3. [HA]:
a
HA
KHHCHA+
= +
+
][][][
for ___________________ HACHA =][
for ___________________
a
HA
KHCHA ][][
+
≅
aHA pKpHCHA +−= log]log[
1]log[−=
dpHHAd
4. When __________:
2][][ HACHAA ==−
3.0log2loglog2
log]log[]log[ −=−===−HAHA
HA CCCHAA
What is the pH of 0.001 M NaAc?
____:
][][][ −+ =+ OHHAH
___________, thus _____:
][][ −= OHHA
Tadeusz Górecki Ionic Equilibria
Page 44
0 2 4 6 8 10 12 14 -14
-12
-10
-8
-6
-4
-2
0
pH
log
Con
cent
ratio
n [M
]
Tadeusz Górecki Ionic Equilibria
Page 45
What happens when the acid concentration is __________?
0.001 M HF, pKa = 3.17
Proton condition: ][][][ −−+ += OHFH
][][ −+ ≅ FH
-14
-12
-10
-8
-6
-4
-2
00 2 4 6 8 10 12 14
pH
log
C
[OH-][H+]
[F-]
[HF]
Tadeusz Górecki Ionic Equilibria
Page 46
-14
-12
-10
-8
-6
-4
-2
00 2 4 6 8 10 12 14
pH
log
CPointerpH=3.26
[OH-][H+]
[F-]
[HF]
Checking the results:
pH = ____
[OH-] = ______
[HF] = ______
=⋅
== −
−−−+
34.3
26.326.3
101010
][]][[
HFFHKa
Mass balance:
=+=+ −−− 34.326.3 1010][][ HFF
Algebraic solution:
0][][ 2 =−+ ++aHAa KCKHH
=+ ][H
pH = ____
Tadeusz Górecki Ionic Equilibria
Page 47
Low concentrations of very weak acids:
5 x 10-5 M HCN, pKa = 9.32
-14
-12
-10
-8
-6
-4
-2
00 2 4 6 8 10 12 14
pH
log
C[OH-][H+]
[HCN] [CN-]
[CN-]+[OH-]
Mixture of acids
Strong acids represented by ______________.
Strong bases represented by ______________.
Typically ___________ on EquiligrapHs.
Each __________ or _____ represented by the expressions:
a
aHA
KHKCA+
= +−
][][
a
BH
KHHCBH+
= +
++
][][][
pH found at the point where _______________.
Tadeusz Górecki Ionic Equilibria
Page 48
0.01 M HAc (Ka = 10-4.75) and 0.001 M HFo (Ka = 10-3.75)
-14
-12
-10
-8
-6
-4
-2
00 2 4 6 8 10 12 14
pH
log
C
[OH-] [H+]
[Ac-][HAc]
[HFo] [Fo-]
[Ac-]+[Fo-]+[OH-]
Proton condition: _________________________
Pointer function:
-14
-12
-10
-8
-6
-4
-2
00 2 4 6 8 10 12 14
pH
log
C
PointerpH=3.3
[OH-] [H+]
[Ac-][HAc]
[HFo] [Fo-]
Tadeusz Górecki Ionic Equilibria
Page 49
Assumptions:
______ negligibly small
__________
][][][][ +++
+ ++
++
=HK
KHKC
KHKCH w
f
ff
a
aa
f
ffaa
KHKC
HKCH
++= ++
+
][][][
Iteration:f
ffaa KH
KCHKCH
++= +
++
][][
][ 2
Circular reference:f
ffaa KH
KCHKCH
++= +
++
][][
][
Mixture of strong and weak acid:
0.001 M HCl and 0.01 M HAc
][][][][ −−−+ ++= OHClAcH
][][
][][ +
−+
+ +++
=HKCl
KHKCH w
a
aa
____________________
]][[][ 2 −++ += ClHKCH aa
Solution: pH = _____
Tadeusz Górecki Ionic Equilibria
Page 50
-14
-12
-10
-8
-6
-4
-2
00 2 4 6 8 10 12 14
pH
log
C
[OH-] [H+]
[Ac-]
[HAc]
[Cl-]
[Ac-]+[Cl-]+[OH-]
Salt of a weak acid and a weak base
Two independent ________________ linked by the condition that they have thesame ___________________.
