graphic method for the determination of titration end-points.pdf

7/24/2019 GRAPHIC METHOD FOR THE DETERMINATION OF TITRATION END-POINTS.pdf

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Talanta.1966. ol. 13.pp. 1431 o 1442. Pergamon ressLtd. Printed n Northern reland

GRAPHIC METHOD FOR THE DETERMINATION

OF TITRATION END-POINTS *

FOLKE INGMAN and EBBE STILL

Department of Analytical and Inorganic Chemistry, Abe Akademi, Abo, Finland

(Received 21 Apr il 1965. Revised 9 Apr il 1966. Accepted 10 May 1966)

Summar-Aa extension of Grans method for the determination of

equivalence points in potentiometric acid-base titrations is presented.

Equations are derived assuming that the stability constants of the

reactions are known. The equations make it possible to locate the

equivalence point with fair accuracy when acids with stability constants

ranging from

KEa N

10 to

Kz* -

lOlo are titrated. The limit of

KL above which Grans equations do not yield satisfactory results is

about 10. Conditional constants and a-coefficients are used to extend

the method to apply to more complex systems, where

more than one

species eacts with the titrant.

AMONG the graphical methods for the determination of titration end-points published

by various authors, those of Gran 1*2 ave attracted considerable attention.

Grans first method1 involves the plotting of either AV/ApH or

AV/AE

as a

function of V, the volume of added titrant, after values of E or pH have been experi-

mentally determined for several values of

V.

In the ideal case the resulting plot

consists of two straight lines, which intersect each other and the V-axis at the

equivalence point. One of the drawbacks of this method is that the accuracy of the

TABLE I.-GRANS SECOND METHOD

Functions plotted

Substance

on the acid side of the

on the alkaline side of the

titrated equivalence point

equivalence point

Strong acid (V, + V)lO(k-pa) =f(V)

(V, + V)lO*H-) = f(V)

Weak acid

V.lO-*= =f(V)

(V, + V)lOp=-k =f( V)

The titrant is in each case assumed to be a strong base.

V, is the

volume of the solution before the titration is started, Vthe volume of added

titrant, and k, k are arbitrarily chosen constants.

plot is influenced by the accuracy of the experimental data, and another that the

lines for titrations of weak electrolytes are more or less curved and do not yield

reliable results, because the change in pH or E at the equivalence point is too small.

The second method of Gran2 is based on an original idea of Ssrensen,8 who

plotted {H}, the antilogarithm of -pH, as a function of V for titrations of strong

protolytes, disregarding the effect of the changing volume. Sorensen employed an

analogous method when titrating halides with silver nitrate. Gran introduced a

correction for the volume change during the course of the titration.

He also extended

his method to titrations of weak protolytes, and to other types of titrations than

those involving neutralisations.

The functions plotted when Grans second method2 is applied to acid-base titrations

are presented in Table I.

+ Presented n

part by E.S. in December 1962 at Finska Kemistsamfundet, Helsingfors.

1431


2/12

1431

F. INGMAN and E. STILL

Grans second method yields excellent results when a moderately weak acid

such as acetic acid is titrated with a strong base. Two straight lines are obtained

and the point where these lines intersect each other and the V-axis is the equivalence

point.

For weak acids with stability constants of 10 to 10s the lines obtained by this

method are no longer straight but slightly curved. Moreover, the asymptotes do

not intersect at the V-axis, and the point where they intersect only occasionally

coincides with the true equivalence point. These deficiencies originate in the simpli-

fying assumptions made by Gran when deriving his equations.

The aim of the present work is to show how it is possible, when the stability

constant for the reaction is known, to derive an expression which, when plotted

against the titrant volume V, yields a straight line that intersects the V-axis at the

equivalence point.

The expression for the titration of a weak acid with a strong

base will first be derived.

It will further be shown how it is possible to generalise this expression by the

introduction of conditional constants and a-coefficients.4 The determination of the

equivalence points of titrations of complex systems is thereby facilitated. As an

example, the titration of a weak acid in the presence of another weak acid or a metal

ion will be considered.

