Development and publication of new titrimetric methods

Tahnta, 1972,Vol. 19,pp. 147to 760. Pemamm Prts. printedin Northem Ireland

DEVELOPMENT AND PUBLICATION TITRIMETRIC METHODS

OF NEW

A. BERKA and J. &VEfK Department of Analytical Chemistry, Charles University, Prague 2, Albertov 2030, Czechoslovakia ROBERT A. CHALMERS Chemistry Department, University of Aberdeen, Scotland

Old Aberdeen,

(Received 30 April 1970. Revised 10 August 1971. Accepted 20 November 1971) Summary-Requirements are laid down for the development of titrimetric methods and for writing up the work for publication. The general principles of various types of titration reaction are discussed, and special attention is paid to the parameters which influence chemical reactions. ALTHOUGH about 200 years have elapsed since the publication of the first papers dealing with titrimetric analysis,l the technique is still as widely used as ever, especially since the development of physicochemical methods of measurement, which permit not only objective detection of the end-point of a titration but also monitoring of the course of the reaction and hence a better understanding of its chemistry. Better understanding in turn leads to improvements in speed, precision, accuracy, sensitivity and/or selectivity of the procedures. In spite of all this, however, many methods are published which leave much to be desired both in their usefulness and in validation of the conditions used. It may be argued that that is the fault of the editors and referees concerned, but it is not really part of their duties to give private tuition in research methods. This paper has therefore been added to those already published on how to develop and write up methods,2*3 with the intention of fulfilling the need for such instruction.

GENERAL REQUIREMENTS OF A TITRIMETRIC METHOD In general, as with other analytical methods, titrimetric procedures should be accurate and precise, simple to use, work under a wide range of conditions, fulfil a definite need and have practical applications (otherwise they are merely academic exercises and of little value) and should be rapid (if they are slow they offer no advantage over gravimetric methods). Some of these criteria are worth further comment. By “accurate and precise” we mean that the results should be correct and reproducible within the limits set by the random errors in measurement, and in the research work on a new method it is imperative that the errors be kept as small as possible. If it is known that a method is capable of giving results correct to within 1 part per thousand (1 ppt) then if a larger error is acceptable for some particular application, the method can be used with confidence even if less care is taken. On the other hand, if the best that can be done with a method gives an error of lx, application of that method is limited to those situations in which a larger error than this can be tolerated. All too often there seems to be a failure to realise that in titrimetry the need to standardize the titrant introduces an additional source of error, since any 3

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mistake made in determining the titre will cause a bias in all the results obtained with the titrant. Consider, for example, the standardization of ceric sulphate with arsenious oxide, with osmium tetroxide as catalyst and ferroin as indicator. To give a reasonable titration volume of O.lM ceric sulphate (i.e., about 30 ml, which can be measured with a reading error of about 0.03 ml or less if care is taken), a weight of about 150 mg of arsenious oxide is required. Suppose this is weighed on a normal fourth-place balance with a standard deviation of 0.05 mg at the weight loading used, and that the balance weights have not been calibrated. The random error in weighing by difference will be about 0.15 mg (95 % confidence limits) and in addition there may be a biased error from the unknown errors in the weights. The manufacturer’s tolerance on weights up to 500 mg is O-05 mg, and since there must be an exchange of at least two fractional weights it would be possible for this bias to amount to at least O-1 mg. If this reinforces the random error, we have already an error of nearly 2 ppt in the weight of primary standard taken, plus an expected reading error of 1 ppt. In addition there is the end-point error arising from the fact that we do not know how much of the last increment added was actually required to reach the end-point and how much was excess. “Splitting” drops is tedious, and this error can be minimized by assuming that the end-point was reached on addition of half the last drop. The error is then only half the drop-size. If a varying amount of indicator is added to replicate samples, there will be a variation in the amount of titrant needed to oxidize the indicator, and if the indicator is too concentrated or too large an amount is added (or both!) another biased error can occur. Obviously care and thought are needed to measure the titre to within 1 ppt, and if the standardization is not done accurately, the results of use of the titrant will not be as meaningful as they should be. How often we see in a paper the statement that a solution was standardized by some method or other, usually described only by a reference, and no information is given as to the precision of the results obtained. Similar remarks apply to calibration of apparatus, for which the results are scarcely ever given. By “simple to use” and “work under a wide range of conditions” we mean that there should be as few procedural steps as possible, since each can lead to a mistake being made, and that tolerances on such factors as pH range, ionic strength, amounts of particular compounds permitted to be present, should be as wide as possible, so that undue care need not be taken over adjustment of conditions. A procedure that requires very close control of pH is not nearly as satisfactory to use as one that operates over a pH range of several units. By “rapid” we mean that reaction should proceed more rapidly than titrant can be added to the system, or at least very nearly so. A procedure in which a wait of several minutes is necessary between additions of titrant is going to be a very irksome one to use, and not at all suitable for routine analysis. Many potentiometric systems suffer from this drawback, when the electrode system used takes some time to reach a stable potential as the titration proceeds. Sometimes, of course, a slow reaction can be combined with a back-titration that is rapid, by adding an excess of reactant, leaving it for a sufficient time, and then titrating the excess. Again, an interfering reaction may be made to occur so slowly that it does not affect the main reaction, or the kinetics may already be sufficiently different for no interference to occur. By “fulfilling a need and having practical application” we mean that a reaction that is suitable only for analysis of a pure solution of the substance to be determined

