GB2036977A

GB2036977A - Unselective electrode for determination of ionic concentrations in solution

Info

Publication number: GB2036977A
Application number: GB7937437A
Authority: GB
Original assignee: INST CERCETARI CHIM
Current assignee: INST CERCETARI CHIM
Priority date: 1978-10-27
Filing date: 1979-10-29
Publication date: 1980-07-02
Also published as: FR2439994A1; DE2943382A1; RO71465B1; RO71465A2

Abstract

The invention provides an electrode for use in determining the total concentration of tree ions in a test solution, the electrode having the property that the variation of its electrode potential with the logarithm of the sum of the free ion concentration-mobility products of electrolyte solution in electro- chemical contact therewith is linear with an intercept and slope which are constant for a given temperature and pressure, and the electrode being unselective and not distinguishing between different free ions. The electrode comprises a reference electrode R, preferably Hg/Hg2Cl2/Cl<-> or Ag/AgCl/Cl<->, in contact with a special solution 4 which in turn contacts the test solution, both contacts preferably being via liquid junctions 3,5. The special solution 4 is a solution of at least one strong electrolyte having a pH close to neutral and with mobility or weighted mean mobility of its cation(s) significantly different from that of its anion(s). One such electrode and another such electrode or a reference electrode form a cell whose constants are obtainable experimentally and from whose measured p.d. the sum of the concentration-mobility products of the free ions of the test solution is obtainable. From this sum the free ion concentration in the test solution is calculated or approximated. Measurement of test solution pH allows adjustment to be made for the presence of H<+> and OH<->. <IMAGE>

Description

SPECIFICATION Determination of ionic concentrations in solution This invention relates to an electrode, method and device for obtaining the sum of the concentrations of all the free ions existing in a solution by determining the sum of the concentrationmobility products of these ions from potentiometric measurements.As the values of ionic mobilities in non-aqueous solutions are less well known, the present invention is discussed mainly in terms of aqueous solutions in which H+ and OH- ions are always present; the mobilities of these ions are known (349.7 and 197.6 Q~cm2Eq~ respectively, at 250C and infinite dilution) and their concentrations can be easily determined by simple measurement of the pH, and by the sum S of the concentrations (in equivalents per liter = Eq/l) of all the free cations (or anions) in the solution is meant the sum of the concentrations of all free cations except H+ (or the sum of the concentrations of all the free anions except OH-)::

S=-ci =ci =ci ions + H+, OH anions + CH cations + H+ Nonetheless, the present invention also applies to non-aqueous solutions.

The determination of the total electrolyte concentration existing in a solution in the form of free ions represents one of the most difficult problems for analytical laboratories and in chemical industry.

Thus, the testing of the ionic purity of reactants (especially of substances that do not dissociate electrolytically), drugs (especially injectable solutions) and other intermediate and end products of the chemical and chemical-pharmaceutical industries; the controlling of deionized water (used in many industries and in laboratories); the analysis of industrial, residual, drinking and mineral waters, or of natural products (such as naphta) from the point of view of the total ionic content; the controlling of ion exchange column depletion and of other devices for water demineralization; and the analysis of the ionic content of biological liquids (serum, urine, cerebrosphinal fluid, etc.) are but a few examples of the numerous fields in which this determination is currently performed.

The conductometric method is known and used to estimate the sum of the free ion concentration in a solution; it is based on the fact that the specific conductivity of a solution is directly proportional to the sum of the products of the concentration and mobility of each ionic species existing in the solution fc1u1. cju*. A disadvantage of this method is that the estimation of the sum of the free ion concentrations can be done only approximately, especially in the case of solutions of unknown composition, because generally one takes into account neither the values of the ionic mobilities (and their variation as a function of the ionic species and of the ionic strength of the solution), nor the solution pH.A further disadvantage is that in the range of small concentrations (S < 1 0-3 Eq/l), which are the most interesting, the conductometric method becomes less and less precise since the specific conductivity of the solutions decrease with dilution, the signal being about 1,uS (this value represents the lower measuring limit of most conductometers) for solutions with a total ionic concentration of about 10-6 Eq/l.

Moreover, conductometric measurements require frequent replatination of the electrodes and the redetermination of the cell constant along with repeated washing which sometimes is quite difficult and has unwished consequences.

