Acid-Base Equilibria in Glacial Acetic Acid. IV. Quantitative

Quantitative Interpretation of Acid-Base Titrations in Glacial Acetic Acid. I. M. Kolthoff, S. Bruckenstein. J. Am. Chem. Soc. , 1957, 79 (1), pp 1–7...
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J O U R N A L OF THE AMERICAN CHEMICAL SOCIETY (Registered in U. S. P a t e n t Office)

VOLUME79

(0Copyright, 1957, by the American

Chemical Society)

NUMBER 1

JANUARY 15, 1957

PHYSICAL AND INORGANIC CHEMISTRY [CONTRIBUTION FROM

THE

SCHOOL O F CHEMISTRY, UNIVERSITY

OF

hIIXNESOTA]

Acid-Base Equilibria in Glacial Acetic Acid. IV. Quantitative Interpretation of Acid-Base Titrations in Glacial Acetic Acid BY I. &I. KOLTHOFF AND S. BRUCKENSTEIK RECEIVED JULY 19, 1956 Acid-base titrations in anhydrous acetic acid are no longer an empirical subject: it is now possible to calculate quantitatively the characteristics of such titrations carried out either potentiometrically or with indicators. The equations governing the shape of potentiometric titration lines of bases in anhydrous acetic acid have been derived and experimentally verified. These relationships have been used to explain the apparent paradoxes described in the classical studies of Conant, Hall and Werner, to predict the shape of the titration line of urea with perchloric acid, the e.m.f. or pure salt solutions, and the change in e.m.f. in the vicinity of the equivalence point in the titration of sodium acetate with perchloric acid. The relationships determining the ratio of the acid to basic color of an indicator base over the titration range in acetic acid have also been established and used to predict the color of p-naphtholbenzein (PNB)in diethylaniline perchlorate and sodium perchlorate solutions. The change in color of PNB on the addition of sodium acetate to a sodium perchlorate solution was found to be in agreement with the calculated values.

In the present paper neutralization curves of bases with perchloric acid have been calculated and it is shown that the theoretical values are in excellent agreement with the experimental data. Similar calculations and determinations can be made with other acids, but since perchloric acid is the strongest acid known in acetic acid, i t is the only one of practical consequence. Also, the color equilibrium of a suitable indicator has been calculated a t and near the equivalence point, and the results compared with experimentally determined data. Potentiometric Titrations : Change of Hydrogen Ion Concentration in Titration of a Base with Perchloric Acid [H+]of a Solution of a Base B.-In a pure solution of a base B the over-all dissociation is given by eq. 1

Introduction After the pioneer work of Conant and co-workers' on neutralization curves of supposedly strong and weak bases in glacial acetic acid a host of papers has been published on the titration of a large variety of bases and some acids. These papers, in which the end-point was found potentiometrically or visually with an indicator, are all of an empirical nature. After determining the dissociation constants of acids, bases and salts2 and after the establishment of the acidity scale in glacial acetic acid it is now possible to explain the apparently abnormal shapes of neutralization curves of bases of different strength as observed by Hall, to calculate potentiometric titration curves, the equivalence potential and the change of pH and potential near the equivalence point. It is also possible to calculate the ratio of acid to basic form of an indicator over the titration range and particularly in the vicinity of the equivalence point, and to present the fundamental equations underlying spectrophotometric titrations. latcve

B

+ HAC J_ B H t + Ac-

(1)

The over-all dissociation constant K B is K B = [BH'] [Ac-]/CB

(2)

in which CB is the total concentration of undissociated base ( [ B ] [BH+ A c ] ) . ? ~ For reasons given previouslyIzaconcentrations of undissociated species and of ions are assumed to be equal to activities. It is easily derived that in a solution of the base

+

(1) (a) N. F. Hall and J. B. Conant, THISJ O U R N A L 49, , 3017 (1927); (b) J. B. Conant and N. F. Hall, ibtd., 49, 3062 (1927); (c) N. F. Hall and T. H . Werner, ibid., SO, 2367 (1928); (d) J. B. Conant and T. H. Werner, ibid.,62, 4486 (1930); (e) N. F. Hall, ibid., 62, 5115 (1930); (f) N. F. Hall, Chem. Revs., 8, 191 (1931). (2) (a) I. M . Kolthoff and S. Bruckenstein, THISJ O U R N A L78, , 1 (1956); (b) S. Bruckenstein and I . M. Kolthoff, i b i d . , 78, 10 (1956); ( c ) 18, 2974 (1956).