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is of such limited usefulness as to be practically worthless unless it is so very much better than any other available method that it is necessarily the method of choice for standardizing solutions of that substance. This was stated very clearly over 30 years ago by Lundell in his paper “Analysis of Things as They Are”,4 a paper that should be compulsory reading for all analytical chemists. The literature is full of “new and improved” methods that are in fact poorer in performance than the ones they seek to replace, and that are often based on standardizations performed bymeans of methods that they criticize and claim to supplant. Many methods have been published for the titrimetric determination of iron, but very few of them are better than the earliest methods of all-oxidation of iron(I1) with dichromates or permanganate.g Unless the method being developed promises to fulfill these criteria, it seems scarcely worth while pursuing it. If it does show promise, however, there must be a proper investigation of the conditions under which it should be used, and a proper assessment of its scope of application and of its reliability. The remainder of this paper will deal with these aspects. Each type of reaction will be dealt with separately, as will standardization and end-point detection. BASIC

CONDITIONS

OF TITRIMETRIC

DETERMINATIONS

Only those reactions which proceed in stoichiometric ratio in a chosen solvent, without side-reactions and consecutive reactions, can serve as a basis for titrimetric determinations. The end-point of the reaction must be detectable by chemical or physical means. Special demands are made of the substance used as titrant. It must be of well defined composition, easily soluble in the chosen solvent so that solutions covering a wide range of concentration can be prepared, and its solutions should either be stable or easily standardized. Some titrants whiuh are unstable because of reactions with the solvent or the atmosphere, or because of volatility or light-sensitivity, can still be used if the active species is generated in situ electrolytically. It is desirable that the substance should be readily available. Although a detailed study of the kinetics is not essential for development of a titrimetric method, it stands to reason that a method that is kinetically slow is not a very useful one, especially for routine work. However, slow reactions may be used in indirect methods if the back-titration reaction is fast. On the other hand, a competing reaction may be suppressed by proper adjustment of the conditions if its rate of reaction is much slower than that of the main reaction. Similarly it is not essential that the mechanism of the reaction be known, though again, knowledge of it may be useful in certain circumstances. The stoichiometry can be expressed in terms of equivalents or of the ratio of molar concentrations, which should be a ratio between small integers. It is worth stating at this point that in titrimetry it is essential to retain both the mole-concept and the concept of normality. Each has its own special field of application, together with an enormous overlap of applicability, where either can be used. For example, in dealing with polymers and many biochemical systems, it is not known (or cannot be known) what the molecular weight is, although it is perfectly easy to determine the number of equivalentsof some reactive group in a given weight of sample. In contrast, normality is meaningless in complexation reactions. For the rest, the objection to the use of equivalents, viz. that a different equivalent

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weight must be used for different reactions of the same substance, is just as much an objection to the use of moles, because the equation must be written down in both cases, and the onlyreal difference is in the point at which the stoichiometriccoefficients are introduced into the calculation. If the equivalent is defined as that weight of material which will react with one mole of hydrogen ions or of electrons or with one equivalent of any other substance, both conventions are referred unambiguously to the mole concept, and there should be no difficulty in understanding and applying both. Assumptions about stoichiometry are best verified by using equimolar solutions of the titrant and titrand and seeing whether the volumes needed to complete the reaction are in some simple whole-number ratio. If they are not, then either the reaction is non-quantitative for kinetic or thermodynamic reasons, or the main reaction is accompanied by side-reactions or consecutive reactions. Because these latter reactions can proceed at a considerably lower velocity than the main reaction, it is convenient to add an excess of titrant and to determine the amount unreacted after a sufficient time, to verify that there is no consecutive reaction. The stoichiometry can also be checked by quantitative determination of the reaction products. In direct titrations (see below), a titration error can be falsely attributed to non-quantitative reaction if the stoichiometry is not checked. It is often difficult, however, to decide whether nonquantitative results are due to the kinetics or the thermodynamics.’ Precipitation reactions

