Choice of chemical conditions in order to obtain linear titration curves in potentiometry

Talsnta,

Vol.

22, pp. 945-952

Pergamon

Press, 1975

Prmted

m Great

E&am

CHOICE OF CH~ICAL CONDITIONS IN ORDER TO OBTAIN LINEAR TITRATION CURVES @I POTENTIOMETRY AXEL JOHANSSON Royal Institute of Technology, Stockholm, Sweden Wecewed 20 August 1975. Accepted 28 August 1975)

Summary - In the titration of an acrd HA wrth a strong base, [HA] dnninishes, on the whole, in proportion to the addition of t&rant. However, [HA] = QA[Hf [A], andiF [A] is kept constant [HA] will be proportional to [II]. Therefore if [H] mstead of [HA] is plotted agaimt ml of titrant added, one obtams a linear titratroncurve. [A] is kept constant by add&on of NaA before trtratronm such high concentration that the formation of A can be neglected durmg the trtratron.When an acid stronger than acetic aad is titrated, sodium acatate can be usad as the added sah. Even mixtures of acids, mono- or polyba&, then yieldstraight titration curves since one is in fact titrating acetic-acidin the presence of excess of acetate. For weaker acids sodium sulphrte is used. In tha oxidationreductron titration of, for example, ferrous iron wtth permanganate, the potential measured ts dependent on the ratio fFe*]/[Fe* . If [Fe”] ISkept constant $ the addition of ferric chlonde before the titration, the potential will be dependent only on [Fe 1. Since this diminishes in proportion to the added volume of t&rant,straight trtration curves can be obtained in thuscase also. No correction for dilution should be made The most widely used method for obtaming linear titration curves 111potentrometric titrimetry is the ao-calIed Gran method.’ s2 In prmcrple this method involves plottmg the concentration of an approprrate sample species as a function of the volume of titrant added during a titration. One can then assume with good approximation that thrs concentration falls in proportion to the amount of titrant added before the equivalence point. After the equivalence point the ~oncen~ation of titrant undergoes a linear rise. For example, in the titration of a strong acid with a strong base th@ hydrogen-ion concentration decreases proportionally before the equivalence point; the hydroxideion concentration increases propo~ion~ly after the equivalence point. The simple expressions which Gran has presented are, however, limited in their apphcation. The expressions are not the same for titration of weak acids as for titration of strong acids, .nerther of these sets of expressions 1s applicable, therefore, to titration of moderately strong acids. In addition, the expressions for weak acids are only valid for acids with stabihty constants between 1O3 and IO’ at normal concentrations ( 1g2 - 1Cr’M). Ingman and Stills have developed Gran’s method for weak acids to include acids with stability constants up to 10’ ‘. Johansson4 has pointed out that the same expression can be used for strong and moderately strong acids and has described an automatic titration method which is based on the expressions derived. These expressions are rather complex but still useful If one has access to a calculator. A simpler method will now be described in which no complicated calculations need be performed, not even correction for dilution during titration. The only calculation done is the transfor945

mation of, for example, pH into hydrogen-ion concentration, IX.. the calculation of the antilogarithm of the pH. If one has access to an instrument which shows antilog pH, this calculation is also elimmated. Johansson6 has described such an mstrument. The titration curve 1s here automatically drawn, but of course one can transform measured pH values for a number of points almost as conveniently with the help of a pocket calculator and plot the titration mrrve by hand. In prmciple, the method involves choosmg the experimental conditions so that: (1) the sample concentration is kept proportional to the concentration that can be measured, (2) the sample concentration dimnushes m proportion to the amount of added titrant. The second condition can also be formulated in thrs way4 the t&ant shall chiefly react with a smgle species m the solution, and thrs reaction ought to be regarded as complete. If the observed values are plotted vs. the volume, a straight line results. When the method is applied to the titration of an acid HA with a strong base, [HA] is plotted against ml of base solution added before the equivalence pomt. [HA] is proportional to [HI [Al accordmg to the equilibrium equation, and if [Al can be kept constant [HA] will be proportional to [HI, which can, of course, be measured. Apphcatton of the method to oxidation-reduction involves keeping one of the components in the redox pair at constant concentration. For example, rf Fe(I1) is titrated with perma~~ate, the potential that 1s measured is dependent on the ratio (Fez+] /[Fe3+1. If fFe3+] ia kept constant, then the potential is dependent only on [Fe”]. [Fe*] or a constant X [Fe’+] can

