Analytica Chimica Acta 476 (2003) 159–165

Development of a method for estimating an accurate equivalencepoint in nickel titration of cyanide ions

Toshihiro Suzuki, Akiharu Hioki∗, Masayasu KurahashiNational Metrology Institute of Japan (NMIJ), National Institute of Advanced Industrial Science and Technology (AIST),

AIST Tsukuba Central 3-10, 1-1-1, Umezono, Tsukuba-shi, Ibaraki 305-8563, Japan

Received 18 February 2002; received in revised form 1 October 2002; accepted 18 October 2002

Abstract

In a nickel titration of cyanide ions using murexide as indicator, an accurate equivalence point was determined by anon-linear least-squares curve-fitting for a titration curve. This method was developed to establish a standard solution forcyanide ions. In a curve-fitting procedure, a theoretical titration curve was calculated, assuming that nickel ion formed onlya 1:4 Ni2+:CN− complex with cyanide ions and formed only a 1:1 complex with murexide. Results of the curve-fitting werereasonable at any pH and any indicator concentration studied. The combined standard uncertainty for a concentration of a1000 mg kg−1 cyanide solution by this method was 0.079%.© 2002 Elsevier Science B.V. All rights reserved.

Keywords:Cyanide ion; Complexometric titration; Equivalence point; Nickel ion; Murexide; Uncertainty

1. Introduction

Cyanide has been used in large quantities in indus-try and cyanide ion is an important ion to be monitoredin the environment. Though many sensitive methodsfor cyanide determination have been proposed[1–10],they are relative methods. Therefore, a standard solu-tion of cyanide ions is inevitably in great demand. Inthe view of development of a primary standard solu-tion, cyanide ions should be determined by primary ordefinitive methods related to the International Systemof Units. Though potentially primary methods usingcoulometry[11] or argentometry[12,13] have beenreported for cyanide determination, high precisionwas not realised. Moreover, the optimum pH for thecoulometry was probably too low to avoid any loss of

∗ Corresponding author. Fax:+81-298-61-6890.E-mail address:aki-hioki@aist.go.jp (A. Hioki).

cyanide. Photometric titrations utilising a formationof a nickel–cyanide complex, [Ni(CN)4]2−, are othercandidates for primary methods; e.g. chelatometrictitration of an excess of nickel ions over cyanideions by ethylenediaminetetraacetic acid (EDTA)[14]and direct titration of nickel ions by cyanide titrant[15,16]. Since those titration systems, however, donot have a very sensitive colour change near theend-point, it is necessary to analyse whole titrationcurves in order to obtain accurate equivalence points.An inflexion point of a titration curve is often regardedas an end-point; however, the inflexion point does notnecessarily agree with the equivalence point. Thereare a few studies in which an equivalence point wasdetermined by an analysis of a titration curve consid-ering equilibria among a metal ion, a chelating agentand an indicator ([17] and references cited therein).In the present study, an accurate equivalence pointwas successfully determined by analysing a titration

0003-2670/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved.PII: S0003-2670(02)01362-4

160 T. Suzuki et al. / Analytica Chimica Acta 476 (2003) 159–165

curve obtained from the nickel titration of cyanideions using murexide as an indicator. In addition, anuncertainty of the titration result was also estimated.

CL = 4

√[A ′]2 − {(VCA0/(v + V ) − vCtit/(v + V ) − 1/β ′

MA )}[A ′] − VCA0/{β ′MA (v + V )}

(β ′ML 4

/β ′MA ){VCA0/(v + V ) − [A ′]}

+4

([A ′] − VCA0

v + V+ vCtit

v + V+ 1

β ′MA

− VCA0

β ′MA (v + V )[A ′]

). (8)

2. Theory

In a nickel titration system of cyanide ions usingmurexide as indicator, it is assumed that nickel ionforms only a 1:1 complex with murexide[18] and thatnickel ion forms only 1:4 complex[19] with cyanideions. In the following discussion, M, L and A denotenickel ion, cyanide ion and murexide, respectively. Forsimplicity, the electrical charges are generally omit-ted. It is assumed that changes of ionic strength andpH during a titration are negligible, at least near theend point. [X′] is defined asαX(Z)[X], whereαX(Z) isthe side-reaction coefficient for interaction ofX withsome speciesZ such as hydrogen ion, hydroxide ion,ammonium ion, etc. Parametreβ ′ denotes the condi-tional overall stability constant. It is supposed that anickel titrant whose concentration and volume areCtitand v, respectively, is added to the titration systemwhose initial volume isV. CM, CL andCA are definedas the total concentrations of M, L and A, respectively.CA0 is also defined as an initial concentration of Aat v = 0. The following equations are obtained fromrelated mass balances and the definitions:

