I NOTES
I
I
Precision and Optimum Acidity in Complexometry Bret W. Budesinsky Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada
THEPRECISION of a comp~exometrictitration is given by the well known (1) equation p%
~460.6ApMl/a~aoa/@c~)
=
(1)
where ApM is the error in determination of actual metal ion concentration at the end point, P is the overall stability constant of the complex ML, CM is the total concentration of metal ion at the end point and (YE, (YOH are the coefficients of side reactions given by N
[Hl"Pn
=
(YH
(2)
The functions of log (YH = f(pH) and log CYOH = f(pH) are known or may be calculated from values of fin and Ps1 so that we can estimate the optimum acidity for a complexometric titration by means of Equation 6. All other complexing reagents (from buffers, etc.) should be absent. If some hydroxo polynuclear complexes (t > 1) are present, the CYOH is also the function of actual concentration of [MI and the formation of the complex of ML is usually slow. To prevent the hydrolysis of metal ion, a second complexing reagent of A is used (e.g., ammonia, acetate, etc.). Its necessary total concentration of CA is given by equation X
QOH
=
S
T
0
0
PiiP-'[HI-' t[Ml1-'[H1-*Pst
(3)
where Pn = [HnL][H]-n[L]-l and pSt = [M@H),][H]8[M]-1. The condition of acidity optimum for a complexometric titration may be seen from ( I ) , Le. (YHCYOH
=
=
minimum
(4)
M
+
(YH(A)
=
~ ( ( Y H c Y o H= ) / ~a ~oH ~ d ( ~ ~ / d p aH~ d a ~ ~ / d=p 0H ( 5 ) and after transformation
(d log (Ya/dpH)opt
+ (d log aOH/&H)opt
=
0
(6)
The same equation may be developed for the optimum acidity of complexes of M,(OH),HiLP, i f j = i = 0 and p = q = 1, see (2). Substituting for aHand (YOH from Equations 2 and 3 one has N
-
[Hl"Pn =
-f~
(7)
C [Hl"Pm 0
(10)
For development of Equation 9, two assumptions were made, the first one of CA >> cMsince the complexes of MA, should be relatively weak, the second one, only M(0H) was taken into account since it is the initiator of every hydrolysis. To use Equations 1 and 4-6, we must replace L Y O by ~ (YA where X (YA
=
0
(cA/~H(A)>~P~
(11)
0
and instead of Equation 8 we have
and
d log a ~ / d p H= - 2 d log a ~ ( ~ ) / d p=HZiii
d log ( Y O H / ~=~ H S
T
IS
T
Equations 7 and 8 show why the right side of Equation 6 has a value of zero. (1) G. Schwarzenbach and H. Flaschka, "Complexometric Titrations," Methuen, London, 1969, p 114. (2) B. Budesinsky, Z . Anal. Chem., 207,247 (1965).
928
(9)
where /311 is the overall stability constant of the complex M(OH), P = [M(OH)]/cM2 lo-*, CM is the total concentration of the metal ion, Pz is the overall stability constant of the complex MA,, C Y ~ ( A )is the coefficient of side reactions of A with protons, Le.
which means
d log a ~ / d p H=
C (CA/CUH(A)>ZP~ 0
ANALYTICAL CHEMISTRY, VOL. 42, NO. 8, JULY 1970
(1 2)
Many acidity conditions in cornplexometry are given by the type of indicator used. The concept of optimum acidity may reverse the situation and eliminate the indicators which do not obey the condition of optimum acidity.
RECEIVED for review October 22, 1969. Accepted April 23, 1970. Work supported by a grant from the National Research Council, Ottawa, Ont.