[H+l = K . / ~ / ( K {B( C B ) ~ K.1 / [ H f l l

1

(3a)

I. hI. KOLTIIOFF AND S. BRUCKENSTEIN

2

in which K, is the autoprotolysis constant of acetic acid while the analytical concentration of the base ( C B ) ~= CB [BH+] = CB j- [Ac-.]. Since all bases are weak electrolytes in acetic acid, the quadratic eq. 3a usually can be applied in the approximate form

+

[H+l = K . / d / K , $

(3b)

The results predicted by eq. 3b accurately account for p H data measured in solutions of pure bases in acetic acid. Hall and WernerlCfound that there is an increase of one p H unit for a hundredfold increase in concentration of base. Similar results also have been reported by Higuchi, Danguilan and Cooper3and by us.2c [H+] in Mixtures of B and its Perchlorate BH +C104-.-For the calculation of hydrogen ion concentration in such mixtures i t is necessary to consider not only the dissociation constant of the base B but also that of the salt, eq. 4a, and of perchloric acid, eq. 4b. The over-all dissociation constants of the salt

1'01. 79

results obtained by Hall arid M'ernerIc in the titration of 0.05 41guanidine and 0.05 J1diethylaniline, respectively, with 1 ill perchloric acid. Tlicse two compounds are among the stronger bases in acetic acid and their over-all dissociation constants are both of the order of 10-jand are also of the same order of magnitude as the dissociation constants of their perchlorates. For example, we have found2c B 5.7s and p k 7 H H C , o , that for diethylaniline ~ K = = 5.79. Under such conditions we can write eq. 4g instead of eq. 4f in mixtures of the base and its perchlorate in which the sum of the concentration of the base and salt is constant and equal to C. I1I-l = { Ka,'Cnj \/'l/~~

(4g)

The above conditions were approximately satisfied by Hall and nTerneric in their titration of 0.05 M guanidine and 0.05 Jl diethylaniline with 1 hl perchloric acid. The sum of the concentrations of free base and perchlorate changed only 5% up to the end-point and can be neglected for our purposes. The above authors plotted PH versus log (1 - X), X being the fraction of the base which has been BNClO4 BH' (2101(4a) titrated and observed a straight line with a slope of HClO4 IfH + clod(4b) one, similar to that found in aqueous medium for the titration of a strong base with a rtrofzg acid (corand the acid are KBHCIO~ = [BH+J[C104-1/ rected for volume change). 'This is quantitatively CBHCIO,and KHCIO,= [ H + ][C104-]/CHc10~, re- accounted for by eq. 4g where [ H + ]is proportional spectively. C refers to the total concentration of to 1/(1 - X ) . l y e now have a quantitative interundissociated species indicated by the subscript. pretation for the apparently paradoxical fact that Equilibria in solutions of BHCIO, are determined the titration lines of guanidine and diethylaniline by the equilibrium constant KFHC"' of the reaction with perchloric acid in acetic acid are similar ill B HC104 & BHC104. The equilibrium constant shape to the titration line of a completely dissociKfBHCLo'= CBHC~OJCBCHCIO, is a function of K,, ated base with a strong acid in water whereas in Kg, KHc1ol and K B H C ~ OThis ~ . ~ relationship ~,~ is solution of the pure bases in acetic acid the pH stated in change with dilution corresponds quantitatively to the behvaior of a typically weak electrolyte. The K,DHCIO' = A ' HCIO,KB/K~KBHCIO, (4C) pK of guanidine and its perchlorate are not known From the rule of electroneutrality, eq. 4d and the but apparently the same relationships hold as for expressions diethylaniline. If KBHCIO, is not equal to K B , the simple expres[H+] [BH+] = :Ac-] lC104-1 (4d) sion (4g) does not hold and the plot of p H versus [BH'] = KBCB[H+]/&, [Ac-] = K,/[H+l and (1 ~- ~X )~ does [C1O,-] = K a K ~ ~ ~ ~ ~iH+l ~ C log ~ ~ a / not R ~yield C ~a straight line. For example, Hall and lVernerlCfound this plot did not an explicit expression for hydrogen ion concentra- yield a straight line in the titration of 0.05 31 sodium acetate with l Mperchloric acid. The reason tion in mixtures of B and BHC104,eq. 4e is that sodium acetate is a weaker electrolyte than sodium perchlorate*' (PKiiaAc = 6.68, f i K S a C I O , = 5.48). In aqueous solution the plot of pH against log is obtained. Unless the base is too weak to give a (1 - X ) / X yields a straight line with a slope of one detectable end-point in the titration K B C B I K ~in the titration of a weak base with a strong acid. >> 1, so that the simpler expression, eq. 4f, can be In acetic acid Hall and Werner did not find an acidbase system which satisfied this relation and they written .~ ascribed the deviation from a straight line to large (4f) [H+] = K , ~ K B E C I O ~ C R4H -C K g~CO d ,K B C B activity coefficient effects. Actually it is clear Ordinarily it is sufficiently accurate to neglect the from eq. 4f that no relationship exists between K B which would yield the above relationdissociation of the base and of the salt and the sol- and KBHC,O, volysis of the salt with respect to their total con- ship. centrations and to assume that CB and CBHCIO~ We may consider here the effect of dilution on the represent the stoichiometric concentrations. When pH of a mixture of a base and its salt. In aqueous solution, the hydrogen ion concentration in a buffer necessary more exact formulations will be used. Equation 4f has been verified for mixtures of mixture of a weak base and its salt with a strong several bases and their salts2cand accounts for the acid as a first approximation is independent of the buffer concentration, depending only on the ratio (3) T. Higuchi, M. I>.Danguilan and A. D. Cooper, J . P h y s . Chem., of the salt to the base. Hall and \Yernerzc found 58, 11ti7 (1954).