946

AXEL JOHANSSON

therefore be measured and plotted agamst the volume of permanganate, thus resulting in a straight lme which mtercepts the volume axis at the equrvalence volume. Under the heading of examples, a more detailed account 1s given of the application of the method to trtration of acrds or bases and to determinatron of the sum of several acrds. In addition, the deterrninatlons of iodrne with thlosulphate and Fe2+ w&h permanganate are treated under redox titrations The expressions given by Gran have shown themselves to be unsuitable for practical application to redox titrations. The fact that there is a linear relation between the sample coneenttation and the volume of trtrant added makes it also possible to conveniently perform so-called one-point titrations. If one knows the approximate ~on~ntration of, for example, an acid in the sample solution, one can add base equivalent to with a pipette approximately 90% of the calculated amount required for reaching the equivalence pomt, Afterwards, the remanung hydrogen-ion concentration (proportional to the remainrng acid concentratron) rameaaured and in this way the total concentration of the aad can easily be determined. In a followrng article examples af such titrations are given. ExPlmnmNTAL Potenr~me~‘c m~~~n~

Potentiometric titrations are usually carried out by means of the cell shown in Frg. 1. reference half-cell

II

sample .WlWion

probe for hydrogen ions, metal ions, electrons etc. I Frg. 1.

Many types of electrodes can act as probes. Hydrogen-ion concentrations are usually measured by glass electrodes. The range of probes for metal ions, anions such as fluonde, and molecules such as ammonia, has been extended by the introduction of various ronselective eIectrodes. The ratlo bt;tdreen different ions 01 molecules atn also be detezmhied by means of redox electrodes, e.g., a #at&urn wire. If the ceil contains a glass electrode in the right-lmnd half-cell the emf of the cell may be described by an equation consrsting of three terms E=.!$o+Qlog[H+]

+l$

(1)

where Q is R TI@ lnI 0. The first term A’@* depends on the type of eeII and includes the standard potenti& the potential of the reference electrode, the asymmetry potential of the glass electrode and the invariant part of and the Iiquid-Iiquid junction potential, where Q.b +~II is % e activity coefficient of hydrogen ions. The second term accounts for the variation of the measured potential with the ~n~~~n of hydrogen ions ao cording to Nemst’s equation if acti+ies are repla&_py concentrations. The third quantity Ej includesthe wutant part of the potential at the IiquWiquid junction and of &Jog m. This division into three terms is perhaps somew t artiflcid but nevertheless very practial. The term za- varies with changhg aridity and lo*c medium. Stro n$ y acidic solutions are avoided with the titration

method described in this paper and rf in addition the iomc strength is kept constant, E, will be close to zero. The term can be neglected at pH >4 (see Table 1 in ref. 7). It follows then from (1) that. (2) and that [II] = const X antilog W/Q)

(3)

This quantity [H] IS recorded by the instrument described in more detail below. Usually it is not necessary to know the value of the constant. It is, however, possible to determine its value by calibratron with solutions of known [H 1. It should be stressed that although the glass electrode in principle responds to hydrogen activity it may nevertheless be caliiated wrth solutions of known hydrogen-ion concentrations.7 If the activrty factor is constant, this leads only to different values of the constant in formula (3). In order to ensure linear plots it is necessary that the Q-value is not only constant, but also correct. Q ISoften called the slope. In the case of the glass electrode, it is constant over a large concentration range. The titration methods suggested here assume constant slope only over a few orders of magaitude.