The main criterion is the value of the solubility product for the substance being precipitated. If CM is the initial concentration of the metal to be precipitated by the titrant, then for 1 ppt error (which we will take as the working error to be aimed at) the final concentration must be 10e3 CM, and for a precipitate ML the apparent solubility product must be 10es C& The apparent solubility product is related to the thermodynamic solubility product by the equations governing the amount of L that may be protonated at the pH of titration and hence unavailable for precipitation, and the amount of M that may be masked by hydrolysis or complexation by other anions present. As pointed out elsewhere ,8 it is easier to use the inverse of the solubility product, which may be called the insolubility constant and treated as a stability constant for the precipitate. Ringbom’s a-coefficient method@ are then easily applied for calculation of the minimum pH etc permissible, as illustrated in Fig. 1, which should be self-explanatory. Similar diagrams can be prepared to take into account masking agents. Once the permissible pH range has been calculated from the known values of stability constants, it should be checked experimentally-stability constants are often determined under highly specialized conditions, and the values obtained may be some orders of magnitude different from those for the conditions of the titration. If the constants are not known, they must either be determined or the pH range etc determined empirically. Errors are most likely to arise from co-precipitation, especially from occlusion, because digestion and other means of reducing co-precipitation are not possible in this case. A typical example is the occlusion of AgCl in the determination of iodide by argentometric titration. lo Normally there should be an exchange reaction between AgCl and I- to give AgI and Cl-, but if the AgCl is occluded within AgI particles the

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preclpltatlon

0

2

4

8

6

IO

12

14

PH

FIG. I.-Precipitation titration of lo-*M metal ion M with l&and H*L, to form ML, where M forms soluble hydroxo-complexes. Kl and KS for HIL are 10’ and lo6 respectively, Ksp for ML is 1O-‘o (i.e., Kins = lOlo). Ka and K4 for M(OH),- and M(OH)**- are 10’ and lOa respectively. K&e% = conditional constant for at least 99.9 % precipitation at the end-point.

exchange cannot take place, and there is an overconsumption of silver nitrate. The error can be eliminated by adding some ammonium carbonate to make diamminosilver(I) the effective titrant, in which case AgCl cannot precipitate. The effect of all other ions likely to be present in practical applications must therefore be checked experimentally. Precipitation reactions may sometimes be made more selective by judicious use of pH control, auxiliary masking agents, etc, but in general the utility of this type of reaction is severely limited by the lack of selectivity. Further problems arise in the detection of the end-point. If a coloured precipitate is produced at the end of the main reaction, as in the Mohr method for halides, conditions must be carefully adjusted so that the overconsumption of titrant in production of a visible amount of coloured product is just compensated for by the underconsumption of titrant caused by the fact that the coloured product begins to be formed before the main reaction is entirely complete .ll The situation may be further aggravated by the presence of ions (such as NH,+) which are normally thought of as harmless.12*13 Adsorption indicators are usually fairly good, but often experience is required to recognize the end-point. Amperometric titration is often used, but the errors are seldom less than 1 ‘A, which is not surprising in view of the l-2’% error usually associated with polarographic methods. If say 10 points are used to construct the titration graph and there is an error of 2 % associated with each, the overall error in assessing the end-point is likely to be about 2/a 74 or about 0.6 %. In addition, it is customary to use small volumes of fairly concentrated titrant (in order to avoid excessive dilution and the need to apply a dilution correction) and the reading errors will be rather large. Potentiometric detection of the end-point is likely to prove the most satisfactory, provided that the electrodes reach potential equilibrium rapidlyotherwise the method will be too slow to be useful except for special or occasional use.