TITRATION OF A WEAK ACID WITH A STRONG BASE

A weak acid HA is titrated with a strong base (sodium hydroxide). The initial

concentration of the acid is denoted by C,, and the initial volume by V,. The

concentration of the strong base is denoted by CNaOHand the volume added by V.

The consumption of the base at the equivalence point is denoted by V,,.

The derivation is based upon the following three conditions:

(a) The law of mass action must hold:

HA+

H 4-A;

KH _ tHA]

HA- H)[A] *

(1)

(For convenience, all signs of charge are omitted in this paper). The constant Kg*

is a mixed constant,

valid at a certain ionic strength. Mixed constants, where

the activities of the hydrogen and hydroxide ions (denoted by {H} and {OH)) are

used in conjunction with concentrations of all other species, are very convenient for

equilibrium calculations, since pH-values are nowadays almost solely determined

potentiometrically. The activity of the hydrogen ion is related to the concentration

by the expression

{H} =_fiJHl.

where f s the activity coefficient of the ion.

(b) The solution must be electrically neutral, meaning that

[Al + [OHI = Wal + [HI.

(c) The equation

ve NsOH = v0cHA

must be valid at the equivalence point.

(2)

(3)

(4)


3/12

Determination of titration end-points

1433

The concentration of the sodium ions is

M = cKaOH

vo+

v

(5)

which, when combined with equation (3), gives

[Al = ?- C H + WI -

WI

v, + v

[HA] = + C,, - [A] = + CNaoH

[HI + [OHI.

(7)

Substitution of (6) and (7) into (1) and subsequent rearrangement of the terms yields

Veq V = V{H}K +

~([Hl- tOHI)(1+ (H}K,H,I

The values of most of the constants have been determined at an ionic strength

of ,U = 0.1. It is thus practical to adjust the ionic strength to this value, and in our

experiments sodium perchlorate was used for this purpose. It may be noted that in

equation (8), the concentrations [H] and [OH], caused by the electroneutrality

rule, occur in addition to the hydrogen ion activity {H} determined potentiometrically.

For accurate analyses the [H] and [OH] values in equation (8) should be calculated

from the activities. This means that at an ionic strength of 0.1, [H] = {H}/10-~08

and [OH] = {OH}/10-0.12.

A comparison of equation (8) with the Gran equations for the titration of a

weak acid reveals that Gran plotted only the first term V{H}K , written in the form

VIO(k-*H), on the acid side of the equivalence point, k being a constant arbitrarily

chosen to yield numerical values that could conveniently be handled. On the alkaline

side of the equivalence point Gran plotted the term

(V. +

v>[OH]/C,,,, against

V. Gran wrote the term in the form (V, + V)lO(pH-K), k being a constant similar

to

k.

When plotted against

V,

equation (8) yields a straight line with a slope of 45.

The titration curves of p-alanine (log K& = 10.2) and ammonium nitrate

(log K& = 9.4) with sodium hydroxide are shown in Fig. 1. The titrations were

performed at an ionic strength of ,u = 0.1. Kiellands values6 were used for the activity

coefficients, and the values of the stability constants were taken from the literature,6

The use of equation (8) is illustrated in Tables II and III and Fig. 2. For comparison,

Fig. 3 shows the curves that result when Grans formulae are used for the titration

of ammonium nitrate.

The method described can be used only if the value of the stability constant

K& is known. This could naturally be considered a serious drawback. The method

is, however, intended for use in cases where no other means are available for the

determination of the equivalence point with satisfactory accuracy. Such cases are

encountered in practice when very weak acids (7 < log K& < 10) are titrated.

The limit beyond which the simple Gran equations do not yield satisfactory results

can be considered as log K& N 7.

For most analytical purposes the value of the stability constant can be estimated

with satisfactory accuracy from the pH value at the point where VN V,,/2, i.e.,

3


4/12

1434

F. INGMANnd E. STILL

12

77

10

9

PH

18

7

6

5

4

1 2 3 4 5vs 7

a g 10

FIG. l.-Titration of 50 ml of 1.07 x lO-SM p-alanine (log KL = 10.2) and titration

of 77 ml of 1.02 x lo-*M ammonium nitrate (log K = 9.36) with O*lOOM sodium

hydroxide. At the equivalence point, the consumption is theoretically 535 ml for

&alanine and 7.85 ml for ammonium nitrate.