][]][[ 1 HAKAH a=−+
][]][[ 2++ = BHKBH a
wKOHH =−+ ]][[
____ balances: ][][][][ BBHAHAC +=+= +−
______ balance: ][][][][ −−++ +=+ OHAHBH
_______________: ][][][][ BOHHHA +=+ −+
Tadeusz Górecki Ionic Equilibria
Page 51
If [H+] and [OH-] _________:
2
2
1 ][][][
a
a
a KHCK
KHHC
+=
+ ++
+
212][ aa KKH ⋅=+
21][ aa KKH ⋅=+
pH _______________ on C (provided the assumption above is fulfilled)!
Example: pH of 0.01 M NH4Ac (pKa1 = 4.75, pKa2 = 9.25)
=+= )(2/1 21 aa pKpKpH
The value of __ is coincidental.
Equilibrium diagram:
-14
-12
-10
-8
-6
-4
-2
00 2 4 6 8 10 12 14
pH
log
C
[OH-] [H+]
[Ac-]
[HAc][NH3]
[NH4+]
Tadeusz Górecki Ionic Equilibria
Page 52
Pointer function:
-14
-12
-10
-8
-6
-4
-2
00 2 4 6 8 10 12 14
pH
log
C
PointerpH=7
[OH-] [H+]
[Ac-]
[HAc][NH3]
[NH4+]
Full solution:
][][][
][][
2
2
1++
++
+
++
=++ H
KKH
CKHKH
HC w
a
a
a
_______ equation in [H+].
The equation is _____________, thus:
+
−
+
+
−=
+++
++
2
2
1 ][1
][1][
][][
a
a
a
w
KHK
KHH
HHK
C
Tadeusz Górecki Ionic Equilibria
Page 53
Example: Dimethylammonium acetate
pKa1 = 4.75 (___________), pKa2 = 10.76 (__________________)
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
0 2 4 6 8-log C
pH
pH = 7.755
General equation for the titration curve
____ balance:ba
aa
VVVCAHA+
=+ − ][][
____ balance:ba
bb
VVVCNa+
=+ ][
][]][[
HAHAKa
+−
=
______ balance: ][][][][ −−++ +=+ OHANaH
Tadeusz Górecki Ionic Equilibria
Page 54
a
a
ba
aa
KHK
VVVCA
+⋅
+= +
−
][][
][][][ ++
+ ++
⋅+
=+
+HK
KHK
VVVC
VVVCH w
a
a
ba
aa
ba
bb
or][
][ ++ +
+⋅=
++
HK
VVVC
VVVCH w
ba
aaHA
ba
bb α
−+
+−
+⋅
=
++
++
+
][][
][][
][
HKHC
HKH
KHKC
VVw
b
w
a
aa
ab
−+
+−⋅=
++
++
][][
][][
HKHC
HKHC
VVw
b
wHAa
ab
α
Titration of a ___________ with a __________:
−+
+−=
++
++
][][
][][
HKHC
HKHC
VVw
b
wa
ab
Simplifying assumptions: before the equivalence point ____________; after theequivalence point ________________
Tadeusz Górecki Ionic Equilibria
Page 55
Example: titration of 10 mL 0.1 M HAc with 0.1 M NaOH
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14Vb
pH
________________
)()(
)()(
bb VpH
VpH
∆∆
≈∂∂
End point determined by the _________ of the ______________. If necessary,________________ can be obtained in the same manner.
________________:
0
2
4
6
8
10
12
14
0 2 4 6 8 10 12 14Vb
pH
d(pH)/dVb
Tadeusz Górecki Ionic Equilibria
Page 56
____ and ________________:
-8
-6
-4
-2
0
2
4
6
8
10
12
14
9.90 9.95 10.00 10.05 10.10
Vb
Another way to plot the titration curve: through _____________ Φ :
aa
bb
VCVC
=Φ
Substitution to the general equation:
−+
++
=Φ +++ ][][
)(][
HHK
VCVV
KHK w
aa
ba
a
a
Iteration – set ________________ and get the ________________
Tadeusz Górecki Ionic Equilibria
Page 57
0
2
4
6
8
10
12
14
0 1 2Fraction titrated
pH
_______________ solution:
b
a
aa
bb
COHH
COHH
VCVC
][][1
][][
−+
−+
−+
−−
==Φα
0
2
4
6
8
10
12
14
0 1 2Fraction titrated
pH
Tadeusz Górecki Ionic Equilibria
Page 58
The plot of _____________________ enables easy comparisons of different_______________.