If it will suffice to plot the Matron curves by hand, one requires, besides the burette, only a pH-meter. It is most advantageous if the meter has a digital readtiut wltb at least 2 or, even better, 3 decimals. If one wishes to register the titration curves automatically, it may be suitable to use an mstrument which transforms pH dire&y into concentration.s Such an instrument works in the following way. For eaoh change of a pH-mtit or a log [H] -unit m the sample solution, the voltage of the ceil in Fii 1. is changed by Q mV. At 25’. 0 = 59.16 mV for a gl& electrode: This &age is mea&$d by a pH-meter, which is basicslly a voltmeter wtth high mput impedance which divides the measured voltage by Q and shows this value on a male. The pH-meter whrch was used ln the %x~~~~ (Orion model 801) also had an output which gave 10 mV for every change of input voltage of Q mV, in other words for every change of one unit in pH. This voltage has then been used to calculate [HI, which is the antdog of -log [HI. The instrument which carries out this operation was made by Optilab AB, Stockholm. The amphtlcation in this antilog apparatus can be adjusted so that one pH unit is equivalent to, for example, 100 mV; 2 pH units are then equivalent to 1000 mV and 3 pH units to 10,000 mV. For every increase of output voltage by IO mV on the pH-meter, the voltage from the antilog unit is multiplied by 10. In or&r to cover the entire pH range without the voltage on the antilog unit becoming too great, one can connect an extra voltage source in -series with the cell to move the scale’s zero point. It is suitable to make the displacement in whore pH-steps (59.16 mV), m other words in whoIe powers of ten on the antilog scale. A Metrohm pH&mulator E 448 has been used as the extra vohage source. In some cases a combiition instrument has been used in which pH-meter, antilog attachment and digital voltmeter are built into one single instrument. This has aIso been built by Optgab AB and can possibly be &led CONC-meter or [ION] -meter sinee it indiostes dire&y a inundation. In most of the experiments described below, the output from the antilog apparatus has been written on a recorder (Metrohm Potentiograph E 336 A) whmh simultaneously shows the added volume of t&rant. The deflection is first adjusted to zero by short-oircuiting of the input. The electrodes are then dipped into the sampIe solution and amplitIcation on the antilog apparatus is adjusted so that fuII deflection is

947

I.&ar titration ctrrvesin potentiometry obtained on the recorder. If one wishesto register only the tJnal tenth of the titration curve, the amplification should then be increasedtenfold. Whenthe titration has pasasd the equivalencepoint, the inverted concentration vahte is @&red, for example If[H]. Here it is suitai~le to adjust the ~p~~~n so that the lines before and after the 8quiv&nc8 point form the same angl8with the axis. Th8 antdog apparatas then switchesautomatically from [H] to lf[H] at the equrvalencevolume.

brium to the left, meaning that the weakest acids cannot be determined by the method suggested. This will be drscussed further in the section “Treatment as c~nd~t~na~ t~~at~~n”, TmW.w curves

The equation of the trtratron curve before the equivalence point can be derived as follows. Assume the initial inaction of the acid is cm, that EXAMPLEg As stated in the introduction, straight titration the sample volume 1s V. ml and that V ml of base curves are obtained if the experimental conditions with concentration CB are added. Further, we can are chosen so that the demands specified there are assume that we add A from the b8gmning in met. This is elucidated m the following examples. concentration Ci. If it rs assumed that A is formed in proportion to addition of hydroxide, A Acid-Base Tmations

(Vo + VItAI = VoCi + VCB We can choose as the first example titration of a weak acid with a strong base. The main reaction The combinatron of (5) and (7) yields during the titration 1s v&g f VCB HA+OK=A-+HaO

[HAJ“&A[HI

On the whole, HA is consumed in proportion to the hydroxide addition before the equival8nGe point, and therefore if [HA] is plotted against ml of hydroxrde, a straight line is obtained. Thrs would be simple if one had access to an electrode which senses [HA], but since [HI is measured, [HA] must be calculated from the equilibrium condition [HAI = gHA[Hl

[Al

x

(4)

(5)

where KDA is the stability constant of the acrd. If one can keep [A] constant, then (6) IDA] a IHI producrng straight lines, although with different slopes, rf [HA] or [HI is plotted against ml of hydroxide. The easiest way to keep [A] constant is to add a salt NaA at the start of the titration, Srnce A is formed durmg the titratron, enough NaA must be added for the change to be neglected. In the titration of O*OlMacetic acid, for example, sodium acetate can be added so that its concentratron 1s l&f. Devrations from the strarght line then become insignrficant. Thus condition 1 (above) is satisfied. At the same time, condition 2, which requires that the hydroxide reacts with only one acid, 1s also met as is shown by the following, Usually when a weak acid is titrated, rt has partially dissociated mto H’ and A and both this ti and HA react with OH. Through the addition of 4 before titration, the dissociation becomes neghgrble. If @01&f acetic acid is titrated and acetate is added so that its concentratron is l&f, -log[H] becomes 6.5, which means that less than one ten-thou~ndth of the acetic acid has dissociated. In order for a straight line to be obtained, however, the reaction HA + Ofr *A+ Ha0 must be complete. Addition of AYdisplaces the equili-

v

+ v

(7)

