Potenliometrit Titrations
F. J. C. Rossotti and
Hazel Rossotti University of Oxford
Using Gran Plots
England
A textbook omission
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A number of recent textbooks
(1-10) of
analytical chemistry discuss potentiometric acid-base titrations, but, none of these mentions Gran’s graphical method (11) of end point determination. Gran's method seems to us to be the best yet suggested, and lias been successfully used for many years in Stockholm and elsewhere for the precise analysis of acids and bases. The method is very simple. A volume V of acid of initial concentration H is titrated with a volume v of strong base of concentration B in the galvanic cell (I) /_
.
'
electrode reversible to hydrogen ions
titration
I
II
solution
|
II
reference,, half-cell ^
.
The potential of cell (I) is given by B
=
RT
E0'
In [H+Hh
-
+ Ej
use a
(F 4- y)lQ-BB/2.10Mr From equations (1), (2), and (5) 10-W +
=
For any value of v before the equivalence point +1 11
V1-
=
V +
G vt(V + y)
VMv‘
=
v
If pH is measured directly, tion defined as =
(F +
=
B(ve
=
(F +
-
V +
v) K
P
use
of a func-
e)10-i>*
(3)
may make
we
[ +]
~
ve,
From equations (2) and (3) =
If,
(i··,
-
v)B7k
instead of pH, the potential E is determined,
(4) we
may
v)Bya
_
(0)
After the equivalence point, m
+
Km
_ ~
J
1
_ -
[OH-j
if„{ F + B(o
-
y)
(7)
vt)
where Kv. is the stoichiometric ionic product of water. For use in the alkaline range, functions analogous to and may be defined in terms of the experimental quantities pH and E respectively, viz. 10 ~4 M the functions ( ) and ( ) gion become curved as the acidity is decreased. If the may linear at the highest acidities used, the equivare plots alence point of the strong acid may again be deter0 or 0 (Fig. 3). mined by extrapolation to (3) If the strong base is contaminated with carbonate, the functions '( ) and '( ) are curved in the region of ve. The value of ve VH/B (where B ([OH-] + 2[C032-]) is the total concentration of base) may be found using only measurements in the acid region v < If the functions '( ) and '{ ) are linear ve (Fig. 4). over an appreciable range of v, they may be extrapolated to cut the abscissa at the point v/ VH/B' (where />' is the total concentration of hydroxyl ions in the solution of base). An estimate of the carbonate ion concentration may therefore be obtained. =
=
=
=
=
Titration of Weak Acid with Strong Base
If an acid HA is not fully dissociated in solution, the free hydrogen ion concentration is no longer given by equation (2) but by the relationship (12) K„[HA]/[A-] [H+] acid constant where Ka is the stoichiometric dissociation of HA. If the titrant is the monacidic base MOH, then =
[A-]
[M+] + [H+]
=
[OH-]
-
Ca
where
CA
tion.
If
[A-]
-
=
-
V
[OH-] (13)
-+- V
[H+] + [OH-]
(14)
is the total concentration of HA in the solui>B
V +
» [H+]
v
linear functions of v, such that t(v) intersects '( ) and ( ) intersects '( ) at the point 0, ve (Fig. 5). Deviations f rom linearity may be due to one or more of the following factors: (1) At the beginning of the titration, condition (15) may not be fulfilled, especially if the acid is only moderately weak. The value of ve must then be found using only that part of the function t(v) or ( ) which is found to be linear (Fig. 5). (2) As v approaches ve, condition (16) may not be fulfilled if the are
-
and =
droxide.
=
y~-v + [H+]
[HA]
Figure 4. Portions of Gran plots ( ) or \//(v) and '[ ) or '[ ) for the titration of a strong acid with a solution containing both carbonate and hy-
05)
[OH-]
-
and VH vB » [H+] V + v -
-
[OH-]
(16)
then from equations (12), (13), and (14) Ka( VH vB
vB)
-
[H+]
=
(17)
By analogy with equations (3), (4), (5), and (6) define the functions2 T
=
y[H+]TH
=
yio-r"
=
Ka(v.
-
we
»)y„
may (18)
and --
«10-^/2.803nr
=
Ka{ve
-
v)yw\0~t.E«' + e¡)f/2mrt
(19)
After the end point, v > ve and equations (7) to (11) are again valid. Since, for a weak acid, [H+] is low even at the beginning of a titration, Ej will probably be negligible. If, moreover, the initial solution of HA is not too concentrated, the ionic strength will not vary grossly throughout the titration, and the terms Ka, Kw, and Then r and 7n will remain approximately constant.
The remarks in footnote to , ', and T below. 2
1
apply to the quantity
r,
and also
Figure 5. Gran plots t[v) or 0(v) and