TABLEII.-/I-ALANNE

log v, + V

V

pU3

CNaOE 1% (W-II - [HD

1 + (HI&

K, - v

::; 955.77 2.71.72 -44.11 3 1 + l~600. = 100*4oo.67 4.47.03 - 0.13.15 = 4.34.88

2.0 9.95 2.72 -3.93

1 + 100.86 = 100.U 3.56 - 0.17 = 3.39

2.5 10.12 2.73 -3.76

1 + 100.08 = 1OO.U 300 - 0.20 = 2.80

3.0 10.28 2.73 -360 1 + 10-0.08

= 100.N 2.50 - 0.25 = 2.25

3.5 10.43 2.73 -3.43 1 + lO-0.as

= lOWI 2.06 - 0.30 = 1.76

40 10.59 2.74 -3.29 1 + lO-0.*0

= 100.16 164 - 040 = 1.24

4.5 10.75 2.74 -3.13 1 + 10-0.65

= 100. 1.27 - 0.53 = 0.74

5.0 10.91 2.75 -2.97 1 + 10-0.1

= 100.08 098 - 0.73 = 0.25

5.5 11.07 2.75 -2.81 1 + 10-0.81

= 100.06 0.59 - 0.98 = -0.39

6.0 11.21 2.75 -2.67 1 + 10-1.0

= 100.04 0.06 - 1.32 = -1.26

V, = 50 ml, log K, = 1400, log K = 10.20 (from Fig. l), log foH = -0.12, logf, = -0.08

VW - V = V(H )K:A +

E(D-U -

[OHD(1+ U-W&I

TABLE III.-AMMONIUM NITRATE

log v, +

v

V

PUS cN,O,

logWH1 -

[HI) 1 -t U-XV&

v,, - v

8.50 290

8.89 2.90

3.0

9.15 2.91

4.0

9.38 2.92

5.0 960

2.92

6.0

9.85 2.93

7.0 10.18 2.93

8.0 10.69 2.94

9.0

11.14 294

10-o 11.37 294

-538

1 + 100.86

5

1(-y.= 7.24 - 0.03 = 7.21

-4.99 1 + 100

= l@*EO 5.91 - 0.03 = 5.88

-4.73 1 + 100.8

= 100. 4.87 - 0.04 = 4.83

-4.50 1

+ 10-0.0 = lOo.P@ 3.82 - 0*05 = 3.77

-4.28 1

+ lO-0.S = lOWSO 2.88 - 0.07 = 281

-4.03

1

+ 10-O.&@ 100. 1.95 - 0.11 = 1.84

-3.70 1

+ lO-o.s* = 100.0 1.06 - 0.20 = 0.86

-3.19 1 + lO-l.88 = 100.0 0.37 - 0.59 = -@22

-2.74 1

+ 10-1.18 = 100.0 0.15 - 1.62 = -1.47

-2.51

1

+ 10-5.0 = lOc .OO 0.10 - 2.69 = -2.59

I, = 77 ml, log Km = 1400, log Kg* = 9.36, logfoX = -0.12, logfH = -0.08

V,, - V = V{H}KL +

ZWl - PHDU + O-IV&)


5/12

Determktion of titration end-points

1435

2

I Y

p ALAN/NE

1

\I

o

I I I\ I ,\I

I

1 3 4 51 6 f X 9mllO

7 I I vu I

I\ I 1

FIG. 2.-Straight lines that result when titration data in Fig. 1 are substituted in

equation (8). The principles of calculation are illustrated in Tables II and III. For

/k&nine the straight line intersects the V-axis at V = 5.22 ml, which corresponds to an

error of -2-4 %.

For ammonium nitrate the straight line intersects the V-axis at V =

7.78 ml, which corresponds to an error of -0.9 %.