+

+

+

+

+

ACID-BASETITRATIONS IN GLACIAL ACETIC ACID

Jan. 5, 1957

3

We will first consider the titration of a weak base that a ten-fold dilution of partially titrated bases causes a decrease in p H of 0.5 unit in acetic acid. (B) in the presence of a large excess of trimethylIf we let [H+]v equal the hydrogen ion concentra- ammonium perchlorate (B ’HC104). Since trimethtion when the total volume is V and the equilib- ylammonium acetate is undoubtedly one of the rium concentrations of salt and base are CBHCIO~stronger bases in acetic acid, there is no tendency B’HC104 e BHC104 f B’ and CB, respectively, while when the volume of the for the reaction B buffer is 10 V and these concentrations are CBHCIO~/to proceed appreciably, and we will neglect it. The 10 and CB/10, and the hydrogen ion concentration perchlorate ion concentration throughout the titra[H+]Iov,we find fromeq. 4f that [H+]v/[H+]~ov= tion is virtually constant and is given by [ClOr-] I O ~ is a large excess l/v’fi. Thus as long as eq. 4f can be written in = ~ K B J H C I O ~ C B *asH Cthere stoichiometric concentrations rather than equilib- of B’HC104 present. Since [H+] = Ks/[Ac-], rium concentrations, there should be a decrease of [Ac-] = KBCB/[BH+] and [BH+] = [CBHCIO~ 0.5 p H unit for each ten-fold dilution. In very K B H C I O , ) / ~ ~eq. ~ ~ 4i - ] describes , the variation of dilute solutions, appreciable dissociation of salt and hydrogen ion during the titration. As a reasonbase occurs, and the reaction B I-ICIO, e BHClO4 KXBHCIO~CBHCIO, may no longer be quantitative so that this re(4i) [H+l = K B C B ~ K B ’ HCB’HCIO, CIO~ lationship would be expected to fail. Such a result was also noted by Hall and Werner. Of course it able approximation CBHCIO~/CB = X/(1 .- X ) , is clear from the above that in an equimolar mix- hence according to eq. 4i a plot of p H against log ture of B and BHC104, K s / [ H + ] is never equal to (1 - X ) / X should yield a straight line of slope one, K B as is true in water. Several authors have as- as was observed experimentally. sumed this to be true in acetic acid. From eq. 4f I n solutions containing trimethylammonium pi t can be shown that in a solution containing C toluenesulfonate (B ’HTs) we must consider the molar B and BHC104 metathesis reaction HClO4 B’HTs F! HTs BH’C104where HTs represents p-toluenesulfonic acid. The equilibrium constant for the reaction as written where KHCIO~ = I n the neutralization of a.very weak base, for is KBHCIO~KB~HT~/KHT~KB~HCIO~ and KHT~= 3.8 X 10-g.2c,4 On the which KBHCIO~ > >Kb, eq. 4f reduces to eq. 4h. It 1.35 X basis of unpublished data we estimate that K B ~ H T ~ / is evident that a plot of e.m.f. versus log KB”CIO, is of the order of 0.1. Using this value the (1 - X) should yield a straight line with a slope of equilibrium constant for the above metathesis reac0.0591 volt. We have verified this relationship tion is approximately 400. Even though we may [H+] - K_~_ ~K _B~ Hc ~~O-~ C B H C I (4h) O~ allow for considerable error in the estimate of K BCB KB~HT~/KB~H i t CisI Oevident ~ that little free perchloric acid can be present during the titration with using urea as the weak base. I n the above discussion the equations which perchloric acid of 0.05 M urea in a 0.2 M solution of govern the slope of the titration lines of bases have trimethylammonium p-toluenesulfonate (B ’HTs) . been derived in the absence of foreign electrolytes. The perchloric acid reacts almost quantitatively They cannot be applied when other salts are pres- with B ’HTs with formation of p-toluenesulfonic ent. I n this connection we may discuss the titra- acid and B’HC104. Thus, the titration corresponds tion of a very weak base like urea carried out by t o that of urea with p-toluenesulfonic acid in the Conant and Wernerld in the presence of 0.2 M tri- presence of a large excess of a sulfonate. This titramethylammonium perchlorate or 0.2 M trimethyl- tion is strictly comparable to that of the base with ammonium p-toluenesulfonate as neutral salts for perchloric acid in the presence of an excess of a the purpose of “keeping the ionic strength constant perchlorate (eq. 4i) and we may write during the titration.” The expression “neutral KXBHT. CBHT~ salt” needs further qualification (vide infra) and (4k) = KBcB~/xB’HT~cB‘HT~ must be used with care in acetic acid. As has been stated in a previous publication,2 concentrations From a comparison of eq. 4i and 4k it follows that can be written with a good approximation instead the plots of PH against log(1 - X ) / X in 0.2 M of activities in acetic acid and activity effects can- B’HClOd and in 0.2 M B’HTs will he identical only not account for the results obtained by Conant and if Z/KBWTS/KB~HC~O~ = KBHTS/KBHCIO~. The difWerner. Quite generally, complications may be ference notes for urea, 0.5 unit, agrees well with the introduced a t high electrolyte concentrations be- value of 0.5 unit calculated using eq. 4i and 4k with cause of ion triplet and quadripole formation. How- the assumption that urea perchlorate is ten times ever, the results reported by Conant and Werner more dissociated than urea 9-toluenesulfonate. can be accounted for on the basis of simple equi[H+] in a Solution of Pure Salt.-The equivalibria. These authors found that in titrations of lence point in the titration of a base with an acid various bases in the presence of the 0.2 M tri(4) The value of K H T ~used here differs Irom the value reported methylammonium salts a plot of p H versus log r e v i o ~ s l y 9by ~ about 10%. In a private communication Prof. L. P. (1 - X)/Xyielded a straight line of slope one. pHammett pointed out that the method of purification used by us for However, the lines obtained with trimethylam- p-HTs would probably yield the monohydrate of the acid. Analysis monium perchlorate did not coincide with those ob- by Karl Fischer titration of a sample of the p-HTs used earlier showed tained with trimethylammonium p-toluenesulfo- that it corresponded to the monohydrate, and accordingly we have recalculated K H T ~by correcting the concentration of 9-HTs for the nate, the difference amounting to 0.5 p H unit in the presence of water. 9-HTs is too weak an acid to react significantly titration of urea. with small amounts of water in acetic acid medium.