(8)

0

If one takes into consideration that according to defimtion VecB z V&h

(9)

where Ve is the equivalence volume, and further assumes that HA is consumed in proportion to addition of hydroxide, then (Vo + V)[HA] = VecD -VCB

(10)

If (8) and (10) are combined, we obtain v,-v

=?(VoC’g

+ VCB)[H]

(11)

if v oCo A >> VCB, then (11) can be formulated as Ve-Vs

constant x [H]

(12)

or, expressed in words, if [HI is plotted as a function of volume V of t&rant added, a straight line is obtained which intersects the volume axis when V = Ve, that is, at the equivalence volume. There should be no correction for dilution. This follows since both HA and A are diluted equally during the titration. In the derivation of the formula, we have made the following assumptions. (1) That V& >> VCB. This corresponds to our cohdition 1, So that deviation from the straight line will not be too great, V& should be 50-l 00 times greater than VCB. If one wishes one can naturally use formula (11) instead of formula (12) for plotting and obtain a completely straight line. The formula can then be written as Ve- V = constant X

IHI

(13)

If vo = 100 ml, CD = 0.1&f and c”A = 1116,the

AXEL JOHANSSON

948

second term in parenthesis = IO3 V. If one uses the simpler formula (11) Instead of (13), the deviation will be greatest around the halfneutralization point. (2) That A IS formed and HA consumed m proportion to the addition of base. ‘Fh~s corresponds to our second condition and assumes that HA and A do not take part in any secondary reactions and that the ~u~b~urn constant rs large enough for the reaction HA + OH + K + H20. (3) That [HI 1s proportional to the antilog of PH. The requirement for this 1s taken up m the ~~odu~ion. In this example, before the titration of an acid HA, a salt of the same acid has been added. This is not necessary. If one wants to titrate hydrochloric acid, for example, one can add sodium acetate in excess. An amount of acetic acid 1s released equivalent to the amount of hydrochloric acid present; this acetic acid is then titrated. Another advantage in connection with this procedure 1s that the solution never becomes so acrdrc that one must take the term Ej in equation (1) into consideration. When titrating a polybasic acid such as oxalic acid m which both proton complexes are stronger acids than acetic acid, rt 1s suitable to choose sodium acetate as the addition. One obtains then a single straight line since it is actually acetic acid one is titrating. The same thing applies to mixtures of acids, which are stronger than or as strong as acetic acid. Chozce of salt to be added

When choosing which salt is best suited as an addition in the titration of an acid or a mixture of acids, ane should above all make sure that condition 2 is met. However, many salts can be considered, and so one should choose a salt which can be obtain analytically pure and which IS inexpensive as well, Suppose one wants to determine an acid HB by titration and adds the salt NaA before titration. The acids HA and HB may be identical but need not be. The following reaction must then be take’n into consideration. HB+A-=HA+Bwith the equrlibnum

(14)

expression

P-W[Bl s -= IHBI IA1 KHB

(15)

If condition 2 is to be fulfilled, equilibrium (14) has to be displaced far to the right; in other words, only the acid HA should be present In concentration worth mentioning. Ai a condition one can set [HA] >lOOmBl .[B] willthenbenearlyequal to C’& the or&ma1 concentration of acid HB. One obtains KHAaKHB

IOOcprB -

[Al

(16)

If [A] = 1M and CfiB = O*OlM

then Km

) KHB

Sodmm acetate can be used in the titration of acids havmg a stability constant less than about 105. For weaker acids one can choose, for example, sodium sulphite with log Km = 7$. The method is not usable for very weak acids (see below). In the titration of bases, the same rules apply, mutates mutandts. Addition of ammonmm chloride 1s suitable for titration of ammonia and stronger bases