2

1

FIG.3.-The straight line (a) that results when the titration data for ammonium nitrate

shown in Fig. 1 are used to compute V, - V from equation (8), and the curves

(b, c, c, c) that result when Grans second method is used. The abscissa of the point

of intersection depends on the value of the arbitrarily chosen constants k and k (cJ

Table I). The values of k used for computing c and c differed by &@30 from the

value of k used for computing c.

when approximately half of the acid has been titrated. If a very high degree of

accuracy is sought, the method developed by Goldman and Meites can be used.

If an incorrect value of the constant has been used, the plot will not have a slope of

45 and will not be linear.

It may be mentioned that the results of the titrations given in Figs. 1 and 2 can

be found without using any graphic procedure by calculating Vea for the various

volumes of titrant (ix., in the last column of Table II, V is added to Feq v).


6/12

1436 F. INGMANnd E. ST~L

However, this procedure is not always appropriate (cJ the titration presented in

Table V).

TITRATION OF A WEAK BASE WITH A STRONG ACID

An analogous expression can be derived for the determination of the equivalence

point when a weak base is titrated with a strong acid (hydrochloric). The equation is :

Veq - V =

V{OH}K,O& +

owl - [HI)0 + WW%d

(9)

where

POW

K% = [Bl(OH)

This case will not be treated in this paper.

TITRATION OF TWO WEAK ACIDS WITH A STRONG BASE

The determination of the total amount of acid in a mixture containing two weak

acids HAr and HA,, is usually quite easily accomplished, provided both acids are

strong enough to be titrated in the conventional manner,

i.e.,

provided that both

K&, and K&11

< 10. When, however, the amount of the stronger acid (here

taken to be HA,) in the mixture is to be determined, complications often arise owing

to the fact that the difference between the stability constants of the two acids is too

small to permit a conventional stepwise titration.

When conditional constants and a-coefficients4 are used, it is quite easy to derive

an expression analogous to the one already derived for the titration of one weak

acid, and this will permit the determination of the first equivalence point.

In this case the equation

HA, + OH

+ A, + H,O

(10)

represents the main reaction.

The reaction

HA,, + OH

=S A,, + H,O

(11)

is considered a side-reaction, the effect of which is taken into account by introducing

the appropriate cr-coefficient.8

The electroneutrality rule states that in this case

Dal + WI = (PHI + LW + [AI1= PHI + LW (12)

Comparison of this equation with equation (3) shows that [OH] should be substituted

for [OH] in equations (6) and (7), and this in turn means that the only change that

need be made in equation (8) is the substitution of [OH] for [OH], which yields

ve,

J-, V(H}K + E (WI - tOHI)(l + (H}K&J.

(13)

As usual, [OH] denotes the concentration of not only the free hydroxide ion but

also of all the hydroxide ion added to the solution that has not reacted with HA,

according to the main reaction.

There will be no noticeable error if the activity


7/12


1437

coefficient foaP

is considered equal to foH. The concentration of hydroxide ion

that has reacted with HAzr is given by [A,,]. Hence

WI1 = [OH] + IM =

%H[OHI

(14)

where

(15)

To test the equation derived several titrations of chloroacetic acid (log K&

=

2GQs in the presence of acetic acid (log K& = 4.7) were performed using sodium

hydroxide. As can be seen from Table IV and Figs. 4 and 5 the results were in close

agreement with the theoretical. Figure 4 shows one of the titrations curves and Fig. 5

shows the straight line that results when Yeq -

Y computed from equation (13) is

plotted against Y to determine the location of the equivalence point.

3

P

I

7

6

3

0 1 2 3 4

5 6 7

---+v

of 50 mi of a solution 0.72 x 10-W in cbloroacetic acid and

0.50

X lO- M

in acetic acid (A log K = log Ii - logKm,, = 1.9) with O*lOOM

sodium hydroxide. At the equivalence point, the consumption is theoretically 360 ml

for chloroacetic acid.