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Conductimetric methods are satisfactory if the conductance can be measured sufficiently precisely (for reasons similar to those discussed for amperometric titrations) and the results are properly interpreted. Redox reactions The primary requirements are a means of converting the determinand into essentially the completely oxidized or reduced form, and a titrant capable of completely reducing or oxidizing the product. Obviously an excess of an auxiliary oxidant or reductant will be required in the first step, and this excess must be easily destroyed without the determinand being affected. The formal potentials for the titrant and determinand couples must be sufficiently far apart for the reaction to be at least 99.9% complete at the end-point; that means a difference of at least 0.36 V for two one-electron reactants, but only 0.09 V for a pair of two-electron reactants. It is important to remember that the products may depend on whether a oneelectron couple is matched with a one- or a two-electron couple. Hydrazine is oxidized to nitrogen by a two-electron oxidant, but to a mixture of ammonia and nitrogen by a one-electron reagent. Examination of the Nernst equation shows that the redox potentials may be profoundly affected by changes in acidity, by complexation, and by precipitation or formation of undissociated compounds. Efict of acidity. The most noticeable effect is on the potentials of couples involving oxy-anions that are oxidized or reduced. Typical examples are the fact that manganate is unstable in acid solution because of disproportionation, but stable in extremely alkaline solutions, and the fact that the interference of vanadium(IV) in the oxidimetric determination of iron(I1) can be eliminated by making the solution 5M in sulphuric acid, and so raising the potential of the V(V)/V(IV) couple to a value comparable to that of the usual oxidants. Another effect is preferential protonation of one half of a couple, as for example the ferrocyanide/ferricyanide couple, or the effect of acidity on the potential of ferroin. A further effect of changes of acidity may be on the kinetics of the reaction. As has recently been shown,14 potassium chlorate can be used successfully as an oxidative titrant if the acidity is made high enough, though even then a catalyst is sometimes desirable as well. Effect of complexation. It is well known that the potential of the iron couple can be shifted in either direction by use of complexing agents, the potential being increased if the iron(I1) complex is more stable than the iron(II1) complex (as with l,lO’phenanthroline) and lowered if the order of stabilities is reversed (as with phosphate, fluoride, EDTA). E$ect of precipitation etc. The potential of the silver couple is decreased by introduction of an anion that forms an insoluble silver salt, the decrease being the greater the more insoluble the compound. Similarly, formation of an undissociated species such as mercuric chloride or cyanide will remove the ions of one form of the couple and hence shift the potential. Importance of the Nernst equation. The Nemst equation not only permits calculation of the equilibrium constant (and hence the feasibility of the reaction) from the potentials of the couples involved, but also permits us to calculate the form of the

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potentiometric titration curve and so choose suitable indicators and decide whether other species may interfere or not by being co-titrated. It also reminds us that we cannot have an absoluteI’ pure oxidant or reductant solution if the solvent is capable of redox action. It is for this reason that certain species are unstable in aqueous medium, even if protected from aerial oxidation. It further reveals that lack of thought has led to an incorrect ascription of chemical properties to certain oxidants. Many textbooks state that dichromate and ceric sulphate can be used for titrations in hydrochloric acid medium but permanganate can not. This statement is only partly true: permanganate can certainly be used, e.g., for titration of antimony(III), in chloride medium. It is only unsuitable for use when the oxidation of chloride is induced by another reaction in the system, such as the oxidation of iron(I1). The reason for this is that the kinetics of chloride oxidation are so slow at moderate acidities that the end-point can be detected without interference from the slow side-reaction. Unfortunately, however, many chemists read more into the statement than is there, and assume that dichromate and ceric sulphate are incapable of oxidizing chloride-an assumption that is completely false, as a practical test will readily verify. Importance of kinetics. From what has just been said about permanganate it will be realized that the reaction kinetics may play a decisive part and override the thermodynamics. A good example is the determination of total iron in silicate rock by removal of silica by the Berzelius method, fusion of the metal oxides with pyrosulphate, dissolution in hydrochloric acid, reduction with the silver reductor, and titration with ceric sulphate, with ferroin as indicator.ls Two difficulties arise: there is a variable blank, and the end-point “returns”, that is, there is a sharp colour change followed by slow return of the reduced form of the indicator, and this behaviour is repeated on further addition of small increments of titrant. Both effects are kinetic in origin. The first arises from reduction of aerial oxygen to hydrogen peroxide in the silver reductor. The peroxide should be further reduced to water, but because the first reduction step is much faster than the second there is a build-up of peroxide, a steady state being reached because of the diffusion controlled supply of further oxygen from the air. The peroxide then reacts with iron(I1) in the initiation and termination steps of the Haber-Weissls mechanism for catalytic decomposition of peroxide: Fez+ + H,02 + Fe2+ + *OH + H,O, + -OH -+ HO,. + H,O, -+

Fea+ + OH- + *OH (initiation) F8+ + OH- (termination) HO,. + H,O H,O + 0, + *OH

propagation

The chain propagation steps are unlikely to have a chance to occur, since the iron is greatly in excess of the peroxide. Similar effects occur with amalgams when they are used in the presence of air. l7 The returning end-point arises because the decomposition reaction takes place in a platinum crucible and some platinum is extracted as Pt(IV) in the fusion process. According to the thermodynamics the Pt(IV) should be reduced to the metal on the silver reductor, but if the reduction is slow and occurs in two stages, uia Pt(II), and if the residence time in the reductor column is too short (short column and/or fast flow-rate) some Pt(I1) passes into the effluent and is oxidized (slowly, of course) after the preferential oxidation of the iron is complete. Fortunately the kinetics are so slow that the first sharp end-point corresponds exactly to the iron titration.15