Also known are the cryoscopic and the ebullioscopic methods. One of their disadvantages arises from the fact that the measured item (variation of the freezing point and of the boiling point respectively) decreases with the lowering of the ionic concentration in solution; another disadvantage lies in that the respective temperature variations are directly proportional to the sum of the concentrations of all the species present in the solution, whether they are ions or electrically uncharged species (i.e. molecules). Moreover, measurement is even less precise than in conductometry, and conversion into concentration values is subject to at least the same errors and approximations as those occurring in the conductometric method.

It is known that the electrode potential of existing electrodes, including that of ion-selective electrodes (e.g. the pH electrode), depends linearly on the logarithm of the concentration (activity) of one or several of the ions present; the dependence factor usually changes greatly with the nature of the ion(s) thus giving selectivity to these electrodes, which multidependence represents a cause of unwished interference. When the total ionic concentration is to be determined, the selective or quasiselective response of such electrodes is a disadvantage. No electrode with identical response to the same ionic concentration or to the same c,u; product (irrespective of the ionic species nature) is known so far.

A composite electrode according to the present invention (with an electrode potential Gs) overcomes the above-mentioned disadvantage by providing "total unselectivity". The potential difference g of the electrochemical chain electrode || test solution (S) (I) gS ED made of this electrode and the solution to be analysed (test solution) with which it comes into contact by means of a liquid junction (represented by|| ), depends on the concentrations and the mobilities of all ionic species in the test solution and the diffusion potential #D of the liquid junction:: 9 = g9 + ED (Il) The electrode of the present invention, termed herein a C-electrode and made of a reference electrode immersed in a special solution, has-under given temperature and pressure conditions-an electrode potential g5 which does not depend on the composition of the test solution and which remains practically constant during the measurements.This is because the components of the electrode potential g5, more exactly the electrode potential g, of the reference electrode and the diffusion pote'ntial EDR which appears at the junction of this reference electrode with the special solution, do not depend on the test solution composition and are constant during the measurements if the temperature and pressure are constant.

The reference electrode is an electrode with an electrode potential g, stable at a given temperature and pressure and practically independent of the solution with which the electrode is put into contact, for instance a second species electrode of the calomel or chlorinated silver electrode type.

The special solution is preferably a strong electrolyte solution (or a mixture of strang electrolytes), having a concentration c and the following characteristics: its pH does not differ greatly from neutral e.g. the pH of distilled water with CO2 dissolved-i.e.

about 5.7); its concentration c is much higher (e.g. 10-' Eq/l) than the total conic concentration of the test solution; the concentration c is much higher than the concentrations of H+, OH C2 and HCQ ions (existing in any aqueous solution in contact with the air), so that these concentrations are negligible in comparison with c; and the values of the anion (u~) and cation (u+) mobilities (the weighted mean mobilities of the anions and cations in the case of electrolyte mixtures) differ considerably one from another.

In all cases the ionic mobilities are expressed in #-1cmȆq-1 and the concentrations in Eq/l; c and S represent the sum of the cation concentrations with and without which is equal to the sum of the anion concentrations with and without, the total free ion concentration and that without the concentrations of (H+) and (OH-) being 2c and 2S respectively.

Knowing these details regarding the structure of the C-electrode, the electrochemical chain (I) (obtained by the immersion of the C-electrode in the test solution) and its potential difference (p.d.) (II) can be written C-electrode reference electrode || special solution (c) test solution(S) 9R EDR g5 ED (I ) g = g, + ED = 9R + EDR + ED (II') Expressing the diffusion potential ED (e.g. by the Henderson formula) and making approximations allowed by the conditions imposed on the special solution, a new equation is obtained: :

which depends only on the concentrations and mobilities of all the free ionic species in the test solution (anions and cations), a and b being parameters which do not depend on the nature and concentrations of the test solution, thus being constant for a given C-electrode: a =b log cb log (u+ + u~) (ine)

where+, u~ and z+, zl represent the mobilities and the algebraic valences of the anion and cation of the special solution, and 2.303 RT/F represents the Nernstfactor (59.1 6 mV at T = 2980 K). Introducing the expression a given by equation (III') in equation (III) and rearranging the terms, the expression for the diffusion potential ED becomes::

which means that its absolute value is directly proportional to the value of the cViciu ratio, i.e. it is higher the smaller is S in comparison with the chosen concentration c. Thus, the potential difference g of the electrochemical chain (I) depends linearly on log #/iciui:

i.e. the C-electrode has a Nernstian response of slope b with respect to the sum of the concentrationmobility products (,u,) of the free ions in solution and it does not selectively differentiate between the various ions.