FIG. 4.-Titration

TABLEV.-MONO~HLOROACETZC CID(HA*) AND ACETIC CID@A~~)

log v, + v

Y ~0.0

ClWOli

[HI - [OH1

I+ W&

VW-- v

0.0 2.59 2.70 1O-%8 _ ~O-l.85=E*(ye.sa

0.5 2.68 2-71 ] O-9.80 IO-4.8 = ,0-W

1.0 2.78 2.71 IO-P.70 *o-*.1, =E*O-8.1

1~5 2.91

2.72

10-1.8 _ IO-4.0P i IO- .86

2.0 3.06 2.72 IO-P.08 10-m = 10-8.03

2.5 3.24 2.73 IO-B.16 10-a.,* 3 IO-a.ao

3.0 348 2.73 IO-0 _ IO-Em =E 10-u*

3.5 3.80 2.73 ~0-9.72_ ,0-w, 5 _ 10-W

4.0 4.14 2.74 IO-.00_ ,O-8 1 _,O-8.87

4.5 4.47 2.74 IO-WJ 10-861= - ,0-2.6

0% + 427 = 4.27

0.74 + 3.09 = 3.83

1.18 + 219 = 3.37

1.30 + 1.35 =I 2.65

I.23 + 0.79 = 2.02

1.02 + 0.38 = I.40

0.70 + 0.05 = 0.75

0.39 - 0.30 =i 0.09

0.20 - 0.78 = -0.58

0.11 - 1.70 = --I*59

v, = 50 ml, log K&, = 2~35, bg K& = 9.24, [HA,,1 - 10-aso, log

aoa = 6-94 log ox = --0*12~

log& = -0.08,

V,, - V- V(H}K +

~GHI- WU)(1 + WK )


8/12

1438 F.

INGMAN

and E. Snu

FIG. 5.--Straight line obtained when titration data plotted in Fig. 4 are used to compute

V,, - V from equation (13). The different steps of the calculations are shown in

Table IV. The straight line intersects the V-axis at V = 3.62 ml, which corresponds

to an error of +0.6x.

TITRATION OF A WEAK ACID IN THE PRESENCE OF A METAL ION

A very weak acid can be made apparently stronger if its conjugate base A produced

in the reaction

HA+OH+A+H,O

(16)

can be forced to take part in a side-reaction. The equilibrium of the main reaction

will then shift to the right and the numerical value of the conditional constant4 of

reaction (16), Kiu = CC&~, will increase. Many metal ions react readily with the

conjugate base of an acid to form a complex according to the scheme

A+M+MA.

(17)

As has been pointed out by Ringborn,

4 this side-reaction permits the titrating of

many acids that are too weak to be titrated directly.

However, the metal ions are themselves acids, and will consequently react to

some extent with hydroxide ions. This side-reaction is undesirable, but cannot be

avoided. It may be written

M+OH+MOH.

(18)

Frequently matters are further complicated by the fact that the metal hydroxide

starts to precipitate at a pH that is very close to the pH at the equivalence point

of the titration. As a result, the titration curve will be deformed as in Fig. 6.

In order to determine the location of the equivalence point on a titration curve of

this shape, it is necessary to employ a method that utilises points on the titration

curve that lie on the acid side of the equivalence point only.

The value of the conditional constant of the acid may be low enough to permit

the use of one of Grans simple equations.

In other cases one may be forced to use

an expression which can be derived similarly to the expressions already presented in

this paper.

The effect of these two side-reactions is taken into account by introducing the

coefficients

:

aA = 1 -I MKMA (19)

QOH M) = 1 + WKHOH 20)


9/12

Determination of titration end points 1439

where Knaa and &on denote the stability constants of the complexes MA and MOH

respectively.

Assuming that a bivalent metal is added to the solution in the form of MB, the

condition of electroneutrality now is:

2[B] + [A] + [OH] = [H] + [Nal+ 2[Ml+

[MAI + [MOW.

(21)

When [MA] + [MOH] is added to both sides and ([Ml + [MA] + [MOH]) is

substituted for [B], it is found that

([Al + [MA]) + (PHI + NOHI) = [A] + [OH] = WI.