Logartthmrc dragrams

For those famihar with them, logarithmic diagrams quickly give information as to whether a certain acid-salt combination is sunable or not. In Fig. 2 the titration of an acid HB is drawn with log KHB = 3.0 and C%B = O.OlM after the addition of sodium acetate to a concentration of 05M. Log Kwc has been assumed to be 4.50 (concentration constant at ionic strength 05). According to equation (14) [HAcl and [Bl are equal at the start. This corresponds to a vertical line through point 1. Here [I-L&] isO*OlM, [HI31 10-s’3M, [Ii] 10’ 3M and [AC] = 05M. Thus, HAc is the only acid 111appreciable concentration. During the titration HAc 1s consumed (and the small con~entratlons of H’ and HB) and one moves to the right from point 1 m the diagram. The situation represented by a vertical line through point 2 1s that which occurs at the equivalence pomt. Here the hydroxide-ion concentration is equal to the acetic acid concentration. (Actually it should be equal to the sum of [HAcl, [HBI and [HI, but the last two concentrations are so luw that they can be neglected.) [HAcl = 104”M, [AC] = OSM, [B] = OOIM. Since the lines for [HAc] and [HI in the logarithmic diagram are parallel during the whole titration from point 1 to point 2, [I-IA] = constant x [H] and thus condition 1 is met. During the titration the acetic acid concentration drops from O*OlM at the start to 1.3 X 10’119 at the equivalence point. The reaction is therefore as good as complete, and since only HAc 1s titrated, one obtains a single straight line. Condition 2 1s met.

Treatment as conditional trtmtion

The method of conditional constants which Ringborn’ has so successfully used in many contexts is here also an excellent tool for calculation of the titration curves and for jud& wkuch acids can be titrated according to the suggested techmque. In order to determine which acids can be t&rated with thrs technique it can be advantageous to regard the method as a conditional titration of H with OH, and we assume as

Linear trtration curves in potentiometry

5 0

1

2

3

L

5

6

PH 7

8

9

lo

11

12

13

-1I-

B -2 -3 -L -5 , -6 , -7 -8 -9 -10 L

Fig. 2. Logarithmic diagram of log C ss a function of pH for the acrd-base pair HB - B after addrtron of sodium acetate A<. Total cont. Cllh = 0.0% log KHB = 3.0, total cont. CAc = O.SM;leg Km,r. = 4.5. before that an acid HB is to be titrated and that a salt NaA IS added. The mam reaction is taken to be H++OH-=HsO and the equilibrium

(17)

equation

[HI [OHI =K,

(18)

Formation of HA and HB are regarded as sidereactions, and one takes these into account by mtroducmg the conditional hydrogen-ion concentration [H’] whrch represents the total concentration of H which 1s not bound to OH. Thus. [H’] = [HI + [HA] + [HB] Furthermore, the srds-reaction Ringboms) is defmed by

coefficient

“H = IH’I /WI

(19) (see (20)

which can be calculated from 9

= 1 +KmfAl

+g&B]

If (18) and (20) are combined, Kfi=Z&,=

(21)

one obtains

[H’][OH]

(22)

where K’ w is the conditronal ran-product of water, which IS constant if I~H is constant. Under these condrtions (oH bemg constant), a titratron of a weak acrd can be treated formally as a titration of a strong acrd, except that the value of the ion-product IS changed. Therefore rf [H] or [II’] is pIotted as a function of added volume of titrant, straight hnes which mtercept the volume axrs at the equivalence volume, although with drfferent slopes, are obtained m both cases. For CXHto be constant, it is necessary above all for [A] to be constant. The term KHh[Bl rs so small that it can be neglected fequatron (21)]. [Al changes

somewhat durrng the titration since new A is far&$, but the requnement for the method is that new A &n be neglected in relation to total A. The value of K& can be calculated from (21) and (22). If KH;A = 104*‘, KHB = 103, [A] = OSM and [b] = 0,01&f, then &YH= lo4 *2 and K& = 1Cr9” (the same example as demonstrated with the logarithmrc diagram). During the titration [H’] changes from 0*01&f to 1@ *9M at the equivalence point, At the hi-neutra~zat~n point [H’l = 0.OOSM. The titration curve is straight almost the whole way and deviatron at the equivalence point rs n+gligible. If one does not plot the area near, thrs pomt but instead extrapolates the strarght portion of th8 curve, one obtams an intercept on. the volume axis at the equivalence volume. Very weak acrds, for example the ammonmm ran *with log KHB = 9.5, give rise to very flat titration curves when titaated in the usual manner. Addition of the corresponding base, ammonia, increases the conditional ion-product to 10-“ *‘, wliic~ means that titration of a 0.01&f solution of NH; is not possrble. For practical purposes, the lme is drawn at acids whmh have a lower stabihty constant than lo*. In one of the examples below, the first two drssociatian steps of the phosphoric acid have been utilized for titration after addition of sodium sulphrte. Examples

