análisis cualitativo
TRANSCRIPT
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Tadeusz Górecki Ionic Equilibria
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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
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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
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______][
]][[ 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
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At 50°C, pKw = ______, and the neutral point is pH = ____. At 25°C in 3 MNaClO4 pKw = _____, and the neutral point is pH = ____.
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____________ 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.
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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 = _____
____________________________________
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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−−+ ===
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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
−+
=+ )(][
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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
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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;
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• ________ [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
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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):
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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 −=+ + ])[(
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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
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Weak monoprotic acids and bases
−+ +↔ AHHA
][]][[
HAAHKa
−+
=
−+ +↔+ OHBHOHB 2
][]][[
BOHBHK b
−+
=
wba KKK =⋅
wba pKpKpK =+
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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).
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Best fit: _______________
Temperature dependence of apK 0 :
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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
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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
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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
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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+
= +
+
][][][
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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
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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 ≅− ][
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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
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0 2 4 6 8 10 12 14 -14
-12
-10
-8
-6
-4
-2
0
pH
log
Con
cent
ratio
n [M
]
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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]
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-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 = ____
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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 _______________.
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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-]
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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 = _____
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-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 +=+ −+
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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+]
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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
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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
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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 ________________
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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
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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 ________________
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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
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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
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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
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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
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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
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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