+

+

+

dz/

+

4

I. M. KOLTHOFF AND S. BRUCKENSTEIN

Vol. 79

corresponds to a solution of the pure salt, and the perchloric acid in acetic acid medium. For our hydrogen ion concentration of such a solution can purposes the dissociation of IHC104 into TI3 ant1 be calculated from eq. 41. For most salts KUCHis C104 - need not bc considered because tlie large ox negligibly small as compared to I ~ B H C I ~ ~ C B I Icess C I Oof~ RHC104 suppresses the dissociation of I I I and we may write eq. 5a instead of 41. If we neg- Cl04 completely. The color of the indicator is theii lect dissociation of all species in solution given by the ratio [IHC104]/[1] where [IHC104] denotes the concentration of the acid and [ I ] that of the basic form. I t has been made clear in a previous paper?; that the color of an indicator in acetic CB = CHBIO~ in a pure salt solution. From the acid is not determined by the pH of the solution definition of the formation constant of the salt, but by the concentration of the free perchloric acid, BHC10i CHCIO~ = [HC104] [H+C104-], the sum of molecC B ~= C B H c i o 4 / K f = CBHCIOXXBHCIO~/ ular and ion pair concentrations (eq. 7a), and the KHCIO~KB. On substituting this expression into eq. 5a, eq. 5b is obtained for the hydrogen ion con- formation (ionization) constant of the indicator perch1orate.j centration in a solution of a pure perchlorate.

+

This expression is of the same form as holds for the salt of a weak acid and weak base in water. I t allows the calculation of the hydrogen ion concentration of a pure salt solution in acetic acid and predicts that it is independent of the concentration of the salt. Experimental data presented later in this paper are quantitatively in agreement with this relationship. I t is of great practical significance since it shows that the equivalence pH or equivalence potential is independent of concentration of the titration system and that titration to the equivalence potential should be much more convenient than the conventional method of potentiometric end-point determination. As a matter of fact, titration to the equivalence potential should give more accurate results than the conventional method especially a t higher dilutions or when the base is very weak. [H+] in Mixtures of Salt with Excess Acid.After the equivalence point an expression for hydrogen ion concentration involving CCHIO~ and C B H C ~isOthe ~ most convenient for calculation purposes. Since CB = C B H c l o 4 / C H c i o e K fBHClOi = K s K ~ ~ ~ ~ ~ 4 C ~ eq. ~Ba ~can~be~ obtained from eq. 4e.

KHCIO~CHCIO(

Equation 6a holds at all points in the titration, but when enough excess of perchloric acid is present, KHBIO~CHCIO, is usually greater than K,, and the simpler expression, eq. Bb, is satisfactory. A sim-

During the course of the titration of B with perchloric acid, C H Cis~given ~ ~ by eq. i'b C l i C I U a = C B H L I O I Jc

[ 711 i

*K:'~~r~o~

and the color of the indicator by eq. i c

Equation i'c illustrates the dependence of the color of an indicator in a mixture of a base and its perchlorate on the ratio of concentrations of the salt and base and not on the concentration of each species individually. Thus, as long as we use approximate equations (neglect solvolysis) i t is found that the color of an indicator base in a mixture of a base and its perchlorate is not affected by dilution. In a previous section we have seen that upon tenfold dilution of the kind of mixture under consideration the $JH decreases by 0.5. This is another striking example of the previously noted fact that there is no direct relation between pH and the color of an indicator in acetic acid. On the other hand, in a mixture of a perchlorate and perchloric acid the ratio acid~to ~basic an indicator de- ~ i I /of K ~ form ~ aof K ~ C ~ base ~ ~ creases to one-tenth upon ten-fold dilution while the pH increases by 0.5 unit. For those concerned with acid-base catalysis it is of interest to consider that in a mixture of a base and its perchlorate the concentration of free perchloric acid remains unchanged with dilution (as