In Fig. 3 titrations of (a) acetic acid, (b) hydrochloric acid, (c) oxalic acid and (d) phosphor&*aad are presented. In trtrations a, b, and c sodium acetate was added so that the concentration was 05M and in d sodium sulphrte so that the concentration was 0*25&f. Acid concentration was O*OlM in cases a and b and approximately O*OOSMin cases c and d. The volume in all four rnstances was 100 ml, Hydrogen-ion inundation

1

2

3

L

5

6

7

8

9

10

11

12

13

IL

15

16

ml Fig. 3. Titrations with strong base of (u) acetic acid, (b) hydrochloric acid, (4 oxalic acid after addition of sodium acetate (04&f). Curve (d) represents a titration wSthstrong base of phosphonc acid after addition of sodium sulphite (0-25&f).Zero on the volume axis has been displaced 1.00 ml for each titration. was recorded in arbitrary units against ml of titrant (0.098OM NaOH + 0.4M NaCl). Zero on the volume axis has been displaced 1 ml for each titration. The curves are practically straight lines. The equivalence volumes read from the curves are 10.22, 10.19, 10.19, and 10.78 ml, and the expected values 10.20, 10.20, 10.20, and 10.82 ml. In titration d the graph is curved in the vminity of the equivalence volume, but the correct value is obtained If the straight part of the graph is extrapolated to the volume axis. In all cases l/[Hl was recorded after the equivalence point. In Fig. 4 curves have been recorded for the titration of 100 ml of approximately 0*01&f NHs with O-l&f HCl (also approximately 0*4&f with respect to NaCl). Curve a represents a normal titration, pH against ml, and curves b and c titrations in which the sample solution was made 05M with respect to N&Cl. In c only the titration curve round the equivalence point was recorded. The expected value was 9.80 ml and the values found 9*80,9-82 and 9-82 ml. It 1s important that the ionic strength is kept constant during the titration and that the right Q-value is used, m other words, that the temperature knob on the pH-meter is adjusted to the right value, since Q varies with temperature. A deviation of a few degrees makes no difference, however. B. Oxidation-Reduction Iodometm

Titrations

tltratzons

Titration of iodine with thiosulphate is a typical example of areas m which the expressions

stated by Gran2 cannot be applied. This is because one must add iodide from the beginning in order to keep the iodine m solution, and the Gran functions assume that one IS dealing only with iodide which rs formed durmg the titration. However, if the amount of iodide added from the beginning is made so large that the iodide formed during the titration can be neglected, one can apply the same principles as in the previous section on acid-base titrations. Iodine concentration 1s plotted as a function of added volume of throsulphate, thus resulting m a strarght line which intercepts the volume axis at the equivalence volume. If the titration is carried out potentiometrically, one measures primarily a cell voltage E which is dependent upon both iodine concentration and iodide concentration. If the latter is regarded as constant, then E wrll be dependent only upon the former. Let us assume that V. ml of an iodine solution with concentration Cl 1s to be t&rated with V ml of a thiosulphate solution with concentration CB. Furthermore, the concentratron of iodide in the iodine solution has been set at concentration e.

f,+ 2s20$- = 3f + sqoa-

(23)

If the titration is followed potentiometrically with a cell m which the probe in the right-hand half-cell in Fig. 1 is a platinum wire, one obtains

Q

E=Eb+-logn

[OXI

(24)

[red1

where EL encompasses normal potential, reference potential and expressions for the mvanable part of

