Acid-Base Titration Curves in Disproportionating Redox Systems Tadeusz MichaJowski and Andrzej Lesiak
Jagiellonian University, 30-060 Krakow, Poland The research field concerning acid-base titrations may seem to be wmpletely exhausted. Although a number of papers have appeared on this subject in the recent literature, one important area has not been exploited at all. It concerns acid-base titrations in disproportionating redox systems. In n previous paper ( 1 1 ,concerning the acidic properties of a~lueoussolutions of Br2. the concept of electron prebalance was introduced. This concept involves sys&ms in which an element (e.g., bromine or iodine)forms more than two species with different oxidation numbers. Electron prebalance can also be related to systems containing more than two elements that participate in electron transitions. All species known in the literature to form from the related elements should be included. The importance of electron prebalance results from the fact that it comprise.;, in veiled form, the stoichiometry of a redox reaction. This is more clearly comprt!hensible from a linear combination of electron prebalance and related concentration balances. Nonredox systems can be considered as a limitingcase of redox svsrems. For example. the DH of NaBr solution can be obtained on the basis bf char& and concentration balances and the ionic product of water K,. Moreover, calculations made using the electron prebalance allow the calculation of the related potential E of the solution. Electron, charge, and concentration balances, together with independent equations for equilibrium constants (e.g., standard potentials and protonation constants) for the species involved in a defined system form a complete set of nonlinear equations that lead to the related titration curve. The problem can be resolved using an appropriate iterative computer program. Disproportionating systems with two bromine compounds (Brzand HBrO) and iodine I2 (involved in different media) are considered below as examples.
Figure 1.The Evs. Vrelationships due to (A) the Br, + NaOH system and (B) the HBrO + NaOH system. wherep = 2 and q = Z for the system Bra + NaOH; andp = 1and q = Z - 1for the system HBrO + NaOH (Z = 35). The values of equilibrium constants involved in the algorithms applied are quoted elsewhere ( I ) . The related titration curves are plotted in coordinates (V, E ) (Fig. 1)and (V, pH) (Fig. 2). Changes in concentration of the wrresponding bromine species (Fig. 3) show which of the reactions occured at defined stages of titration. Bm
+ NaOH System
From the very beginning of.titration, the disproportionation proceeds mainly according to the following reaction. 3Brz + 3Hz0 = BrO, + 5BF + 6H'
Titration of Bromine Species
The balances related to a titrand + titrant system obtained after addition of V mL of C = 0.1 mom NaOH to V, = 100 mL of C, =0.01mom X(where Xis Brz or HBrO) are as follows.
20
5
10
15
20
1
Volume NaOH (cmS)
Figure 2. The pH vs. Vrelationships due to (A) the Br, + NaOH system and (B) the HBrO + NaOH system. 632
Journal of Chemical Education
In other words, 5 mmol of HBrO corresponds to 1mmol of OH-. Then the first inflection point, visiblein Figures 1B and 2B, corresponds to
c,v, C V e -= 2 mL of the titrant added 5
At V = 2 mL, pH = 3.84 and E = 1.233 V At V = 0, correspondingto C. =0.01mom HBrO, we have pH = 2.742 and E = 1.310V The scheme of disproportionation changes gradually at further stages of the titration. Near the main inflection point it is aeseribeaby 3HBrO = BrOi + 2Br- + 3Hf Volume NaOH (cm3)
(9)
The protons evolved are neutralized with NaOH. Then 3HBrO + 30H- = BrOa + 2BC + 3H20
.,
.............................................. Bvo;
(10)
Thus, every 1mmol of HBrO corresponds to 1mmol of NaOH. Bra-
s
-a
-10
HBrO
which corresponds to pH = 7.83 andE = 0.984 V The titrand-titrant systems considered above comprise the solutions of pure reagents (Brz,HBrO) titrated with an appropriate titrant. Some other factors can influence acidbase and redox equilibria as well. Tirations in Iodine Media
Figure 3. The log [XJ vs. Vrelationshipsfordifferentbromine species qdue to (A) the Br, + NaOH system and (0) the HBrO + NaOH system. This reaction predominates over the competetive ones more significantly near the equivalence point, where the efficiencyof the main competetive reaction (Fig. 3A)
We provide theoretical titration curves related to the Ip + NaOH system, in the presence of I- or HzC03as acwmpanying species. (The latter is considered as entering the titraud and titrant composition.) The titration in a twophase system (H20/CC14)will be also considered. To introduce a generalized notation, we write the balances adaptable for the system obtained aRer addition of V mL of titrant (C mom NaOH and (1-SIC' mol'L HzCOd into V. mL of titrand (C. mom Ip; f i t mom KI; and SC' mom HzC03)in equilibrium with yW. mL of CC4. Denoting W = V, +V and assuming additivity of volume, we get (2= 53)
is about lo4times smaller than for the reaction in eq 4. The protons evolved in eq 4 are titrated with NaOH
where 3 mmol of Brz corresponds to 6 mmol of OH-. In other words, 1mmol of Br2 corresponds to 2 mmol of OH-. At V = 2C,VJC = 20 mL we find pH = 7.95 and E = 0.973 V HBrO + NaOH System
On the initial stage of titratiou (see Fig. 3B), a great part of HBrO disproportionates according to
and the H+evolved is neutralized with NaOH.