( 5 ) Rigorously, eq. ?a should be written Ci~cloJCr = K:HC'o'. C~clo,, b u t as long as t h e indicator base is weak, and the indicatur salt completely ionized, CI = [ I ] and C I H C I O=~ [IHCIO4I. These conditions are met b y p-naphtholbenzein, a commonly used indicator in acetic acid medium, and there is no experimental evidence t o indi[€I-I = KHCI O ~ C H C I O , I ~ \ / K I I L I O , C THK CB I OH~C I O ~ C B H C Icate O ~ t h a t t h e above conditions do not hold equally well for other indicator bases used in titrations in acetic acid. In a previous paper2.' (6b) t h e constant K:HC104 = [IHCIOi]/'[I] [HCIOI] was defined, where ilar expression has been verified previouslyzn for [HCIOi] represents the concentration of un-ionized perchloric acid in hydrochloric acid and some of its salts. Of course, solution. T h e ratio K:HCio4/K~HC'o' = 1 + KFClo4, where K?c'o' = [ H +ClO~-]/[HCIOi], [H +CIO4-] representing the concentration of is not much smaller than when KBHCIQ the ionized form of perchloric acid in solution, ;.e., C A C I O= ~ [H+ClOP] then eq. 6b simplifies to [HCIOa]. T h e distinction between K:HCio' and K:HclO' is of little consequence f o r a weak acid such as hydrochloric or p-tolaenesulfonic KHCIO~CHCIO~ acid for which KTX is much less t h a n one, b u t is significant f o r il [I%-] = (6c) 1/KBHC104CBHC104 strong acid such a s perchloric acid Professor Ernest Grunwald of the in the immediate vicinity of the equivalence point. University of Florida kindly brought t o our attention t h a t we did not distinguish between [HClOI] and CHc104when we applied eq. R of ref 2a t o perchloric a n d hydrobromic acid solutions. His criticism i i Titrations with Indicators valid and t h e conclusions drawn from eq. 16d. 17, 17a and 17b of ref Indicator Color in Mixtures a Weak a n d 2a It is not possible t o obtain K?'Io' from our data are incorrect. its Perchlorate.--m'e consider the color of an indi- since t h e correct form of eq. 17 is K~AXKiHX/k'jf2104KHX 1 (nrtt cator base, I, during the titration of a base with 1 K"'O4).

KHCIO~,

+

of

Base

+

3

ACID-BASE TITRATIONS I N GLACIAL ACETICACID

Jan. 5, 1957

long as the approximate equations hold), while in a mixture of perchloric acid and a base perchlorate the concentration of free base is unaffected by dilution. Returning to the color change of an indicator during the titration of a base with perchloric acid we write eq. 7d instead of 7c y [IHClOal - K I HI C l O 4 , --

5

Methods and Reagents.-Potentiometric measurements with the chloranil electrode as pH electrode and the modified calomel electrode as reference electrode were performed as previously described.20 I n some solutions it required a t least 24 hours before the chloranil electrode had attained its equilibrium potential. Measurements involving the glasscalomel electrode system were performed using a Beckman Model H-2 pH meter and the electrodes supplied with this instrument. The glass electrode measurements were carried out for orientation purposes and commercial C.P. glacial acetic acid was used without further purification. These experimental data were not used for any exact calculations. The spectrophotometric technique and all reagents used were described in previous papers.*a~b~sO pH of Acetic Acid.-Considering the high resistance and the poor buffer capacity of the pure solvents the measurements were not as reproducible as those obtained in wellbuffered or more conducting solutions. Using three separate batches of solvent the following values of the e.m.f. were measured: 0.474, 0.464, and 0.480 volt. The pH may be calculated from eq. 8 in which 0.9095 represents the standard potential of the chloranil electrode with respect to the acetic acid

KpHClo4 1 - X Dl An expression of the same form is found in aqueous medium for the titration of a weak base. This expression is of great practical value, both in water and in glacial acetic acid, where the end-point is not found visually, but graphically in a spectrophotometric titration using an indicator with a KiHC'O' of the same order of magnitude as KfBHC'T4.6 In connection with the above it is noted that the PH = (0.9095 - E)/0.0591 (8) experimental value of the so-called acidity function calomel electrode.20 The average value pH = 7.4 & Ho in a mixture of a weak base and its salt is pro- 0.1 is in gratifying agreement with the value of 7.2 calportional to the negative logarithm of the concen- culated from the pK of acetic acid, 14.45.20 In fact, this tration of free acid but there is no simple relation close agreement is probably fortuitous. Neutralization Curve of Urea in Anhydrous Acetic Acid.between Ho and the hydrogen ion concentration. ml. of 0.0547 M urea was titrated with 0.9643 M According to eq. 7d a plot of HOversus a log (1 -X)/ Fifteen perchloric acid using a chloranil indicator electrode. The X should give a straight line with a slope of unity. reference electrode was a platinum wire sealed into the Hall and Meyer' determined Ho in mixtures of sul- buret which delivered the perchloric acid previously satufuric acid with urea and with antipyrine and found rated with chloranil and tetrachlorohydroquinone. From the neutralization curve, Kg, of urea and eq. 3b and 4f straight line plots with slopes of 1.05 and 0.83, re- the dissociation constant of urea perchlorate is found to be spectively. No correction was made for the sol- approximately This is lo5 times larger than KB of urea and eq. 4h should hold. A plot of e.m.f. versus volysis of the salt. log dx/(l - X)is shown in Fig. 1 and the observed slope Indicator Color in a Solution of a Pure Salt.In a pure solution of a salt, BHCIO4, corresponding is 0.064 v. as compared to the predicted value of 0.0591 v. to the eauivalence point in the titration of B with a t 25'.

