Titrimetric Methods and Their Curves. Gravimetric, Volumetric, Coulometric Titrations.

1. Titrimetric Methods; Precipitation
Titrimetry.
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2. Titrimetry
• Volumetric titrimetry
• Coulometric titrimetry
• Gravimetric titrimetry

3. Some terms used in volumetric
titrimetry
• Standard solution: A reagent of exactly
known concentration that used in a
titrimetric analysis
• Titriation: A process in which a standard
reagent is added to a solution of an analyte
until the reaction between the analyte and
reagent is judged to be complete.

4. • Back-titration: a process in which the excess
of a standard solution used to consume an
analyte is determined by titration with a
second standard solution.

5. Equivalence Points and End
Points
• Equivalent point: the point in a titration when the
amount of added standard reagent is exactly
equivalent to the amount of analyte.
• End point: the point in a titration when a physical
change occurs that is associated with the condition
of the chemical equivalence.
• Indicators are often added to the analyte solution to
produced an observable physical change at or near
the equivalence point.

6. • Titration error (Et) : the difference in
volume or mass between the equivalence
point and the end point
Et = Vep – Veq
Vep : the actual volume of reagent required to
reach the end point
Veq : the theoretical volume to reach the
equivalence point

7. Indicators
• Physical change:
 the appearance or disappearance of a color,
 the change in color,
 the appearance or disappearance of turbidity.

8. Figure: The titration process.
Typical setup for carrying out a
titration. The apparatus consists of a
buret, a buret stand and clamp with a
white porcelain base to provide an
appropriate background for viewing
indicator changes, and a wide-mouth
Erlenmeyer flask containing a
precisely known volume of the
solution to be titrated. The solution is
normally delivered into the flask
using a pipet, as shown in.

9. Figure 13-1: The titration process.
Detail of the buret graduations.
Normally, the bret is filled with
titratnt solution to within 1 or 2
mL of the zero position at the
top. The initial volume of the
buret is read to the nearest ± 0.01
mL. The reference point on the
meniscus and the proper position
of the eye for reading are
depicted in figure.

10. Figure 13-1
The titration process.
Before the titration begins.
The solution to be titrated, an
acid in this example, is placed
in the flask and the indicator
is added as shown in the
photo. The indicator in this
case is phenolphthalein,
which turns pink in basic
solution.

11. Figure 13-1
The titration process.
During titration. The titrant
is added to the flask with
swirling until the color of
the indicator persists. In the
initial region of the titration,
titrant may be added rather
rapidly, but as the end point
is approached, increasingly
smaller portions are added;
at the end point, less than
half a drop of titrant should
cause the indicator to
change color.

12. 339
Figure: The titration process.
Titration end point. The end point is achieved when the barely
perceptible pink color of phenolphthalein persists. The flask on
the left shows the titration less than half a drop prior to the end
point; the middle flask shows the end point. The final reading of
the buret is made at this point, and the volume of base delivered
in the titration is calculated from the difference between the initial
and final buret readings. The flask on the right shows what
happens when a slight excess of base is added to the titration
mixture. The solution turns a deep pink color, and the end point
has been exceeded. In color plate 9, the color change at the end
point is much easier to see than in this black-and-white version.

13. Primary Standards
◎Primary Standard: A highly purified compound that
serves as a reference material in volumetric and
mass titrimetric method
1. High purity
2. Atmospheric stability
3. Absence of hydrate water
4. Modest cost
5. Reasonable solubility in the titration medium
6. Reasonably large molar mass

14. • Secondary standard: a compound whose
purity has been established by chemically
analysis and that serves as the reference
material for a titrimetric method

15. Standard Solution
• Standard Solution
1. Be sufficiently stable
2. React rapidly
3. React more or less complete
4. Undergo a selective reaction

16. • Two basic methods are used to establish the
concentration of such solutions:
(1) Direct method ～ ～ careful weighed quantity of
primary standard is dissolved in a suitable solvent and
dilute to exactly know volume.
(2) Standardization: the titrant to be standardized is used
to titrate
a weighed quantity of a primary standard
a weighed quantity of a secondary standard
a measured volume of another standard solution

17. Volumetric Calculations
◎Some Useful Algebraic Relationship
 definition of mole
nA =
mA
MA
mol =
mass A (g)
molar mass A (g/mol)
A: A species

18. ◎Some Useful Algebraic Relationship
definition of molar concentration
cA =
nA
V (L)
M =
mole A
V (L)
mol = V (L) x cA (mol A/ L)
V: the volume of the solution

19. • Weight or gravimetric titrimetry
～～ the mass of titrant is measured.
Gravimetric Titrimetry

20. Calculations Associated with
Weight Titrations
• Weight molarity (MW) : the number of moles of
reagent in 1 kg solution
0.1 Mw NaCl(aq) ～～
= 0.1 mol of the NaCl in 1 kg of solution
= 0.1 mmol in 1g of the solution
weight molarity =
mole A
solution (kg)

21. • Calibration of glassware and tedious cleaning to ensure
proper drainage are completely eliminated.
• Temperature corrections are unnecessary because weight
molarity does not change with temperature, in contrast to
volume molarity.
• Weight measurements can be made with considerably
greater precision and accutacy
• Weight titrations are more easily automated than are
volumetric titrations.
Advantages of Weight
Titrations

22. • End point ～～ physical change that near
equivalent point
Two most widely used end point
(1) changes in color due to the reagent, the analyte, or
an indicator
(2) change in potential of an electrode that responds
to the concentration of the reagent or the analyte
Titration Curves in Titrimetric
Methods