Examples:
• Different _________ of the acid
0
2
4
6
8
10
12
14
0 1 2Fraction titrated
pH
• Different ___ values
0
2
4
6
8
10
12
14
0 1 2Fraction titrated
pH
Ka = 1e-6Ka = 1e-5Ka = 1e-4
Ca = Cb = 0.01 M
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30 35 40Vb
pH
Va = 10 mLVa = 20 mL
Va = 30 mL
0
2
4
6
8
10
12
14
0 5 10 15 20Vb
pH
Ka = 1e-6Ka = 1e-5Ka = 1e-4
Ca = Cb = 0.01 M
Tadeusz Górecki Ionic Equilibria
Page 59
• Different __________________________:
0
2
4
6
8
10
12
14
0 1 2
Fraction titrated
pH
Ca = 0.0001 M
Ca = 0.001 M
Ca = 0.01M
pKa = 4.75Cb = 0.01 M
• Different concentrations of the _____:
0
2
4
6
8
10
12
14
0 1 2
Fraction titrated
pH
Cb = 0.0001 M
Cb = 0.001 M
Cb = 0.01 M
pKa = 4.75Ca = 0.01 M
0
2
4
6
8
10
12
14
0 5 10 15Vb
pH
Ca = 0.0001 M Ca = 0.001 M
Ca = 0.01 M
pKa = 4.75Cb = 0.01 M
0
2
4
6
8
10
12
14
0 500 1000 1500 2000Vb
pH
Cb = 0.0001 MCb = 0.001 M
Cb = 0.01 M
pKa = 4.75Ca = 0.01 M
Tadeusz Górecki Ionic Equilibria
Page 60
Titration of a ___________ with a _________:
][][ +
+ ++
⋅=+
+ −+ HK
VVVC
VVVCH w
ba
aaA
ba
bbBH
αα
bBH
aA
aa
bb
COHH
COHH
VCVC
][][
][][
−+
−+
−+
−−
==Φ+
−
α
α
where +
+
+== +
++
BHBBH KH
HC
BH][
][][α ;
HA
HA
HAA KH
KCA
+== +
−
−
][][α
0
2
4
6
8
10
12
14
0 1 2Fraction titrated
pH
Strong base Kb = 5
pKa = 4.75pKb = 5Ca = 0.01 M
0
2
4
6
8
10
12
14
0 5 10 15 20Vb
pH
Strong base
Kb = 5
pKa = 4.75pKb = 5Ca = 0.01 MVa = 10 mL
Tadeusz Górecki Ionic Equilibria
Page 61
Titration error
At the equivalence point ________
aabb VCVC ='
where Vb’ is Vb at the _______________
b
aab C
VCV ='
Titration error:
1111''
'.. −Φ=−=−=−=
−= ep
aa
epb
b
aa
ep
b
ep
b
bep
VCVC
CVC
VVV
VVV
eT
At the equivalence point and its vicinity:
b
ab
a
ba
CCC
VVV +
=+
Also, near the equivalence point, ____________ , thus _____________
aaa
a
KH
KHH
KHK ][
][][1
][1
+
+
+
+ −≅+
−=−+
=−α
−+
+−=−Φ ++ ][][
)(11 HHK
VCVV w
aa
baep α
a
w
aa
baep K
HHHK
VCVV ][][
][)(1
++
+ −
−+
=−Φ
a
epep
ep
w
ba
baep K
HH
HK
CCCC ][
][][
)(1+
++ −
−
+=−Φ
Tadeusz Górecki Ionic Equilibria
Page 62
Example: 0.1 M HAc, 0.1 M NaOH, pHep = __ instead of pH = _____ at theequivalence point
=−−=−Φ −
−−−
75.4
886
1010)1010)(20(1ep
Titration of a weak base with a strong acid:
ep
a
ep
wep
ba
baep H
KHKH
CCCC
][][][)(1 ++
+ −
−
+=−Φ