EFFECTOF WATERON ,ICID--BASE EQUILIBRIA IN ACETICACID
Nov. 20, 1957
and which would maintain the temperature constant t o within 0.1" were found adequate. In the event that equilibrium was not reached before the bath was nearly spent, a
[CONTKIDUTION FROM
5'315
fresh bath could be substituted for the depleted one rapidly enough S O that the sample tube did not warm. ST.LOUIS,RIISSOURI
THE SCHOOL O F CHEMISTRY,
UNIVEKSITY O F
MINNESOTA]
Acid-Base Equilibria in Glacial Acetic Acid. V. The Effect of Water on Potentiometric and Indicator End-Points in Acid-Base Titrations in Acetic Acid BY S. BRUCKENSTEIN AND I. M. KOLTHOFF RECEIVED JUNE 14, 1957 The effect of watcr 011 acid-base equilibria in acetic acid can be calculated quantitatively for titratious carried out potelltiornetrically or with indicators. The equations governing the shape of potentiometric titration lincs of bases in acetic acid as a function of water concentratiou have been derived and experimentally verified. These relatiomhips have been used t o calculate the change in e.m.f. in the vicinity of, a t and after the equivalence point for bases of differeut concentration and strength. They predict that titration to an equivalence potential, which is independent of concentration of base, will be a n accurate procedure. The relationships determining the ratio of acid to basic color of a n indicator base over the titration range in water Containing acetic acid also have been established and tested aud used t o predict the color change of p-naphtholbenzein (PXB) in a sodium perchlorate solution.
Water is an undesirable contaminant in the a chloranil electrode as the hydrogen ion indicator titration of bases in acetic acid.ld6 With increas- electrode. Since the acetate ion concentration is ing water concentration the magnitude of the first negligible in such a solution, we can write derivative in a potentiometric titration of a base [H+] [H30+] = [Clod-] Pa) and the sharpness of the color change of an indicator in the region of the equivalence point de- From the expressions of the various equilibrium creases. Furthermore3 the potentiometric end- constants we find [ClO,-] = KHC]O~CHCIO~/ [H+] point is found after the equivalence point, and the and [H30+] = KH,OCH,O[H+]/K~. After reartitration error increases with the water content o€ rangement, equation 2a may be written as the acetic acid. Water is a weak base in acetic acid, and it is possible to calculate quantitatively its effect upon titration curves in acetic acid7d and particularly upon the break in potential and the The symbol C refers to the equilibrium concentrasharpness of the color change of an indicator near tion of the species indicated by the subscript and the equivalence point, using the various equilib- K, = [H+][AC-].~From the stoichiometric conrium constants for acids, bases and salts reported centrations of perchloric acid and water added, in previous papers.'"-' ( C H C I 0 , ) t and ( C H ~ O )respectively, ~, and KfHa0C104 Water reacts with perchloric acid to form hydro- it is possible to calculate equilibrium concentranium perchlorate according to equation 1. The tions of water and perchloric acid. Thus, if CH,O equilibrium constant for the reaction as written, is plotted versus C H C ~ O ~ ~ [aH straight + ] ~ , line of KfI130CIOa slope K s K ~ ~ i ~ , /and K ~ intercept 2 ~ -K,/KH,o should result. Such a plot of the experimental reHzO HClOa J_ HaOC104 (1) sults yielded a straight line, and K H ~ was O calculated from the intercept using the previously deis 34.7b I n order to account quantitatively for the termined value of K , = 3.55 X 10-15.7c KH~OCIO, effect of water over the entire region of a titration could then be calculated from the relationship curve it is necessary to know the over-all dissocia- KfH3OClo4 = K H C ~ O ~ K H ~ O / K ~ K in Hwhich ~OC,O~,~ tion constant of water as a base, KH,o, and the the dissociation constant of hydronium perchlorate over-all dissociation constant of hydronium per- is the only unknown. o ~ . simple way of determinchlorate, K H ~ o c ~ One The Effect of Water on pH over the Entire ing these constants is to study the change in hy- Region of an Acid-Base Titration Curve. Solutions drogen ion concentration of a perchloric acid solu- of Water and a Pure Base.-The pH of a mixture tion as a function of the water concentration, using containing water and another base, B, in acetic acid can be calculated by substituting into the (1) J. B. Conant and N . F.Hall, THISJ O U R N A L , 49, 3047 (1927). ( 2 ) (a) J. S. Fritz, Anal. Chem., 22, 1028 (1950); (b) J. S. Fritz electroneutrality rule equation 3a
+
+
and M. 0. Fulda, ibid., 25, 1837 (1953); ( c ) J. S. Fritz, ibid., 26, 1701 (1054). (3) P. C . Markunas and J. A. Riddick, ibid., 24, 1837 (1952). (4) C. W. Pifer and E. G. Wollish, ibid.,24, 300 (1952). ( 5 ) A. H. Beckett, R. M. C a m p and H . W. Martin, J. €'haunt. a n d Pharmacol., 4, 399 (1952). (6) A. Anastasi, U. Gallo and L. Novacic, ibid., 7,263 (1955). (7) (a) I. M . Kolthoff and S. Brtickenstein, THISJ O U R N A L , 78, 1 (1956); (b) S . Bruckenstein and I. >I. Kolthoff, ibid.,78,10 (1956); (c) 78, 2974 (195C); (d) I. M . Kolthuff and S. Bruckenstein, ibid., 79, 1 (1957).