(22)

A comparison of this equation with equation (3) shows that the following changes

should now be made in equation (8): K,Hk = K /ccAcMI should be substituted for

K , and [OH] should be substituted for [OH]. The final result is then

V., - V = V{H}Kgf + F([H] - [OH])(l + {H}K,f)

(23)

NaOH

Not e If a univalent metal is added as MrBr, the solution will be electrically

neutral when

WI1 + [Al + COHI = [HI + Ml + Ml.

(24)

As tB,l = [WI + MA1 + MOHI,

substitution will again lead to equation (22).

However, most of the metals that can be used for the purpose discussed are bivalent.

To determine whether equation (23) is valid in practice, an aqueous solution of

acetylacetone (about lO_aM) containing an approximately three-fold excess of copper-

(II) salt was titrated with sodium hydroxide. In this titration the reaction between

copper ions and the acid proceeds towards completion during the titration; therefore

the conditional constant Kgf

will not be constant but will attain the calculated

value at the end of the titration. Nevertheless, an approximately straight line will

be obtained, and the intersection with the V axis will coincide with the equivalence

point.

The stability constant is

KHfIA IV.@,

corresponding to

KiH =

105.1.

When

the appropriate values

= 1 +

10-1.51(j3.2 = 106.7

uA(Cu)

(25)

and

aOB~Cu~ f

1 + 10-1.5105.7= 104.?

(26)

are inserted, the conditional constant of the base formed will be

Ki,u =

ctA(CujKzH 10e*71051 lo,_6

-_Z

104.2

(27)

a0H(Cu)

This constant corresponds to an acid constant of 10s.4 which determines the shape

of the titration curve.0 The titration is thus a borderline case and could possibly

be accomplished with visual end point indication, were it not for the fact that copper

hydroxide begins to precipitate at pH very close to that at the equivalence point.

Furthermore, the colour of the copper compounds may affect the colour change of

the indicator.


10/12

1440

F. INGMAN and E. STILL

The titration results given in Table V and Figs. 6 and 7 are seen to be in good

agreement with the theoretically calculated values. The ionic strength in this titration

is not 0.1 but O-13. This, however, means a difference in the log f a alue of only

O-01, which is neglected.

Figure 6 also illustrates the difficulties encountered when an attempt is made to

locate the equivalence point on a titration curve which is deformed by the precipita-

tion of a metal hydroxide. The pH of the equivalence point is 5.0 andcopper hydroxide

begins to precipitate at pH

N 5.2 (if the solubility product of copper hydroxide is

10-18.2, he point where precipitation should occur can be calculated to be pH N 5.6).

72

10

9

8

t

ri7

6

0 1 2 3 4 5 6 7

-v

FIG. 6.-Titration of 50 ml of 0.91 x 10-eM acetylacetone (log K = 8.9) containing

about a three-fold excess of copper ([C&t,, = 0.04M) with O.lOOM

SOCCU~

hydroxide. At the equivalence point the consumption is theoretically 4.55 ml.

TABLE V.-ACXTYLACETONECOMPLEXEDWITHCOPPER

log v, + V

V

p{W

CNsOH log

([HI - W-U)

H,Aj

1 -t-{J KHA K, - v

o-0 2.63

2.70 -2.55

1 + lO-0.aa

= 100.X 000 + 200 = 200

1.0 2.76

2.71 - 2.68

1 + 10-M

= loo.* 0.31 + 1.41 = 1.72

2.0 2.93

2.72 -2.85

1 + 10-0.88

= 100.08 0.42 + 089 = 1.31

3.0 3.19

2,73 -3.11

1 + 10-0.84

= 100.06 0.35 + 047 = 0.82

3.5 3.38

2.73 -3.30

1 + 10-L

= 100.08 0.26 + 029 = 0.55

4.0 3.66

274 -3.58

1 + lO-X.01

= 1OwJa 0.16 + 0.15 = 0.31

4.5 4.30 2.74 -422 1 + 10-8.06= 100.00 0.04 + 0.03 = 0.07

V, =

50 ml, log

K =

8.95, log

Kct i =

8.2, log

KcuOH =

5.7, [Cu] = 3 x lo-* gives log

tLA(cu)= 6.7, log aOHICu, 2.25, and log Kz iA = 2.25

logfn = -0.08, logfen = -0.12

H,A'

V,, - V= VIWKHA + E WI - [OHl)(l + {H)@iA)


11/12


1441

Oo 1 2 3

4 5 ml

v

FIG. 7.-Straight line obtained when titration data plotted in Fig. 6 for a titration of

acetylacetone complexed with copper are used to calculate V,, - Vfrom e

uation (231.

a

he intermediate and final results of the calculations are collected in Ta

le V. The

straight line intersects the V axis at F = 4.63 ml, which corresponds to an error of

+1-s %.

