(Potentiometric Titrations)

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???????????????????????????? (Potentiometric
Titrations)
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Slide by Charoenkwan Kraiya, Ph.D.
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???????????????????????????? (Potentiometric
Titrations)
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Slide by Charoenkwan Kraiya, Ph.D.
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???????????????????????????? (Potentiometric
Titrations)
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1. Method of Bisection
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??? ??????????????????? ??????????????????????????
??????????????? X ????????????????????????????????
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Slide by Charoenkwan Kraiya, Ph.D.
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????????????
1. Method of Bisection
??????????????????????? Bisection

• ??????????????????????????????????????????????????
  ??????
• ??????????????????????????????????????????????????
  ?
• ??????????????????????????????????????????????????
  ??????????????????????????? (1) ?????? A
  ?????????? (2) ?????? B
• ??????????????????????????????????????????????????
  ???????????????????????? (1) ?????? C ??????????
  (2) ?????? D
• X ?????????????????????? AB
• Y ?????????????????????? CD
• ??????? XY ????????????? O ?????? O
  ???????????????????????????????????????????

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????????????
2. Construction Method
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????????
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????????????
2. Construction Method
??????????????????????? Construction

1. ?????????????????? (slope)
2. ??????????????????????????????????????????????????
   ???????????????? (1) ?????? A
3. ??????????????????????????????????????????????????
   ??????????? (1) ?????? B
4. ?????? B ??????????????????
5. ?????? A ??????????????????
6. ?????? A ????????????????? ??????? (4) ?????? C
7. ?????? B ????????????????? ??????? (5) ?????? D