[H']
+ [BH']
f [H30+]= [.IC-]
(33)
the expressions [BH+] = KnCn[H+I/K,, [H,O+l = KH,OCH,O[H+]/K~ and [=lc-] = K,/[H+] to yield
( 8 ) T h e nomenclature used in t h e present paper is t h e same a s in the preceding papers in this series.
S. BRUCKENSTEIN AKD I. ill. KOLTHOFF
5916
In the present paper we find that K H ~ = O 2.95 X Thus when KBCB is greater than about and the water concentration is less than about 0.5 Xj there should be no detectable water effect on the @Hof the solution of a base. At concentrations of water greater than 0.5 -11a decrease in hydrogen ion activity as measured electrometrically has been reported in solutions of bases4J At such high concentrations of water the properties (dielectric constant) of the solvent change and all equilibrium constants are affected in a complex manner. Solutions of Water, Base and BHC1O4.-1n a partially neutralized base solution containing water the rule of electroneutrality is [H+]
+ [BH+] + [Ha0+]
=
+
[-IC-] [Clod-]
(3:~)
Solving for the hydrogen ion concentration in terms of CB, CBHCIOa and C H ~ using O the constants K B , KBHCIO~ and K,, equation 4b is obtained for the hydrogen ion concentration of a mixture of a
d K 8
+
KB C B (4b) KBCB K H ~ O C H ~ O
+
Yol. 79
that ( c B ) . v = (C1IClOa)w
f
CHIOCIOP
f b
(4f j
where b represents the analytical concentration of ba:e. Equation 4f can be written in a more useful form by using K$laOCIO1 to obtain an expression for ( C B ) ~in~ terms . of ( C H C I Oarid ~ ) ~C~H ~as O (Cu'lv
= (CIir1c>J\>(1
+
+
Kir130cI"~Cir2~~) b
(4g)
Combining equation 4g with the expression for yields the quadratic expression
KfBHClo4 (CB),?Z
- biCui,, -
Substituting equation 4h into 4d gives equation 4i which describes the way in which the ratio of hydro-
(di)
gen ion concentrations depends on water content. base and its salt containing an equilibrium concenThis expression cannot be simplified further. tration of water equal to CH~O.Denoting [H+]o, Qualitatively it shows that the effect of water in( C B ) and ~ ( CBIICIOa)O as the equilibrium concentra- creases with increasing water content and decreastions of the various species in anhydrous solvent, ing values of b and of K B (or KfBHC104). As an illustration some values of the effect of and [H+Iw,( C B ) and ~ (CBHCIOJ,~. as the equilibrium concentrations of the various species in solvent con- water on the pH near the end-point are calculated taining an equilibrium concentration of water, 1 7 ~ ~ 0 ,for three systems which are of practical interest. LTe assume that the total water content of the solit follows from equation 4b that vent is initially 0.1 -11and that it is unchanged during the titration. Table I lists pH, and @Ho values near the end-point in the titration with perchloric acid (no volume change) of 0.1 -11and 0.01 -11B with = 5.00 and of 0.1 -11B with pKn = 9.00. ~ K B H CiIsOazsumed , to be 5.00 in all (4Ci cases. The equations from which the values a t In most practical cases the reaction BHC104 HzO and after the cyuivalence Foitit are calculated are B H3OClO4 can be neglected until close to deri\-ed in the following cection. From the anthe equivalence point. The larger the value of K B , alytical view roint it is of interest to note from the closer the equivalence point can be approached Table I that the effect of watcr (0.1 111)on the pH before we must allow for this reaction. Over the is negligible up to 9'J.9yc neutralization in the region where this approximation holds, (CB), = titration of 0.01 -11or more coiicentrated solution ( C B ) ~(,C B H C I O J=~ (CBHCIO~)", and water will have of a base with a di5Cociation constant of the order hardly any effect on the PH. This has been verified of 10-j. In the titration of a 0.1 J1solution of very experimentally for sodium acetate-sodium perchlo- weak base with a pk' of 9.00 the effect of water is negligible until 'JJcineutralization. t-pon further rate mixtures. When the equivalence point is approacbed, we neutraliiation the water effect becomes inorc and must distinguish between the various equilibrium more noticeable. However. since the break i n poconcentrations in anhydrous and water-containing tential a t the equivalence point is very small, even solvent. As a good approximation in this region, in the absence of water, i t is not necessary to conis much sider the in\-,)lied q u a t i o n 4 j in any titration of in both these solutions, KBHCIO~CBHCI~, greater than K B C B , KBCB is in most practical redsonnble accuracy in which the end-point is decases much greater than K , and KH?oCH,O, while tected by a potential or color change xt or i l e a the (CBHCI& = (CBHCIQ)". Thus equation 3c sim- eyui bTalence point. Effect of Water on Solutions of Pure I3HCI0,. plifies to Equation & hokk generally and is applicable to a pure salt solution 'r: here 2, = 0. For such a solution equation 4j c m be greatly siinplified and we find Neglecting ionic dissociation of the various specie? in solution, it follows from equations 1 and 4e