(7d)

250

I

e i . 7e is obtained. -[IHClOa] =___.

[I1

K:HC1o' dKjpi5-i

dr-

BHC'O4

(7e)

This predicts that the ratio of acid color to base color is proportional to the square root of the concentration of salt present. For example, if for a given indicator [IHClO4]/[1] = 1 in a 0.1 M salt solution, the ratio decreases to 0.1 in 0.001 M salt solution. Thus the color of an indicator a t the equivalence point varies with the concentration of the base titrated, while we have seen that the pH (potential of electrode) is independent of the salt concentration. Experimental The main purpose of the present experimental work was to study the order of agreement between calculated and experimental values of pH and of ratios of acid to base color of an indicator in a variety of solutions. I n practical analytical work acetic acid with varying small amounts of water is used, which may greatly affect the pH and the color of an indicator. The acetic acid used in most of the present work had a water content of 0.01% and in some experiments even this trace of water was removed. I n a subsequent paper the effect of water upon potentiometric titrations and titrations with indicators will be calculated and compared with experimentally observed effects. (6) T. Higuchi, C . R.Rehm and C. H. Barnstein, Anal. Chem., 28, 1506 (1956). (7) N. F. Hall and F. Meyer, TBISJOURNAL, 62, 2493 (1940).

-0 5

0.5

00

log

10

E. I- x

Fig, 1.--Test of eq. 4h. The titration of 0.0547 M urea with 0.964 i W perchloric acid.

pH of a Salt Solution.-Equation 5b states that the pH of a solution of a pure perchlorate should be independent of the concentration of the salt. I t can be extended to any salt since none of the assumptions involved in the derivation are restricted to perchloric acid. Preliminary experiments were performed in commercial glacial acetic acid containing 0.2% water using the glass-calomel electrode system, and the results obtained with ten salts are shown in Table I. The data verify the independence of pH upon concentration, but cannot be interpreted quantitatively because of the uncertainties introduced by the use of the glass electrode and water in the commercial glacial acetic acid. For this reason e.m.f. but not pH values are reported in Table I. In Table I1 the results with the chloranil-calomel electrode cell are given for four salts in acetic acid containing 0.01% water. The data in the column headed pH,,, were calculated by averaging the e.m.f. data of the preceding column and using this average e.m.f. in eq. 8. The data in the column headed PHcslcd were calculated from eq. 5b using values of the dissociation constant reported previously.zo The pH values found are practically independent of dilution in the concentration range used and, realizing the poor

I. hl. KOLTIIOFF AND S . BRUCKENSTEIN

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ITOl.

79

buffer capacity of the solutions, no serious discrepancies are apparent between observed and calculated pH values.

also of practical importance as they provide quantitative information on the magnitude of the break in potential a t the end-point. In Table 111 experimental values of the TABLE I difference in e.1n.f. between 0.1 -11 sodium perchlorate EFFECTOF DILUTIONUPON THE APPARENTpH OF SOME solution and the same solution with slight amounts of free perchloric acid or sodium acetate are compared with the SALTSOLUTIONS IN COMMERCIAL GLACIAL ACETICACID calculated figures. Increments of 0.500 Xsodium acetate or E.m.f. (v.) in 0.964 M perchloric acid were added to 20.00 ml. of 0.100 AI Salt Satd. soln. 1/10 satd. s o h . 1/100 satd. soln. sodium perchlorate. The complete absence of water was NaC10, 0.599 0.599 0.599 assured by adding 0.95 mole of acetic anhydride per liter of 0.1 JP sodium perchlorate solution and heating for 12 KC1 ,538 .536 .535 hours at 105' in a sealed flask. The concentration of acetic NaCl .,540 .541 .531 anhydride was in fourfold excess based on the water content LiC1" ,569 .560 .557 of the untreated acid. In order t o minimize liquid junction KBr .548 ,560 .550 potentials and errors which might arise from contamination of the solution from the standard half-cell, an €-Itype cell NaBr ,568 ,570 .563 was used which consisted of two compartments joined by a LiBr" ,690 .600 .590 ten-cm. fine sintered glass disc. Both Compartments were KXOS .472 .478 .480 filled with 0.1 M sodium perchlorate previously saturated Sah-03 ,487 ,488 .490 with chloranil and tetrachlorohydroquinone and increments of either perchloric acid or sodium acetate solution were LiNQ ,510 .so9 .507 added from microburet to one o f the cornpartments. The Initial molarity = 1.0. data obtained with the cell. TABLE 11 CsCl,O2( satd. ) Pt Sac104 (0.1 ill, pH OF PURESALTSOLUTIONS IN ACETICACID AT 25' 1 CsClr(OH)?(satd.) LIolar E.m.f.,

I

Salt

Sodium perchlorate

concn.

v.