Volume 71 Number 8 August 1994
633
The species entering the balances in eqs 11-14 are involved in the relations for physicochemical data (24). pH =-log [w] lag [ O M = -14 + pH [I,] log -- 2 4 E - 0.6195) [ri2[Id log -= 2A(E - 0.545)
[rI3
no-I = 2A(E - 0.49)+ 2pH - 28 log [r]
0
5
10
Volume
15
20
:
NaOH (ema)
[HI01 -= lO.6- pH log [Io-I log [IOjl = 6A(E - 1.08) + 6pH rri [HI031 log ---= 0.79 -pH [IO,] log-
[HsIO,] = 8A(E - 1.24)+ 7pH [ri [HJOJ log ----= -3.3 [HsIO~I
log-
[H31@7
rr1 log-
+ pH
= 8A(E - 0.37)+ 9pH - 126
[HCOg
= 10.1-pH
[ C O ~ [H.$O,I
log-=
[CO~I
16.4-2pH
where A = 16.92 a t 25 'C; and E is the redox potential in volts.
Figure4. The graphs of (A) Evs. Vand (6) pH vs. Vrelationships for aqueous media. (For further details see text.) range. (In other words, the virtual assumption that iodine does not precipitate is applied.)
[I2(0)1- 82,6 -[I,]
is the distribution constant for iodine between organic (o, CC4) and aqueous phases (6). The Titration Curves The titration curves found a t V, = 100 mL, C, = 0.01 mom, and Col= 0.1 m o m are given in Figures 4 and 5. Further data are specified below. Titration curves related to aqueous media are collected in Figure 4; A1 and B l are enlareed . framnents of A' and B'. (The scale of the correspending variables is changed then?.! Some curves due to extraction svstpms H.,O/CCI, are eiven in Fi~wre5. The curves in ~ i ~ u4r a;e plotted for o and dikerent P, 6, and E values.
-
y=
p = & = 0 (curue 1) Solubility of iodine in water equals s = 1.33 x lo3 m o m a t t = 25 "C (2.5) (s < C,). Thus, a part of iodine remains undissolved at the initial stage (V< 11.2 mL) of titration (a = 1in eqs 11and 12). The related part of curve 1is obtained by setting [I21 = s and assuming concentration of solid iodine, [Iz(s)l, as one of the variables. Further part of the curve involves eq 15, a = 0. The dashed line 1' was plotted under the assumption that eq 15 is valid over a whole V
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Journal of Chemical Education
In the presence ofa sufficientexwssof iodide, Iz(s]does not exist as the equilibrium solid phase ra = 01; 12w 1- = 13.
The titration curves are dotted for C' = 0.001 (curve 3) and C' = 0.0005 (curve 4, in.titrant. The titrant can be considered as a mixture of NaOH and Na2C03r7,.
H&O8 enters the titrand composition; C' = 0.001 (curve 5) and C' = 0.0005 (curve 6).
H&03 enters both titrand and titrant, a t equal eoncentrations. Curves 7 and 8 are plotted for C' = 0.001 and C' = 0.0005. The curves in Figure 5 are plotted for y = 1, E = 0, and different P values.
The aqueous solution is in equilibrium with W, = 100 rnL (curve 1)and W, = 10 mL (curve 2) of CC4. KI and H2CO8 do not enter the system considered.
0.354 0
. . . . 5. . . . 10 . . . . . 15 . . . . .20. . . . .: . Volume NaOH (cm')
Figure 7. The Evs. V(diagram a) and the pH vs. V(diagrarn b) relationships for the system considered in example 61.
.
4.451(curve I),6.866(2,3,4), 4.654(5,7), 4.807 (68). and 4.961 (8)in Figure 7B 4.771(I),4.485(2),6.995(3),and 6.938(4)inFigure 8B
E values found at V = 0 are 0.812( 1 )and 0.608(2-8)in Figure 7A 0.791(1),0.809(2),0.579(3),and 0.6M)(4)in Figure 8A
4.54
0
........................ 5
10
15
Volume
25
20
NaOH (cma)
Changes in concentration of iodine species due to the titrand + titrant system related to curve 1in Figure 4 are given in Figure 6. Among others, it should be noticed that disproportionationof iodine in alkaline media proceeds according to the reaction 31~ + OH- = 103 + 5 r + ~ H Z O
Figure 5. The graphs of (A) Evs. Vand (B) pH vs. Vrelationships in extraction ( H 2 0 + CCI,) systems. (Forfurther details see text.)