+
+
U€IClOj
2 B + HClOi
(-le 1
EFFECTOF WATER
Nov. 20, 1957
ON
ACID-BASEEQUILIBRIA IN
CALCULATED VALUESOF pHo AND pH, IN VICINITY OF THE EQCIVALENCE POINTIN THE TITRATION OF BASES WITH PERCHLORIC ACID" %
~ K = B 5 00 0 1 .VI Base pHw
pHo
90 99 99.9 100 100.1 101 110
10.45 9.45 8.45 7.16 5.87 4.88 3.90
10.45 9.45 8.46 7.48 6.51 5.52 4.54
~ K =B 5 00 0 01 M Base $Ha pHw
9.94 8.94 7.95 7.16 6.38 5.38 4.41
5917
ACID
[H+lw=
TABLE I
Neutral
ACETIC
9.94 8 94 7.99 7.48 6.98 6.03
~ K =B 9 00
0 1 M Base $Ha OHw
6.48 5.54 5.20 5.16 5.12 4.79 3.90
6.48 5.68 5.49 5.48 5.47 5.30 4.54
d\/KHCIO4CHCIOp
+
KHC IO~CE 10, C
+
KHaOClO,CHsC104
KBHClOpCBHClO,
(6b)
Since KrH30C104 = K H C ~ O , K H ~ O ~ / K H ~ O =C I O ~ K ~ [H30C104]/[HzO][HC104], equation 6b can be written as [H+lw = __-
KHC~O~CHCIOI
ti
+
KHClo~cHClO4)
KBEClOrCBHClOr
(W
We find the numerical value of KH,o/K~ to be 83. 5.05 Equation Gc cannot be simplified further. Neglecting ionic dissociation anddenoting w as the analytiThese data were calculated, allowing for dissociation of the various species into ions. P K H C l O 4 = 4.87; PKBHCIO~ cal concentration of water and a as the analytical = 5.00; PK, = 14.45. Constant volume was assumed. concentration of perchloric acid, we have the rela( C H 1 0 ) t = 0.1 L l f . tion C H C ~ O ~CHaOC104 = a CB I t is of interest to note that the dissociation constants of the base, acid and BHClO4 do not enter Substituting for CH,0C104 from KrFJaoClo4gives into equation 5a. The reason is clear, when we equation 6d as the explicit expression for the equilibconsider the expressions for the hydrogen ion con- rium concentration of perchloric acid. centration in the (equation 5b), and in the f cB_presence of water (equation 5c). CHClOi = (64 1 KfHa0C104C~2~ From equation 5c it follows that the effect of Depending on the numerical value of KfBHClo4 water on the p H of a salt is there will be a region just past the end-point where the solvolysis of the salt is appreciable, i . e . , CB is of the same order of magnitude as a , and the quadratic expression obtained by combining equation 6d with KfBHClo4 yields
+
+
+
independent of the salt concentration. This conclusion is also of practical importance in the potentiometric titration of bases with perchloric acid to the equivalence potential. This potential is independent of the concentration of the salt a t the equivalence point both in the absence and presence of water. When using this method of end-point detection it is not even necessary to determine the exact water content of the solvent, if some pure BHCIO4 is available. The potential of the indicator electrode in a solution of RHC104 gives the equivalence potential. When the potential in a solution of BHC104 is known in pure acetic acid, the water content of the solvent can be calculated roughly from equation 5a. Such a simple determination gives a t least the order of magnitude of the water content and allows the conclusion whether the solvent is suitable for a given titration. Some calculated values of #Hw and pHo are given in Table I. Effect of Water in Solutions of BHCIOI and HC104.-The rule of electroneutrality for a solution of a mixture of water, perchloric acid and a perchlorate can be written [H+]
+ [BH'] + [HaO+l = [Clod-]
(1 f
K f H 3 0 C 1 0 ' ~ H z O ) C 2 H C I O ~- U C H C l 0 4
-
CBHC10&/KfBHC104
0
(6e)
Equation 6e must be used just after the equivalence point to obtain the equilibrium concentration of perchloric acid. For all practical cases, CH*O = w in this region, and [HfIw is obtained using equations 6e and 6c. ,4s the analytical concentration of perchloric acid is increased, the contribution of the solvolysis of the perchlorate to the equilibrium concentration of perchloric acid becomes more and more negligible and equation 6f may be used to calculate CHCIO,, provided a