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CHALMERS

Induced reactions. The Haber-Weiss mechanism just quoted is an example of an induced catalytic reaction. When such reactions can occur, they constitute a hidden source of error, which may be extremely large. In the oxidation of tin(I1) with dichromate, for example, induced aerial oxidation accounts for oxidation of no less than 98% of the tin.ls On the other hand, induced coupled reactions, in which a definite stoichiometry exists between the inductor and the acceptor systems, may be used quantitatively. End-point detection. Indicators and potentiometry are the means usually chosen for end-point detection. Naturally the indicator potential must be matched to the equivalence point potential of the system, either by choice of indicator or by shift of a potential (e.g., addition of phosphoric acid when diphenylamine is used as indicator for iron(I1) oxidation). Potentiometry is satisfactory subject to the usual proviso about the speed of electrode equilibration. Spectrophotometric titration is possible if one component of the titration system has suitable absorption characteristics differing from those of the others, but if the end-point section of the curve is too rounded, dilution corrections may be necessary and are rather tedious to apply. Complexation and acid-base reactions The basis of these reactions is formation of a highly stable (i.e., little dissociated) species such as a metal complex or water. The main criterion for successful application to titrimetry is therefore the apparent equilibrium constant for the reaction under the conditions used. In complexation reactions, if the initial metal ion concentration is CM then for the error to be 1 ppt or less, the concentration of free metal at the endpoint must be < 10” CM, and this must also be the total concentration of uncomplexed titrant in the titration solution. It follows that the minimum value for the apparent stability constant of the complex is CM/1O-6CM2or 106/Cnr. It is therefore advisable to use fairly concentrated solutions for titration of metals that form only weak complexes. The Ringborn conditional constant method can again be used to predict the minimum pH required for complete titration. It is not always recognized, however, that it is really the indicator reaction which sets the lower boundary of the permissible pH range. In the case of a weak metal-indicator complex it would be possible to find a pH at which the metal-titrant complex could be formed quantitatively while the metal-indicator complex was formed scarcely or not at all. The upper boundary of the pH range is set either by the hydrolysis characteristics of the metal ion or by the nature of the indicator. Almost all metallochromic indicators are also acid-base indicators, the colours of their metal complexes being essentially those of the species obtained on removal of one proton (sometimes more) from the indicator. For a colour change to occur at the end-point, from the colour of the metal-indicator complex to that of the free indicator, the pH must be below that at which the indicator would be deprotonated anyway. The whole system is illustrated in Fig. 2. It is possible to achieve selectivity of complexation by pH control if the metal ions present form complexes with the titrant, with sufficiently different stability constants (Fig. 2). For ions giving complexes with similar stabilities, auxiliary masking agents are used to achieve selectivity. When the pH is adjusted it is important to remember that the buffer system must not contain ions that can act as competing ligands.lg It is also important to remember that the buffer must have sufficient capacity to absorb the protons released during the complexation reaction.

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I og K;,

,’

FIG. 2.-Complexation titration of lO-PM metal ion M with l&and HL to form ML, with indicator HI. Km = 1016; &I = lOlo; KHI = 10’; HL is EDTA. Gg.so/. = conditional constant for at least 99.9 % completion of complexation at the end-point.

Acid-base reactions can be treated as a special case of complexation, in the simpler cases there being competition between two anions to form an undissociated species with protons. The decisive factor is the equilibrium constant for the reaction HA+OH-$A-+H,O

F&A4N-1

Kw

Keq = [HA][OH-] = K,, where & = [H,O]/ [H+] [OH-] ; Ku* = [HA]/ [H+] [A-] If the initial concentration of acid is C n4, then for 99.9% neutralization the final concentration is lo3 Cna, and since at equilibrium [HA] = [OH-], it follows that Keqmust be greater than 106/Cu* for quantitative titration ([A-] will be approximately equal to CnA at equivalence). If we approximate a little and use “mixed” stability constants, we can call the activity of water unity and take K, as 1014. In that case KHA must be less than K, -CHa/106, i.e., less than 108C HA, for quantitative titration. If the acid is weaker than this, either a larger error must be accepted or the conditions must be changed to make the acid appear to be stronger. One way of doing this is to introduce a metal ion that will form a complex with A-, thus releasing protons from HA; care must be taken, however, to choose a metal ion that will not itself interfere by a hydrolysis reaction. The more common method is to change the