23. Types of Titration Curves
• Titration curve: plots of a concentration-related
variable as a function of reagent volume.
• Two general types of titration curves:
sigmoidal curve
linear segment curve

24. Figure 13-2
Two types of titration curves.
The p-function of analyte is plotted as a
function of reagent volume
Measurements are made on both sides
the equivalent point

25. Concentration Changes during Titrations
• The equivalent point in a titration is characterized by
major changes in the relative concentrations of reagent
and analyte.
• Example:
Ag+
+ SCN-
AgSCN(s)

27. Figure 13-3
Titration curve for the
titration of 50.00 mL
of 0.1000 M AgNO3
with 0.1000 M
KSCN.

28. • Precipitation Titrimetry: based on the reactions
that yield ionic compounds of limited solubility
(mid-1800s)
slow rate of formation of most precipitates
most important precipitating reagent is AgNO3, used
to determination of the halides, the halide-like
anion,
Argentometric methods
Precipitation Titrimetry

29. Precipitation Titration Curves Involving
Silver Ion
• Ag+
+ (halides)-
Ag (halides) (ppt)
• To construct titration curves, three type of
calculations are required
preequivalence
equivalence
postequivalence

30. 354

31. ◎ The Effect of Concentration on
Titration Curve
Figure 13-4
Titration curve for A,
50.00mL of 0.0500 M
NaCl with 0.1000 M
AgNO3, and B, 50.00mL
of 0.00500 M NaCl with
0.0100 M AgNO3.
355

32. 356
Figure 13-5
Effect of reaction completeness
on precipitation titration curves.
For each curve, 50.00m of a
0.0500 M solution of the anon
was titrated with 0.1000 M
AgNO3. Note that smaller values
of Ksp give much sharper breaks
at the end point.
The Effect of Reaction Completeness on
Titration Curve

33. ◎ Titration Curves for Mixtures of Anions
Titration of 50.00mL solution (0.05M I-
, 0.0800M Cl-
)
with 0.1000M AgNO3
Ag+
(aq) + I-
(aq) AgI (s) Ksp = 8.3 x 10-17
Ag+
(aq) + Cl-
(aq) AgCl (s) Ksp = 1.8 x 10-10
How much iodide is precipitated before appreciable
amount of AgCl form.

34. [Ag+
] [I-
]
[Ag+
] [Cl-
]
=
8.3 x 10-17
1.82 x 10-10
= 4.56 x 10-7
[I-
] = 4.56 x 10-7
[Cl-
]
After 25.00mL of titrant have been added
cCl = [Cl-
] =
50.00 x 0.0800
50.00 + 25.00
= 0.0533 M
[I-
] = 4.56 x 10-7
x 0.0533 = 2.43 x 10-8
M

35. The percentage of I-
unprecipitated:
no. mmol I-
= (75.00 mL) x (2.43 x 10-8
M)
= (75.00 mL) x (2.43 x 10-8
mmol/ mL)
= 1.82 x 10-6
original no. mmol I-
= (50.00mL) x (0.05 mmol/ mL) = 2.50
I-
unprecipitated =
1.82 x 10-6
2.50
x 100% = 7.3 x 10-5
%

36. 357
Figure 13-6
Titration curves for
50.00mL of a solution
0.0800 M in Cl-
and
0.0500 M in I-
or Br-
.

37. • As Cl-
begins to precipitate,
Ksp = [Ag+
] [Cl-
] = 1.82 x 10-10
[Ag+
] = = 3.41 x 10-91.82 x 10-10
0.0533
pAg = - log( 3.41 x 10-9
) = 8.47

38. • After 30.00 mL of AgNO3 had been added
cCl = [Cl-
] =
50.00 x 0.0800 + 50.00 x 0.0500 - 30.00 x 0.100
50.00 + 30.00
= 0.0438 M
[Ag+
] = = 4.16 x 10-91.82 x 10-10
0.0438
pAg = 8.38

40. Chapter13 p
Three types of end points are encountered in
titrations with AgNO3 (silver nitrile)
1. Chemical
2. Potentiometric
3. Amperometric
◎ Indicators for Argentometric
Titrations

41. Chemically Indicator
• The color change should occur over a
limited range in p-function of the reagent or
the analyte.
• The color change should take place within
the steep portion of the titration curve for
the analyte.

42. Chromate Ion: The Mohr
Method• Sodium chromate (Na2CrO4)
~ ~ determination of Cl-
, Br-
, CN-
~ ~ form a brick-red silver chromate (Ag2CrO4)
Ag+
+ Cl-
AgCl (s)
2Ag+
+ CrO4
2-
Ag2CrO4 (s)
white
red
titration reaction
indictor reaction

43. The silver concentration at chemical
equivalence :
[Ag+
] = Ksp = 1.82 x 10-10
= 1.35 x 10-5
M
√ √
(1.35 x 10-5
)2
1.2 x 10-12
[CrO4
2-
] = =
[Ag+
]2
= 6.6 x 10-3
M
Ksp

44. Adsorption Indictor: The Fajans
Method
• Adsorption Indictor: an organic compound
that tends to be absorbed onto the surface of
the solid in a precipitate titration
Fluorescein

45. Iron (III) Ion: The Volhard
Method
• Silver ions are titrated with a standard solution of
thiocyanate ion:
• Iron (III) serves as the indictor:
Ag+
+ SCN-
AgSCN (s)
Fe3+
+ SCN-
FeSCN2+
red