β ′ML 4

= [ML ′4]

[M ′][L ′]4(1)

β ′MA = [MA ′]

[M ′][A ′](2)

CM = [M′]+ [

MA ′]+ [ML ′

4

](3)

CA = [A ′]+ [

MA ′] (4)

CL = [L ′]+ 4

[ML ′

4

](5)

CM = Ctitv

v + V(6)

CA = CA0V

v + V. (7)

Equation (8)is obtained fromEqs. (1)–(7)by elimi-natingCM, CA, [M ′], [L ′], [ML ′

4] and [MA′]:

On the other hand, whenvEP is defined as the titrantvolume up to an equivalence point,Eq. (9)is obtainedfrom the relation that the total molar amount of Lalways equals four times the total molar amount of Mat the equivalence point:

CL = 4vEPCtit

v + V. (9)

It is difficult to solve Eqs. (8) and (9)for [A ′].However, fromEqs. (8) and (9)the value of [A′]corresponding to each value ofv can be numeri-cally calculated for any combination of parameterssuch asβ ′

MA , β ′ML 4

and vEP when CA0, Ctit and Vare known. Since the value of [MA′] can be calcu-lated using the value of [A′] and Eq. (4), the ab-sorbanceE of the system being titrated is given asfollows:

E = εA ′ [A ′] + εMA ′ [MA ′] (10)

whereεA ′ and εMA ′ are the apparent molar absorp-tivities of A and MA under a given experimentalcondition, respectively. The value ofεA ′ or εMA ′ isobtained from the absorbance in the region where[A ′] = CA or [MA ′] = CA is substantially valid.Possible biases of the absorbances used for the cal-culation of the molar absorptivities cancel out ifthe biases are constant in the range of the analysis.Consequently, a titration curve can be analysed by anon-linear least-squares method applied to the threeparametersβ ′

MA , β ′ML 4

and vEP. The parameters aredetermined by minimising a sum of squares of resid-uals on absorbances near an end-point. The key pointof the present study is the original approach to fita titration data of a 1:4 metal–ligand system alongwith a 1:1 metal–indicator complex in the directionof absorbance. Alternatively, the sum of the squaresof the residuals can be minimised in the direction oftitrant volume. Though in the latter fitting approach

T. Suzuki et al. / Analytica Chimica Acta 476 (2003) 159–165 161

the data analysis is simple and easy, it tends to lead toa large error for an equivalence point when the fittingrange on a titration curve is too wide. Therefore, thefitting approach in the direction of absorbance wasadopted.

3. Experimental

3.1. Apparatus

An automatic titration apparatus AT-420win (KyotoElectronics, Japan) equipped with 20 cm3 piston buretwas used. The buret volume was calibrated by weigh-ing the discharge of water considering both air buoy-ancy and evaporation during the discharge. The densityof a solution was determined with a DA-101B auto-matic densimeter (Kyoto Electronics). Colour changesof the indicator were measured with a P-114 opti-cal fibre dip-type sensor (Kyoto Electronics). Tracemetals in the potassium cyanide were determined byan inductively coupled plasma atomic emission spec-trometer (ICP-AES) SPS3000 (Seiko Instruments,Japan). All operations were performed in a room at25±1◦C.

3.2. Reagents

Reagent-grade chemicals were used unless other-wise specified. Water was purified by a Milli-Q SPICP-MS system (Millipore Corp., Japan). Murex-ide (Dojindo Laboratories Kumamoto, Japan) wasrecrystallised from a saturated aqueous solution ofammonium chloride and dried under vacuum at roomtemperature[18]. The purity of the murexide wasdetermined by elemental analysis and a mole ratiomethod with nickel ion (vide infra). About 0.06 g ofthe murexide was broken up and diluted with 24 gof powdered sodium chloride. A nickel titrant (ca.0.01 mol dm−3) was prepared by dissolving ca. 1 g ofhigh purity nickel (>99.99%, Johnson Matthey, Roys-ton, Herts, UK) in 30 cm3 of 6.6 mol dm−3 nitric acidand diluting to 1.7 kg with 0.2 mol dm−3 ammonia.The high purity nickel was, previously, washed with2.9 mol dm−3 hydrochloric acid, water and ethanol toremove any grease and oxide, and dried for 0.5 h at55◦C. A cyanide solution was prepared by dissolv-ing 2.5 g of potassium cyanide (Wako Pure Chemical

Industries, Japan) in ca. 100 g of a 1 mol dm−3

potassium hydroxide solution and diluting to 1 kgwith a 1 mol dm−3 potassium hydroxide solution.Air-buoyancy correction was always applied to anyweighing.