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value of Keq by changing the solvent system. The use of and choice of non-aqueous solvents have been adequately discussed in various monographs20-22 and need not be dwelt on here. End-point detection. The most common methods for end-point detection are by means of indicators, potentiometry, spectrophotometry, conductimetry and thermometry or enthalpimetry. In complexation reactions the indicator must of necessity form with the determinand ion a complex that is less stable than the complex formed by the determinand and titrant. If the two complexes are of comparable stability there will be an end-point error that is a function of the amount of indicator added. An example is the use of Xylenol Orange for titration of lead with EDTA. It is also essential that the indicator should not be “blocked” by the presence of other metal ions that form with it complexes more stable than the determinand-indicator complex. Adequate buffering is also necessary to prevent appearance of a false end-point by virtue of decomposition of the indicator complex by reaction with the protons released as the main reaction proceeds. It is also most important that the transition interval should be as sharp as possible. If an appreciable volume of titrant is required to traverse the end-point colour change, and two elements are being determined in the same sample by titration of the sum followed by masking of one and titration of the complexant released, there will be an error if the “sum” titration end-point is taken as appearance of the free indicator colour but the back-titration end-point is the colour of metal-indicator complex. It is essential to use the same end-point colour in both cases. The general theory of these indicators has been well covered by Ringbom.s The theory of acidbase indicators is well known, and it need only be stressed that the pK value of the indicator must match the pH at the equivalence point, and that adequate precautions must be taken to avoid interference by carbon dioxide in the atmosphere. Potentiometry has already been discussed, and fortunately the glass electrode has a very rapid response and equilibration, so is ideal for potentiometric acid-base titration. The limitations of conductimetry (and amperometry) have been dealt with above and will apply here also. Spectrophotometry has been dealt with in a monograph,23 and the theory of spectrophotometric complexation titrations adequately covered.24*25 Thermometric and enthalpimetric methods are relatively new, but are really useful only if relatively large errors (1% or more) are acceptable. Perusal of some of the literature on these methods shows that when comparisons are made between thermometric and classical indicator methods, the errors reported for the latter are very often greatly in excess of the values that are obtainable by careful work. Interferences. In complexation reactions, interfering ions may be dealt with by pH control or selective masking, as pointed out above. A subtle form of interference may arise, however, from the use of masking agents. It sometimes happens that a masking agent added to sequester an interfering element can act as a bridging ligand to form a mixed-metal binuclear complex with the determinand ion. If this complex happens to be inert (i.e., kinetically stabilized) then the determinand ion will not react with the titrant. Such is the case with aluminium in the presence of uranyl ions and citrate.26 Similar cases are those of copper in the presence of chromium and citrate,27 and copper in presence of aluminium and tartrate. In acid-base reactions, the interferences are those caused by the presence of other acids or bases besides the determinand. If the strengths of the various species differ

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sufficiently it may be possible to titrate them consecutively, provided means of detecting the end-points are available. If the strengths are comparable, selective complexation or a change of solvent may give sufficient differentiation. GENERAL

FACTORS

INFLUENCING

TITRIMETRIC

METHODS

Ionic strength and variations in concentration

The ionic strength can affect both the velocity and the quantitativeness ofa chemical reaction, the effect being largely a function of the charges on the reacting species.29*so In a titration there must inevitably be a change in ionic strength in the course of the reaction, but fortunately most analytical procedures require the use of concentrations at which activity coefficients change relatively little with variation in ionic strength,al so it is unlikely that the ionic strength will be a serious factor. If it is, the effect can usually be “swamped” by addition of a large and constant amount of an indifferent electrolyte. Changes in the concentration of the reactants cause a change in the reaction velocity. This is seen in the decrease in the reaction velocity near the equivalence point, a feature of practical utility (the entering stream of titrant reacts immediately in the early part of a titration, but disperses sluggishly near the end-point, so that at the point of entry the indicator has changed colour). It is therefore convenient to keep the reactant concentrations fairly constant during the preliminary investigations. Later the concentrations can be varied, especially with a view to finding the lowest concentrations that can be used satisfactorily. Temperature

A change in temperature influences the reaction velocity and the equilibrium constant, and sometimes even the stoichiometry. Sometimes a higher temperature is used deliberately to make a slow reaction more practicable, and sometimes a very low temperature is used to make an interfering reaction so slow that its effect is nullified (so-called “kinetic masking”). Ideally, room temperature should be the optimum, but it is necessary to investigate the effect of changing the temperature because “room” temperature may vary from a few degrees in winter in Scotland to 30” or more in summer in India. High temperatures are undesirable because they may cause unfavourable effects such as decrease in stability of reactants, thermal decomposition, reaction with solvent, increasing probability of side-reactions occurring. If higher temperatures are unavoidable, a “safe” range must be found in which these undesirable effects do not occur. Catalysis

Catalysts are sometimes added to change the reaction velocity or the mechanism of reaction, especially in redox systems. Catalysts are associated with particular reactions, and there is no general theory for prediction of which catalyst will prove convenient. Catalysts are usually found by trial and error, with the initial choice based on experience. Sometimes autocatalysis occurs, in which a reaction product itself catalyses the reaction. Induced reactions are sometimes used, but as pointed out above, unwanted ones can be a source of error.