EXPERIMENTAL

The experimental work was performed using a Metrohm Potentiograph E 336 recording potenti-

ometer equipped with an EA 107 glass electrode and an EA 404 saturated calomel reference electrode.

All solutions were prepared from reagent-grade chemicals. Special care was taken to ensure that

the O~lOOM sodium hydroxide solution was free from carbonate. The following procedure was

followed in the titrations:

A lO-ml sample of an approximately 5 x lo-*Macid solution was transferred to a W-ml beaker.

Any additions of other acids or metal salts were made and the solution was diluted to 50 ml after

the addition of sodium perchlorate to adjust the ionic strength to 0.1, The solution was titrated

with @lOOM sodium hydroxide solution with magnetic stirring at the slowest practical speed of

titration.

Esumb-On propose une extension de la mdthode de Gran pour

determiner les points d%quivalence dam les titrages potentiometriques

acide-base. On dtduit des equations en supposant que les constantes

de stabilite des reactions sont connues.

Les equations rendent possible

la localisation du point d&privalence avec une assez grande precision

lorsquon titre des acides dont les constantes de stabilite se situent

entre K N 10 et KS N lOlo.

La limite de KL au-dessus

de laquelle les equations de Gran ne donnent pas de resultats satis-

faisants est denviron 10. On utilise. des constantes conditionnelles et

des coefficients a atin detendre la mtthode pour lappliquer a des

systemes plus complexes, oh plus dune esp&ce reagit avec lagent de

titrage.

Zusammeafassnng-Es wird eine Erweiterung der Granschen Methode

zur Bestimmung von Aquivalenzpunkten bei potentiometrischen

+%ure-Basen-Titrationen gezeigt. Unter der Voraussetzung, daB die

Stabilitltskonstanten der Rcaktionen bekannt sind, werden Gleich-

ungep abgeleitet. Die Gleichungen ermbglichen die Lokalisierung

des Aquivalenzpunktes mit ziemlicher Genauigkeit, wenn Stiuren mit

Stabilitiitskonstanten von K~A 10 bis K - lOlo titriert

werden. Die Grenze von

K ,

tiber welcher die Granschen Gleich-

ungen keine zufriedenstellenden Ergebnisse liefem, ist ungefahr 10.

Mediumabhangige Stabilittbskonstanten und a-KoefIizienten zur

Erweiterung der Methode gebraucht, urn sie auf kompliziertere

Systeme anzuwenden, wo mehr als eine Spezies mit dem Titranten

reagiert.


12/12

1442 F.

INGMAN

and E. SELL

REFERENCES

1. G. Gran, Acta Chem. and., 1950,4,559.

2. G. Gran, Analyst, 1952,77,661.

3. P. Sprrensen, Kern. Maanedsblad, 1951,32,13.

4. A. Ringbom,

Complexation in Analytical Chemistry,

Wiley/Interscience, New York/London, 1963.

5. I. M. Kolthoff and P. J. Elving, Treatise on Anal ytical Chemistry, Part I, Vol. 1, p. 242.

Interscience,

New York, 1959.

6. A. E. Martell and L. G. Sillkn, Stabil ity Constants of Metal-ion Complexes, Special Publication

No. 17. The Chemical Society, London, 1964.

7. J. A. Goldman and E. Meites, Anal . Chim. Acta, 1964,30, 28.

8. E. W&n&en, Tukzntu, 1963,

10 221.

9. B. Eklund and A. Ringbom, Finska Kemists. Medd., 1962,71, 53.

graphic method for the determination of titration end-points.pdf

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