3.3. Titration procedure

Ten gram of the cyanide solution was weighed intoa 200 cm3 beaker and 70 g of water, 5 cm3 of 25 m/m%ammonia, 2 cm3 of 1 mol dm−3 ammonium chlorideand 0.2 g of the diluted powder of murexide wereadded. The pH of the mixed solution was ca. 12.6. Ifnecessary, the pH was adjusted with a potassium hy-droxide solution or nitric acid. The mixed solution wastitrated with the nickel titrant, and the colour changewas monitored at 562 nm, which was near the wave-length of the absorption maximum of non-complexedmurexide.

4. Results and discussion

4.1. Loss of cyanide ions at preparationand weighing

Since potassium cyanide is hygroscopic, it wasweighed rapidly for preparation of a cyanide solution.There was the possibility of a decrease in concentra-tion of a cyanide solution due to evaporation as hydro-gen cyanide at preparation, storage or weighing of thesolution. Cyanide solutions (ca. 1000 mg kg−1) wereprepared with 0.01, 0.1, 0.5 and 1 mol dm−3 potassiumhydroxide. The measured cyanide concentration in0.01 or 0.1 mol dm−3 potassium hydroxide was 0.26or 0.16% lower, respectively, than that in 1 mol dm−3

potassium hydroxide, while there was no differencebetween the measured cyanide concentrations in 0.5and 1 mol dm−3 potassium hydroxide. In the courseof preparing a 1000 mg kg−1 cyanide solution, a muchhigher concentration was involved. The cyanide con-tents (ca. 10 g kg−1) of 0.5 and 1 mol dm−3 potassiumhydroxide in beakers did not change even after stand-ing overnight at 25◦C. Therefore, it was concludedthat any concentration decrease due to preparationwas negligible if >0.5 mol dm−3 potassium hydroxidewas used. The stability of cyanide solutions dur-ing long storage will be reported elsewhere. In the

162 T. Suzuki et al. / Analytica Chimica Acta 476 (2003) 159–165

Fig. 1. Decomposition rate of murexide and nickel–murexidecomplex. (�) Free murexide (1.7 × 10−5 mol dm−3), (�)nickel–murexide complex (Ni: 0.9 × 10−3 mol dm−3, murex-ide: 1.6 × 10−5 mol dm−3). Other composition of the solution:[NH3] = 0.76 mol dm−3, [Cl−] = 0.02 mol dm−3. Measurementtime is 14 min.

present study, a cyanide solution was prepared with1 mol dm−3 potassium hydroxide the day before use.

4.2. Stability of murexide in solution

Though murexide is unstable, it is favourable forthis work because it is easy to purify and forms onlya 1:1 nickel–murexide complex which is preferable toanalyse a titration curve. Since murexide is unstable insolution, its concentration was corrected at each step inthe course of a titration by considering the decomposi-tion of murexide. The decomposition rate of murexidewas obtained from the decrease in an absorbance un-der the experimental conditions (Fig. 1). Free murex-ide at pH 12.0 was most stable between pH 10.5 andpH 13.0, but the nickel–murexide complex was morestable at lower pH. Since it took about 10 min for atitration, ca. 4.2% of the murexide decomposed in thetitration system at pH 12.0. This correction for murex-ide decomposition improved the agreement between atheoretical titration curve and an experimental one andreduced the systematic error of the equivalence pointby 0.05%.

Fig. 2. Examples of curves for nickel titration of cyanide ionsusing murexide as an indicator. (�) CA/CL = 1.3 × 10−3,(�) CA/CL = 2.9 × 10−3, (×) CA/CL = 4.5 × 10−3,(�) CA/CL = 6.1 × 10−3, (�) CA/CL = 7.5 × 10−3.CL = 3.8 × 10−3 mol dm−3 at the equivalence point. The pHvalue is 12.0. The solid curves were obtained by the non-linearleast-squares curve-fitting of the experimental data. The marks “” and “(�)” indicate inflextion points and estimated equivalencepoints, respectively.