(16)
It exceeds the main competetive reaction Iz + 20H-= 10- + 1- + H20
(17)
by about 2.5 x lo9.
p=1
KI enters the titrand composition. Curves 3 and 4 are lotted for W"= 100 mL and W. = 10 rnL of CC1.. The sohiions titratedare character& by low buffer capacities (a steeo course in the initial Darts of the curves in Fieures 7B pH values found for V = 0 are
-
A Qualitative Reaction The literature (8)provides an interesting qualitative reaction for M e founded on addition of magnesium salt to 12 + KI solution, previously alkalinized with an excess of NaOH. The iodine thus formed is adsorbed on magnesium hydroxide precipitate, turning it red-brown. The magnesium salt addition may formally be treated as titration. Let VmL of C* = 0.2 moVLMgS04be added to V, = 5 mL of the solution containing Iz (C, = 0.1 mol/L), KI (Col= 0.4
-Ir,,.
-8 -10
....
10-
-12 KIO,
-14
0
5
10
15
20
25
Volume NaOH (cm')
Figure 6. The grapns of log [ X J vs. Vrelavonsn ps fordlnerent lodme specoes X ndlcated at tne corresponomg cmes
Volume MgSO, (cm')
Figure 8. The log [Xi]vs. Vrelationships for iodine species Xi Volume 71 Number 8 August 1994
635
Conclusion
The paper provides first examples of resolution of acidbase titration curves in redox systems. It was possible only after formulating the electron prebalance concept, which yields a set of equations necessary to resolve the problem posed. General properties of electron prebalance due to a defined titrand-titrant system (stated on numerous examples) can be formulated as follows.
-2-
M
-4-
*
-6-
-87 0
2
1 Volume &SO4
3
(cma)
Figure 9. The log s vs. Vreladonship for Mg(OH)2.
mol/L), and NaOH (C = 0.3 moVL). The related plots of E vs. V and pH vs. V are given in Figure 7. The log [Xi] vs. V n w e s for some iodine species (Xi)are plotted in Figure 8. Equations 11and 12 (at a = y = 0, P = 1) and the following equations were applied.
pK,= 10.74 [MgOm = @'[M&[OKI log
= 2.6
Growth in the value of V causes
.
decrease in pH value growth i n solubility ( 8 ) of magnesium hydroxide (Fig. 9)
s = [M?]
+ lMgOH+l+ [MgSOJ + [MgIOa
However, some redox equilibria (e.g., ones with a solvent (water) involved) are frequently hindered by kinetic effects. Therefore, some reagents (e.g., HBrO, KMnO,, or chromous salts) are stable in aqueous solutions. This must be taken into account when arranging the corresponding electron prebalances. Participation of a reagent both in acid-base and in redox reactions makes an essential complication in the related titration curve. (See the section on the HBrO and NaOH svstem.) Atomic number Z for bromine, involved in eq 1, exDresses the number of electrons in the bromine atom. Despite its defmite meaning, it can be replaced by an arbitrary number z, for example, z = 0. Equation 1is thus replaceable by linear combination of eqs 1 and 2. Such a procedure is well-known in elementary algebra. For example, multiplying eq 2 by a number a and subtracting it from eq 1gives
wherez=Z-aandq'=q-a.Forexample,q'=Z-a=z fortheBrz+NaOHsystemandq'=Z-1-a=z-1 for the HBrO + NaOH system. Similar remarks can be made for other redox systems. All calculations were done on an IBM PC 386 computer according to iteration procedure with Levenberg-Marquardt algorithm applied. Literature Cited 1. MiehaJowsK, T . J C k m . Educ. aeeepted for print. 2. Durdo-bao*forekmisl(inRussiao);N~olskyB.P,Ed.;I(hirms:Mmoow,Vol.3,1964. 3. Lune,Yu.Yu.Dui&-bad m analyfiml h m i s l r y (in Rusian): Khimia, 1989. 4. Chariot G. h a r&Tctio~chimwlms en solu1ion:Ihnolv~ouulitoti"o mi"&&Mas. . . M" Cie: Pane, 1989. 5. Lmgane, J. J. Electmnoly(irn1 C h i s h y ; Interscience New York,1958. 6. Ramette, R. W. C k m l m l E q u i l ~ ~ u m M d h l y s i s ; A d d i s m - W ~ ~ 1Reading: ey; MA.
et
where (3) [MglO$ = 1 0 ~ ' ~ ~ g ~ l [ 1 0 ~ ~ .growth i n t h e concentration of Is a n d Ii ( t h e color of MdOHh)
636
It involves the stoichiometry of the reactions that occur. It is valid throughout a whale volume V range of titrant added. It can be related to systems containing one, two, or more elements that participate in electron transitions. A n y element considered in redox equilibria can farm the speeiea with more than two oxidation numbers. Moreover, any of the species can enter some side reactions in the system. It can be applied for systems not possessing appreciable redox properties. A n y element of the system considered can be included in electron prebalance as one that participates in electmn transitions.
Journal of Chemical Education
1981.
I. Michalowski,T. J Ckm.Edue. 11188.65,181. 8. Kreshkw, A. PPrinciple~o f h o l y l i m l CkmisVy (in Ruasiao); Vol 1, Khimia: Mmemv, 1976.