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A. BERKA, J. SEVE~Kand R. A. CHALMERS

Stability of reagents It sometimes happens that though a titrant may be stable in aqueous solution when it is being stored, it may become less stable under the conditions used for the titration, especially if these are particularly drastic in terms of acidity or alkalinity. The effect is most likely to be observed in an indirect procedure, in which an excess of reagent must be added and the mixture left for some time for the reaction to reach completion, followed by back-titration of the excess. In such cases it is necessary to check the stability of the reagent by running a number of blank determinations with different amounts of reagent present. Indicator solutions may not be stable on storage, especially in the case of complexometric indicators. Xylenol Orange, for example, oxidizes slowly in aqueous solution, and the oxidation product will give a coloured complex only with copper(I1). The storage life of all reagents should be checked and appropriate recommendations made for their preparation. End-point sharpness The accuracy of a titration will be partly determined by the volume of titrant required to traverse the end-point, and on how accurately the end-point can be located within that volume. As discussed in specialist texts and articles,32 the equivalence point may not exactly correspond to the end-point, and a correction may be necessary. The correction may be calculated or empirical. The “sharpness index” or “relative precision”33 may be used as a means of indicating the size of the end-point error. It is essential that some numerical value be given for the sharpness. If indicators are used, the volume of titrant needed to give the complete colour change must be determined and reported, and if possible the colours should be described in terms of the C.I.E. indices.34 Other infruences Electromagnetic radiation, usually in the form of visible or ultraviolet light, can not only affect the stability of the reactants but may also participate in the reaction or accelerate or introduce side-reactions. It is therefore sometimes necessary to perform titrations under special lighting conditions, and in indirect determinations it is often necessary to keep the reaction mixture in the dark during the reaction period before the back-titration. Ultrasonic waves have occasionally been used to affect the course of a reaction. Pressure changes, though often used in technology, are not used in titrations, because of the experimental complications introduced. RESULTS

AND

APPLICATIONS

Once the method has been worked out, it is necessary to validate it by standardization, and by application to standard samples containing the species of interest. The standardization is customarily done by preparing a standard solution of known concentration and titrating equal portions of it. In our opinion this is not a sound practice. First, all measurements are made by volume, and as discussed by Conway,as it is then necessary to calibrate all apparatus used, so that the personal error may be

Development

and publication

of new titrimetric methods

759

assessed. Secondly, once the first titration has been done, the tendency is to add rapidly almost the required volume of titrant to the second sample and only the last few drops are added slowly. The result is a variable drainage error, if a normal gravity-feed burette is used. 3s Furthermore, if fractions of a division are estimated in reading the burette, there is an unconscious urge to make the readings agree as closely as possible. It is much more reliable to make up the standard solution by weight and to take different weight fractions of it. Each titration must then be done more or less individually without reference to the others (unless the operator is unable to resist doing mental arithmetic), and the error in the amount of sample taken will be virtually eliminated. If a sufficiently wide range of sample weights is taken, a plot of “taken” against “found” will reveal any bias in the results, and the existence of any “blank” correction. Repetition of the procedure in the presence of the other elements expected to occur in any applications will reveal the extent of any interference by these species. The concentration ratios used must be realistic.3 Finally, the method must be applied to standard samples of the materials for which it is suitable, and the results compared statistically with those obtained by the best previously existing methods. It is essential to have enough replicate determinations to make the statistics meaningful, and the Snedecor F-test or “Student’s” i should be applied as a criterion of significant improvement.36 PUBLICATION

OF RESULTS

If the work has been successful, then in the preparation of a paper for publication it is necessary to report on all the features dealt with above. In particular, attention must be paid to the following points. 1. Stability of reagents, and special precautions to be taken in their preparation and storage. 2. Standardization of reagents and calibration of apparatus, with details given of the errors actually obtained. 3. Proof of the stoichiometry, and establishment of the tolerance ranges3’ for concentrations of reactants, interferents, and other species necessarily present. 4. The speed of the reaction, especially with regard to end-point detection and to the standing time in the case of indirect determinations. 5. The nature of the end-point detection, with specification of sharpness of any colour changes, details of indicator corrections or other end-point corrections. In cases of “dead-stop” methods etc, the response time of the indicating system should be expressed in terms of amount of titrant added, if the titrant is being added automatically or generated electrolytically. In coulometric work the current efficiency must be determined, and the timing error should be established and reported. 6. In description of the procedure, all tolerances on amounts of reagents should be clearly stated, and any special precautions stated.37 7. There must be adequate validation of results, supported by statistical analysis. 8. Applications of the method must be proposed and at least some of them validated experimentally. There must be a proper comparison with existing methods. 9. If possible, the method should be tested by someone who has not used it before, and those results quoted as well.