4.3. Analysis of nickel titration system of cyanide ions

Under the proposed titration procedure, while thenickel–cyanide complex substantially had no absorp-tion, the nickel titrant had an absorption maximaat 595 nm. The baseline absorbance increased by0.0007 cm−3 of the titrant after passing an equiva-lence point; therefore, the absorbances used forεMA ′calculation were corrected for the baseline rise. Theabsorption from the excess nickel titrant was negligi-ble in the region of curve-fitting. Titration data wereanalysed by the equations shown inSection 2.

Typical titration curves are represented inFig. 2. Atheoretical titration curve calculated with optimisedparameters successfully explained an experimentaltitration curve under any conditions of pH and in-dicator concentration studied. An apparent cyanideconcentration calculated from an inflexion point ofan experimental titration curve or from an intersec-tion of both the tangent at the inflexion point and theline extrapolated from the region where [MA′] = CA

T. Suzuki et al. / Analytica Chimica Acta 476 (2003) 159–165 163

Fig. 3. Dependence of four kinds of end-points on an indicatorconcentration. The concentration of cyanide ions was calculatedby using the equivalence point calculated by curve-fitting (�), theinflextion point (�) or the intersection of both the tangent at theinflextion point and the line extrapolated from the region where[MA ′] = CA (�) or [A ′] = CA (�) are substantially valid. Theexperimental conditions were the same as inFig. 2.

are substantially valid depending on the shape of atitration curve which changed with indicator concen-tration. However, a cyanide concentration calculated

from the equivalence point did not depend on an in-dicator concentration (Fig. 3). A shape of a titrationcurve in this system scarcely depended on pH valuebetween 10.5 and 13.0; the cyanide concentration ex-perimentally estimated from the equivalence point wascertainly independent of pH value.

The stability constantsβML 4 and βMA were ob-tained by considering side-reactions (Table 1). Theside-reaction coefficients under the experimental con-ditions were calculated from the stability constants ofHA [20], H2A [20], HCN, NiOH[21], and [Ni(NH3)n]

Table 1Stability constants determined from the nickel titration of cyanideions using murexide as indicator

pH CA/CL LogβMA LogβML4

11.1 0.0044 14.0 29.311.3 0.0044 14.1 29.312.0a 0.0044 14.2 30.412.5 0.0048 14.6 30.913.0 0.0044 15.0 30.612.1 0.0013 14.1 30.912.1 0.0029 14.2 30.512.0a 0.0044 14.2 30.412.0 0.0061 14.3 30.712.0 0.0075 14.3 30.6

Average stabilityconstants

14.3 ± 0.3b 30.3 ± 0.6b

Reported stabilityconstant[19]

– 30.5± 0.3

a Identical data; either was used for the average calculation.b Symbol ‘±’ indicates the standard deviation for a value.

(n = 1–6) [22]; e.g. αM(OH,NH3) = 2.86 × 108,αL(H) = 1.00 andαA(H) = 1.03 at pH 12.0. Theequivalence point from the curve-fitting was not influ-enced by errors in the side-reaction coefficients. Onthe other hand, they influenced the calculation ofβMAandβML 4; however, the stability constants did not de-pend on an indicator concentration and pH andβML 4

was also in good agreement with the reported value.An experimental titration curve was also analysed

considering additional formation of possible com-plexes, i.e., ML, ML2 and ML3.

vCtit

v + V=(

1 +4∑

n=1

β ′MLn

[L ′]n + {Vβ ′MA CA0/(v + V )}∑4

n=1nβ′MLn

[L ′]n∑4n=1nβ

′MLn

[L ′]n + β ′MA (CL − [L ′])

)CL − [L ′]∑4

n=1nβ′MLn

[L ′]n(11)

[A ′] = CA∑4

n=1nβ′MLn

[L ′]n∑4n=1nβ

′MLn

[L ′]n + β ′MA (CL − [L ′])

. (12)

Equations (11) and (12)were obtained in the sameway as the derivation ofEq. (8). FromEqs. (9), (11)and (12)the absorbanceE of the system was given,and the titration curve was similarly analysed by anon-linear least-squares method applied to the six pa-rametersβ ′

MA , β ′ML , β ′

ML 2, β ′

ML 3, β ′

ML 4andvEP. Under

each of many experimental conditions studied, bothcurve-fitting procedures of six parameters and threeparameters (β ′