951

Linear titration curves in potentiometry

10

7-

B

_I

0

7

6

5

L

3

2

1

( 0

2

1

3

L

5

6

7

6

9

10

11

12

ml

13

1L

15

Fig. 4. Titrations of 100 ml of approx. O.OlM NHs with O.lM HCl. Curve (cl) represents a normal titration curve, pH agamst ml; curves (b) and (c) are titrations in which the sample solution was made 0.W with respect to NH&l. In (c) the sensitivity was mcreased tenfold. the activity factors and liquid-hquid junction potentials. If the activity factors and liquidliquid junction potentials can be kept constant, do will be constant Q, as before, is RTF-’ In 10 and n is 2 in this case. If one assumes complete reaction then

voc’i [red]=-

VCB

+vo+v

[ox] =_VoC1 - -=-VCB v,+V Wo+v)

(25)

vo+v cs (P-e--v) 2(&.o+v)

(26)

where Ve = equivalence volume, defined by V&g/Z

= V&i

(26a)

(25) and (26) yield [ox] -= [red]

CB (Ve-v)

(27)

2( VoCy + VC,)

If VCB << V,Ci)and then

(27) is substituted

into (24),

2 (E-E;)

v,_v=

2vocF1oQ -x

(28)

cB or 2E

Ve- V = constant X 1OQ

(29)

Thus If antilog 2E/Q IS plotted as a function of titrant volume V, one obtains a straight line which intercepts the volume axis at V = Ve. In Fig. 5 a titration of 10.00 ml of cu. O*OSAf iodme and 90 ml of water with O*lOOM thiosulphate is represented. The sample solution was 0*8M with respect to KI and the thiosul hate ionic strength was adjusted to 0.8 with K g 1. A platinum wire was used as the mdicator electrode and an Orion double-junction electrode Model 90-02-00 as reference electrode. The mstrument yields a constant x antilog 2E/Q, and this value has been plotted manually against volume of thiosulphate. The intercept on the volume,axis shows Ve = 10.50 ml, which is equal to the true value. Tztrarron of Fe(ZZ) If all non m a sample 1s m ferrous form, Gran’s functions for evaluation of a titration can be applied. If there is ferric ion present the titration curve 1s not straight and an evaluation according to Gran is difficult to perform. As m the previous section, one can avoid difficulties by addmg an excess of ferric iron from the begmning. According to Nernst’s formula [Fe2+] = [Fe3+l antilog (E&E)/Q

(30)

If [Fe37 is kept constant, [Fe2’l will be proportional to antilog (constant -E)/Q . Titration of ferrous iron with permanganate or with cerium(IV) yields linear titration curves d

952

Fig. 5. A titration of 100 ml of approx. 0*005&fiodine (0.8M KI) with O*lOOOMthiosulphate (0 8M KU).

the solutions are made 0-W with respect to Fe3* Samples 1:64.8,65.0 %Fe (true value 64.9%) before the start It 1s suitable to use ferric chloride. Samples2:71.1,71.5 %Fe(truevalue 71.1%) Tltratlon solutions of Ce(IV) are usually very acidic, and m that case the sample sohitlons must Acknqtiedgement-I am indebted to Mrs Meredith Dahlin be adjusted to the s$e acidity and to the same for translating the manuscript. This work was supported concentration of complexing agents if the titration by the Swedish’Natural Science Research Council. c&es are to be linear. Example. About 125 mg of two staddard ymples of’ iron oxides were weighed. These were dissolved in acid and the solutibns treated according to Zimmerman-Reinhardt in the idual way. Five g’ of ferric chloride hexahydrate weie then added to each sari@Ie sol&tion. Each sample was diluted to ca. 100 ml and titrated with 0*02M permanganatkr. D’uring the last tenth of the titrat&n, &‘tUog (-E/Q) was registered from full scale dn the! grap’h to near z$ro. The results were.

REFERENCES 1. 2. 3. 4. 5. 6.

P. S$rensen, Kern Maanadblad, 1951, 32,13 G. Gran, Analyst, 1952,77,661. F IngmanandE. Still, Tafanta, 1966, 13,143l.

A. Johansson, Analyst, 1970,95,535. A Johansson and L. Pehrsson, IbId., 1970,95,652. A. Johansson, Ta&mfa,1974,21,1269

7. F. lngmaa, A. Johansson, S. Johansson and R. Karlsson, Anal. Chim Acta, 1973,64,113.

8. A. Rin&vm, Complexation m Analytical Chemistry, Wdey/Intersclence, New York, 1963.