0.0582 ,0923 .1300 ,213 0.0201 ,0409 ,0559 ,0918 0 . 006s ,0125 ,0253 ,0519 0.00802 ,0192 .0481 .054

0.5370 .5405 ,5390 ,5380 0.5310 ,5300 ,5290 ,5325 0.6O5O ,6055 ,6075 ,6055 0.4210 ,4250 ,4240 .4210

PH..,

PHeaiod

I HC104 (or NaAc) (C,

II XaClOd(0.1 M)

M),C&l,Oz(satd.)

CGCL(OH)2(satd.)

are given in Table 111. The calculated e.m.f. values 6.27 6.32 reported in the last column of this table were obtained by Dieth ylanilinium using either eq. 4e or Ba and the following constants: = 6.68, P K H c ~ = ~4.87, ~ P K N ~ C I=O 5.45 ~ and pK, = perchlorate 14.45.2c In these equations C K ~ A CECIO, ~, and Cxacio, represent the actual equilibrium concentrations of these 6.41 6.77 species in solution. Calculations were made by successive 2,5-Dichloroaniliiiiurn approximations by initially neglecting dissociation of the various species, but taking into account solvolysis, getting an perchlorate estimate of the various ionic concentrations and correcting the stoichiometric concentrations appropriately to get an .5.13 4.94 estimate of these equilibrium concentrations. This proces Sodium p-toluenesulwas repeated until the hydrogen ion concentration remained The agreement between expericonstant within 1%. fonate mental and calculated values in Table I11 is excellent. I t is evident from Table I11 that the titration of 0.1 M 8.07 8.10 sodium acetate to the equivalence potential easily can be with an accuracy of 0.027, if the end-point potential pH Near the Equivalence Point in the Titration of Sodium made not differ more than 10 mv. from the equivalence Acetate with Perchloric Acid.-The shapes of the neutraliza- does tion curves with perchloric acid of sodium acetate and potential. Color of an Indicator Base in a Salt Solution at and near diethylaniline were obtained with the chloranil electrode. Equivalence Point.-In order that as stringent a test The data agreed with those of Hall and Werner1oand there- the as possible be applied to examine the equations giving the fore are not reported here. As stated in the theoretical of the color of an indicator base upon the comsection the shapes of these curves were found to be identical dependence position of the solution the ratio of acid to basic form of pwith those constructed from calculated data using eq. 4f. naphtholbenzein (PKB) was determined spectrophotoNo data are found in the literature of the change of PH metrically in the very poorly buffered solutions of diethylin anhydrous acetic acid just before and after the equivaand sodium perchlorate and in the latter solution Imce point. Such data are not only of theoretical but are anilinium with traces of sodium acetate. Both these salt solutions are extremely slightly solvolyzed, the logarithm of the TABLE 111 formation constant, K~AC'04, as calculated using eq. 4c and the constants reported in a previous paperz0having the CHANGEOF E.M.F.BETWEEN 0.8y0BEFORE AND 0.8% AFTER THE EQUIVALENCE POINT IN TITRATION OF SODIUM ACETATE value of 8.38 and 9.58 for sodium and diethylaniliniuni perchlorate, respectively. These solutions are extremely WITH PERCHLORIC ACID sensitive to minute traces of acids or bases (especially Concentration of sodium perchlorate = 0.100 hl water) since they are virtually completely unbuffered. The experimental problenl is comparable t o that of deterE.m.f. in mv. "2101,M X 10' 0bsd.a Calcd. mining the pH of a solution o f sodium chloride or ammonium chloride with indicators in aqueous solution. For these 8.00 97.5, 96.0 94.1 reasons the over-all reproducibility of an experiment is 4.00 80.0 76.6 considerably less than the spectrophotometric litnit of 2.00 59.5 59.1 approximately 2% in determining ratio R = [IHClOd]/,[I\ 41.5, 4 4 . 0 42.1 1 .(IO for p-naphtholbenzein. For example, in a 0.108 M solution of sodium perchlorate in :Icetic acid containing 0.01% NaAc, M X 10' water, values obtained for R in three separate experiments 1 .00 -42.0, -44.0 -41.6 were 1.77, 1.34 and 2.35 with an average value of R of 1.8 2 , 00 -62.0 -58.6 f 0.3. However, this uncertainty of 20y0 in the mean value of R is not unreasonable in view of the extreme sensi4.00 -79.5, -78.5 -76.2 tivity of the system t o traces of impurities (including water). -94.0 8.00 -91.5 In our discussion of the dependence of R upon salt and All data are rounded to the nearest 0.5 mv., and repre- base concentration the simplifying assumption wai made that the amount of perchloric acid reacting with the sent individual experiments.

indicator is negligibly small. I n the poorly buffered solutions under consideration this is not precisely true and the amount of perchloric acid reacting with the indicator must be taken into account. Defining p according to eq. !)a and b as the molarity of the base added to the pure salt solution, eq. 9b follows.

p

= CBHC104

+ CB =

CB = b

CB (CBEClO4/CB

+ 1)

+ CHCIO,+ JIHC10~1

(9a)

ment. This procedure is justified since the uncertainty in the calculated value, 9.58, is sufficiently large to include the value 9.78. The experimental results agree satisfactorily with the calculated values.