MA , β ′ML 4

and vEP) gave substantiallythe same set of values ofβMA , βML 4 and vEP, and

164 T. Suzuki et al. / Analytica Chimica Acta 476 (2003) 159–165

the six parameter procedure gave values of>/ 1015 toβML , βML 2 andβML 3. Judging from the result, the in-fluence of ML, ML2 and ML3 was negligible. Undersome limited experimental conditions the six parame-ter procedure gave the best fits to experimental curveswhenβML 3 andβML 4 were 1022.0 to 1023.8 and 1030.3

to 1030.8, respectively; these stability constants couldindicate the presence of ML3. Since these results wereobtained only under the conditions of lower pH andhigher indicator concentration, it was presumed thatthe higher values ofβML 3 were just caused by unsup-posed small strain of the experimental curves whichcould be originated from linearity of absorbance mea-surement or pH dependence of the absorbance of theexcess nickel titrant, etc. In factβML 3 has been re-ported to be<2 × 1016 [19]; this value indicates theabsence of ML3. Even ifβML 3 was 2×1020, the influ-ence on an estimated equivalence point is<0.0001%.Therefore, the influence was regarded to be negligible,if any.

4.4. Quantification of the uncertainty

The uncertainty of the equivalence point was deter-mined by combining the uncertainties of the factorsrelated to the calculation of the equivalence point, suchas an initial volume of the titration system, accuracy ofthe buret volume, correction of the absorbance base-line and purity of the indicator. The relative standarduncertainty of the equivalence point caused by the ini-tial volume and other random errors was included ina repeatability of the titrations (0.019%). The relativestandard uncertainty of the buret volume was estimatedby the repeatability of its calibration (0.003%). Sinceit was believed that the absorbance-baseline rise afteran inflexion point could be measured with the preci-sion of 0.0005 absorbance, the relative standard un-certainty of the equivalence point caused by the factorwas calculated from the possible error of the measuredbaseline rise (0.026%). In the present titration system,the concentration of the indicator was calculated onthe basis of the purity determined by the mole ratiomethod (99.6%). On the other hand, the purity of theindicator had to be 92% at least judging from the resultof the elemental analysis. Therefore, the curve-fittingprocedure for each titration curve was repeatedly car-ried out by assuming several values among 92–100%as the indicator purity (Fig. 4). The largest difference

Fig. 4. Dependence of the apparent cyanide concentration as aresult of the curve fitting on the supposed indicater purity. The pHvalue is 12.0. The value ofCA/CL is 4.5×10−3 at the equivalencepoint.

between the equivalence point using 99.6% and thatusing any other purity was regarded as the possibleerror of the adopted equivalence point. The relativestandard uncertainty caused by the uncertainty of theindicator purity was calculated by dividing the possi-ble error by

√3, assuming a rectangular distribution

(0.068%). Since some metal ions which formed com-plexes with cyanide ions could lead to a negative errorfor the titration result, an uncertainty resulting fromimpurity metals was estimated from the total amountof the impurity metals in the potassium cyanide. Theerror of the titration result was estimated as−0.035%at the most extreme from ICP-AES determinations,supposing that all of the impurity metal ions formedmore stable complexes with cyanide ions than nickelions; then, the co-ordination number was assumed as4. The relative standard uncertainty caused by the im-purity metals (0.020%) was calculated by dividing themost extreme error by

√3, assuming a rectangular dis-

tribution. Finally, combining the standard uncertainties(Fig. 5), the expanded uncertainty for the concentra-tion of a cyanide solution was estimated to be 0.16%using a coverage factor of 2. In this case, since theeffect of the indicator purity, the correction of base-line rise after an inflexion point, the effects of impu-rity metals and the repeatability of titrations are the

T. Suzuki et al. / Analytica Chimica Acta 476 (2003) 159–165 165

Fig. 5. Combination of the uncertainty components. The width of each line shows the relative magnitude of uncertainty.

main sources of the combined standard uncertainty,the standard uncertainties of the other factors are notalways required to be estimated.

5. Conclusions

The proposed method allows determination ofmg-level cyanide without any standard of the ions atrelatively high pH values where the ions are muchstabilised. Since the method achieves a high precisionand a small uncertainty, it is suitable for calibrationof a standard solution of cyanide ions, stability mea-surement of cyanide ions or a cyanide salt for longstorage, and purity determination of a cyanide salt.

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