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????????????
2. Construction Method
??????????????????????? Construction
8) ?????????? CD ?????????????????????????????????
? E ?????? E ?????????????????????????????????????
?????????????????????????
Slide by Charoenkwan Kraiya, Ph.D.
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????????????
3. Derivative Method
?????????????????????????????????????????????????
??? (???? pH) ???????????????????????????????????
(?E/?V) ???????????????????????????
??????????????????????? ?????????????????????
(First derivative curve)
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???
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????????????
3. Derivative Method
???????????? ?E2/?V2 ???????????????????????????
??????????????????????? ????????????????????????
(Second derivative curve)
Second derivative curve
First derivative curve
? ?????? ?E2/?V2 ????????? ???????????????????????
???
Slide by Charoenkwan Kraiya, Ph.D.
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????????????
4. Grans plot
?????????????????????????????????? (antilog)
??????????? ??????????????????
???????????????????????? X ??? ???????????????????
??????????????????
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4. Grans plot
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4. Grans plot
???? ?????????????????????????????????????????????
?????????????????? Ag/AgCl ???????????????????????
????????????????????????? (SCE)
???????????????????? ??????????????? Ag/AgCl
?????????????????? ??? SCE ?????????
??????????????????
Ecell ECathod EAnode (E?AgCl 0.0592
logCl-) - ESCE
Slide by Charoenkwan Kraiya, Ph.D.
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Slide by Charoenkwan Kraiya, Ph.D.
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???????? VCl ?????????????????????? Cl-
?????????????? CCl ???????????????????????
????? Cl- ?????????????????? VAg
?????????????????????? Ag CAg
???????????????????????????????????? Ag
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?????????????????????? Cl- ?????????????????? Ag
?????? ????????
????????????? (VCl VAg)antilog (-16.5Ecell)
vs. VAg ???????????????
??????????? ??????????????????????????
??????????????????????????????????????????
antilog ???????? VAg ???????????
Slide by Charoenkwan Kraiya, Ph.D.
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????????????
4. Grans plot
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??????????????????????????? ??????????????????????
??? ???????????????????????????????????????????
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???????????????????????????????????
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??
????????? ??????????????? ????????
???-??? (acid-base) ????????????? ?????????????????? ????????????????? ?????????????????, ??????????????, ?????????, ????? ??????????????????????????? ???????????????????????-???????
??????? (precipitation) ????????????????? ????????????????? ????????????????? ????????????????????????? ????????????????? ?????????????????????????? ?????????????????????????????????????????????????? ??????????????????????????????????????
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???????????????????????????????????
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??
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??????????????? (complexation) ????????????? ????????????????? ???????????? EDTA ??????????????????????????????????????
??????? (redox) ??????????????????? ???? Pt, Au, etc.
Slide by Charoenkwan Kraiya, Ph.D.
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Determining Dissociation Constants
An approximate numerical value for the
dissociation constant of a weak acid or base can
be estimated from potentiometric titration
curves. This quantity can be computed from the pH
at any point along the curve, but a very
convenient point is the half-titration point.
At this point on the curve HA ? A
Therefore
Slide by Charoenkwan Kraiya, Ph.D.
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It is important to note that the use of
concentrations instead of activities may cause
the value of Ka to differ from its published
value by a factor of 2 or more. A more correct
form of the dissociation constant for HA is
Since the glass electrode provides a good
approximation of aH3O, the measured value of Ka
differs from the thermodynamic value by the ratio
of the two activity coefficients ?A-/?HA.
Slide by Charoenkwan Kraiya, Ph.D.
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Example To determine K1 and K2 for H3PO4 from
titration data, careful pH measurements are made
after 0.5 and 1.5 mol of base are added for each
mole of acid. It is then assumed that the
hydrogen ion activities computed from these data
are identical to the desired dissociation
constants. Calculate the relative error
incurred by the assumption if the ionic strength
is 0.1 at the time of each measurement. Given K1
and K2 for H3PO4 are 7.11 x 10-3 and 6.34 x 10-8,
respectively. The activity coefficient for H2PO4-
is 0.78 and that for HPO42- is 0.36.
From the titration data with the assumption
or
Slide by Charoenkwan Kraiya, Ph.D.
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Therefore,
For K1
For K2
Slide by Charoenkwan Kraiya, Ph.D.
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????????????????????????????????????? (Potentiomet
ric Determination of Equilibrium Constants)
??????????????????? (solubility-product
constants, Ksp) ??????????????????????,
????????????????????????????? (complex-formation
constants, Kf) ????????????????????????
??????????????????????? (dissociation constant,
Ka) ?????????????????????? ??????????
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Slide by Charoenkwan Kraiya, Ph.D.
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Example Calculate the formation constant Kf for
Ag(CN)2- Ag 2CN- Ag(CN)2- If the
cell SCE Ag(CN)2-(7.5 x 10-3 M), CN-
(0.0250 M) Ag develops a potential of -0.625 V.
Emeasured Eind Eref Eind -0.625
V 0.244 V -0.381 V
Slide by Charoenkwan Kraiya, Ph.D.
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At the indicator electrode
Slide by Charoenkwan Kraiya, Ph.D.
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In theory, any electrode system in which hydrogen
ions are participants can be used to evaluate
dissociation constants for acids and bases.
Example Calculate the dissociation constant KHP
for the weak acid HP if the cell SCE HP
(0.01 M), NaP (0.040 M) Pt, H2 (1.00
atm) develops a potential of -0.591 V.
Emeasured Eind Eref Eind -0.591
V 0.244 V -0.347 V
Slide by Charoenkwan Kraiya, Ph.D.
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At the hydrogen indicator electrode
Slide by Charoenkwan Kraiya, Ph.D.
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???????????????????????????????????????????
????????????????????????????????????????????
??????????????????????? (HA) ??????????????
?????? Ka ??? HA ??????? A-
??????????????????????????????? HA ????? 50
???????? Ka ? H ???? pKa ? pH ?????????? pH
????????????????????? ?????????????????????? 50
????????? pKa ?????????? ?????????????????????????
???????????? ?????????????????? ??????????????
Slide by Charoenkwan Kraiya, Ph.D.
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1. Skoog,D.A., West,D.M.,Holler,F.J. and
Crouch,s.m. Fundamentals of Analytical
Chemistry 8th ed. Saunders College
Publishing, 2004.
2. Harris,D.C. Quantitative Chemical
Analysis 5th ed. W. H. Freeman and
Company Publishing, 1998.
3. ??????? ?????????? ????????????????????
?? ????????????? 2 ????????????????????
???????????, ????????, 2542.
4. ?????? ???????????? ?????????????
????????????? 7 ???????????????????????????????,
????????, 2546.
Slide by Charoenkwan Kraiya, Ph.D.