TABLE IV RATIOOF ACID TO BASE FORMS OF p-NAPHTHOLBENZEIN IN SOLUTIONS OF DIETHYLANILINIUM AND SODIUM PERCHLO-

(9b)

Eliminating CB by combining eq. 9a and 9b and substituting into the result CHC104 = R/KiHC’04and C B H C I O , / ~as B obtained from eq. 7c yields eq. 9c. Since [IHClOd] = ( C I ) ~ R / J R 1)

+

RATE Perchlorate, Acetate, Cation

Sodium

the quadratic expression is R , eq. 9d results. I n the immediate vicinity of the equivalence point K:HC104/KiHC104 R is much larger than one, allowing eq. 9d to be simplified to eq. 9e which becomes eq. 9f in a pure salt solution

p*4

BHClO4

p

=

7

POLAROGRAPHY OF METALLIC MONOLAYERS

Jan. 5, 1957

R -I- 11[ b

4-

K~HClok b

p =;R2-KZHCIC4

[x +

1

+ k%] (CA + m]

R

(9d)

>>

+

[CONTRIBUTION FROM THE

M X 106

0.0132 .0272 .0537 .lo8 .lo8 .lo8 .lo8

0.00 .OO .OO .00 2.20 4.40

.lo8 .lo8

17.6 34.9 0.00 .OO .00 .OO

Diethylanilinium

a

The last result is identical to eq. 7e when l/K:HC104 (Cr)t/(R 1). The experimental results obtained using 3.78 X M PSB with sodium perchlorate (0.013 to 0.11 M ) and diethylanilinium perchlorate (0.023 to 0.18 M ) in the absence of free base are given in Table I V . The calculated values of R listed in this table were obtained using eq. 9f, log K:HC’O4 = 5.00,2a log KpC’O4 = 8 38 and log K:HCI04 = 9.78 where B represents diethylanikne. The value 9.78 was used for the logarithm of the formation constant (Kr) of diethylanilinium perchlorate instead of 9.58 as calculated with eq. 4c because it gave better agreement with experi-

M

0.0226 .0444 .0902 .173 Average of 3 experiments.

8.80

[IHCIO41/ [I] Obsd. Calcd.

0.46 .71 1.1 1.8’ 1.3 0.94 .60 -35 .19 0.15 .23 .39

.61

0.67 .98 1.4 2.0

1.2 0.83 .48 .25 .13 0.17 .24 .34

.48

The effect of sodium acetate (2.2 to 34.9 X M) on 0.108 M sodium perchlorate solution is also shown in Table I\’. The calculated values of R were obtained using eq. 9e and the agreement between experiment and predicted values is satisfactory. The data in Table I V indicate that in the titration of 0.1 M sodium acetate with perchloric acid (no volume change) the ratio of the acid to basic form of PNB changes from 0.5 at (3.1% before to 1.8 a t the equivalence point. This is a reasonably sharp color change, but of several orders of magnitude smaller than is observed in the titration of a strong 0.1 ill base with a strong acid in water.

MINNEAPOLIS, MINNESOTA

REFINING TECHNICAL AND RESEARCH DIVISIONS,HUMBLE OIL AND REFINING COMPANY]

Polarography of Metallic Monolayers BY M. 111. NICHOLSON RECEIVED AUGUST6, 1956 The current due to electrolytic dissolution of a thin film in a linear voltage scanning process depends on the changing activity of the solid phase. Starting with Fick’s second law of diffusion and an unabridged form of the Nernst equation, a system is derived for calculating the polarographic dissolution curve of a fractional metallic monolayer. Comparison is made with the behavior of a bulk metal deposit. Agreement with experimental data is good for silver, fair for lead and poor for copper, on a platinum electrode. The principles developed here should be useful in analytical applications of film polarography and in the study of electrodeposition phenomena.

The electrochemistry of fractional monolayers Both of these authors have studied the problem by has been a subject of interest for many years but is electrodeposition of radioactive elements from exnot very well developed. Herzfeld’ first pointed tremely dilute solutions. Although the role of out that the Nernst equation in its classical form active spots sometimes appears to predominate,6 cannot be applied in such cases because it fails to it is possible in other instances to interpret results consider variations in the activity of the solid in terms of a relatively uniform deposit, using modiphase. The complexity of surface phenomena fications of the Nernst equation.B which influence electrochemical behavior in the The anodic dissolution of a metal film is exammonolayer region is evident in discussions by ined here on the hypothesis of a statistically uniHaissinsky2s3 and in a recent review by R ~ g e r s . ~form surface layer, in which the activity is proportional to the fraction of the electrode covered. (1) K.F. Herzfeld, Pkysik. Z.,13, 29 (1913). Experimentally, the dissolution current of an elec(2) M. Haissinsky, “filectrochimie des Substances Radioactives et des Solutions Extrernement Dilukes,” Hermann, Paris, 1946. (3) hl. Haissinsky, Exoerientia, 8, 125 (1952). (4) L. B. Rogers, Record Chem. Progr., 16, 197 (1955).

(5) M. Haissinsky and A. Coche, J. Chem. Soc., S397 (1949). (6) .I B. Rogers and A. F. Stehney, J . Electrochem. Soc., 96, 25 (1949).