760

A. BERKA, J. .%&Ix and R. A. CHALMERS R&ume-On a Btabli les conditions necessaires pour le developpement de mtthodes titrimktriques et pour la redaction du travail pour publication. On discute des principes gen6raux de divers types de reaction de titrage, et l’on p&e particulierement attention aux parametres qui influent sur les reactions chimiques. Zusanunenfassaag-Die Anforderungen an die Ausarbeitung titrimetrischer Methoden und an zu publizierende Manuskripte mit solchen Themen werden aufgeftihrt. Die allgemeinen Grundlagen fur verschiedene Typen von Titrationsreaktionen werden eriirtert und dabei besonderes Gewicht auf die Parameter gelegt, die chemische Reaktionen beeinflussen. REFERENCES

Beckurts, Massanalyse, Vieweg Verlag, Braunschweig, 1913. F. Kirkbriaht. Talanta. 1966. 13. 1. Erdey, L. solos and R.-A. Chalmers, ibid., 1970, 17, 1143. E. F. Lundell, Znd. Eng. Chem., Anal. Ed., 1933,5,221. Penny, Chem. Gaz., 1850,8,330. F. Margueritte, Compt. Rend., 1846, 22, 587. e.g., K. Sriraman, Talanta, 1971, 18,361. 8. R. A. Chalmers. Awects of Analvtical Chemistrv. Oliver and Bovd. Edinbureh. 1968. 9. A. Ringbom, Comp?exation in Analytical Chemt%ry, Interscien&, New York: 1964. 10. I. M. Kolthoff, Z. Anal. Chem., 1927,70,395 (see also K. Fajans and 0. Hassel, Z. Electrochem., 1923,29,495). 11. R. Belcher, A. M. G. Macdonald and E. Parry, Anal. Chim. Acta, 1957, 16, 524. J. Block and 0. B. Waters, Talanta, 1967, 14, 1130. :I E. Wanninen, ibid., 1968, 15, 717. C. R. Murty and G. G. Rao, ibid., 1972, 19,45. ::: R. A. Chalmers and C. C. Miller, Analyst, 1952, 77,2. 16. F. Haber and J. Weiss, Naturwissen., 1932, 20,948; Proc. Roy. Sot., 1934, A147, 332. 17. R. A. Chalmers, D. E. Edmond and W. Moser, Anal. Chim. Acta, 1966, 35,404. 18. E. Lenssen and J. Liiwenthal, J. Prakt. Chem., 1862,87, 193. 19. A. Ringbom, op. cit., p. 93. 20. W. Huber, Titrations in Non-Aqueous Solvents, Academic Press, New York, 1967. 21. I. Kucharsky and L. Safaffk, Titrations in Non-Aqueous Solvents, Elsevier, London, 1965. 22. I. Gyenes, Titration in Non-Aqueous Media, Iliffe, London, 1967. 23. J. B. Headridge, Photometric Titrations, 2nd Ed., Pergamon. Oxford, 1961. 24. J. M. H. For&in, P. Karsten and H. L. Kies, Anal. chim. Acta, 1954,10,356. 25. H. Flaschka and S. Khalafalla. Z. Anal. Chem.. 1957. 156.401. 10. 26. G. L. Boorman and W. B. Holbrook, Anal. Chem., 1959,k, 27. H. M. N. H. Irving and W. R. Tomlinson, Talanta, 1968,15,1267. 28. H. Flaschka, J. Butcher and R. Speights, ibid., 1961, 8,400. 29. J. C. Jungers, Cinetique chimique appli uee, SocietC des Editions Technic, Paris, 1958. 30. R. BrdiEka, Grundlagen derphysikalisc a en Chemie, Deutscher Verlag der Wissenschaften, Berlin, 1963. 31. A. Ringbom, op. cit., p. 24. 32. e.g., H. A. Laitinen, Chemical Analysis, McGraw-Hill, New York, 1960. E. Bishop, in Comprehensive AnaIyticaZ Chemistry, Vol. IB (eds. C. L. Wilson and D. W. Wilson), Elsevier, Amsterdam, 1960. 33. A. A. Benedetti-Pichler, Essentials of Quantitative Analysis, Ronald Press, New York, 1956. e.g., S. Kotrlg and K. Vytias, TaZanta, 1971, 18,253. ::: E. J. Conway, Micro-Dtjusion Analysis and Volumetric Error, Crosby Lockwood, London, 1947. 36. K. Eckschlager, Errors, Measurements and Results in Chemical Analysis, pp. 111 and 118. Van Nostrand Reinhold, London, 1969. 37. A. L. Wilson, Talanta, 1970, 17,21, 31. 1. 2. 3. 4. 5. 6. 7.

H. G. L. G. F.