In the present invention the method of determining the sum of the concentration-mobility products, #iciui, of all the free ions existing in a solution is theoretically expressed by the equations (II') and (III) and is based on the use of the above mentioned C-electrode to make up a concentration cell with transport of the type C-electrode I || test solution(S) || electrode II

in which the C-electrode immersed in the test solution makes up the first half-cell, while the electrode (II) of electrode potential g11, immersed in the same test solution, makes up the second half-cell.In the preferred embodiment of this method, the electrode (II) is a C-electrode too, but the composition of its special solution differs from that of the first C-electrode, and this has several advantages that will be mentioned below. The p.d. of the cell (IV) which can be expressed as follows: U = gI - gII = gSI - gII + #DI = (V) = gRI + #DRI - gII + aI + bIlog #iciui = const + B log #iciui depends lineary on log #iciui too.The values of the parameters a' = gRI + #DRI + aI and bI depend only on the C-electrode used (and not on the test solution); supposing that the value of the p.d. gII of the second half-cell is known, then by measuring the p.d. U of the cell (IV) one can immediately determine #iciui, the sum of the concentration-mobility products of all the free ions of the test solution.

To make the expression general, in the p.d. g11 of the half-cell on the right hand side there is included the diffusion potential EDli corresponding to the junction between the electrode Il and the test solution, which can be practically zero, or can have a different value if the electrode II is a C-electrode too, when the two values a" and b" corresponding to this potential EDIl are different from zero; consequently in the final expression of U all the other terms are included in the constant, while the resultant slope B is equal to b, if and only if EQl = 0.

In fact, the values of the parameters a' and b depend not only on the characteristics of the special solution and of the reference electrode which is part of the C-electrode, but also on the way in which the liquid junctions of cell (IV) are realized. Thus, the values of the intercept and of the slope in equation (V) must be experimentally determined for a given concentration cell and a given experimental device at the given working temperature and pressure. This can be done by plotting the calibration line U vs log ,c,u, for test solutions of known compositions (e.g.NaCI solutions with known pH and concentrations S1, S2,..., for which

the mobilities uNa, uCl, uH and uOH being known and in a concentration range chosen in such a way that the condition (1/2)#ici # c is permanently fulfilled, all the experimental determinations being done at the chosen working temperature and pressure. The intercept and the slope B of the experimental straight line have the dimensions of a p.d.Evidently, the calibration line, once obtained, may be used to determine the ,zc,u, value corresponding to any test solution which is analyzed with that experimental device at the given working temperature and pressure, and for which the condition (1/2) c c is always fulfilled (this can be seen experimentally from the fact that the measured value of U must lie within the range of values of the calibration straight line).

The method of this invention can be used-just like the conductometric method-to determine the value #iciui, but in addition it avoids the above mentioned disadvantages of the conductometric method due to the fact that the measured property-the p.d.U of the cell (IV)-increases in absolute value with dilution of the test solution (see relation (III"'), thus providing high accuracy of measurement in the range of small concentrations (the p.d. being hundreds of mV for values of (1/2) #ici of the 10-6Eq/l order of magnitude, if c is of the 10-1Eq/l order of magnitude); the experimental determination is simple and rapid and does not require supplementary operations (platination of electrodes, etc.) because it consists of an immersion of the two electrodes in the test solution and a simple potentiometric measurement related to the calibration straight line, U vs log fc,ui.

The apparatus required for the present invention is simple, consisting of the concentration cell with transport (IV), maintained at the working temperature by means of a thermostat and of a mV-pHmeter with very high input impedance (e.g. > 1 210128). When making up the cell (IV) care must be taken that the liquid junctions provide as free as possible ion diffusion and do not allow rapid mixing of the solutions. Under these conditions, the time stability of the diffusion potentials is assured during the measurements.

The expressions (III) of the diffusion potential ED corresponding to the junction between the Celectrode and the test solution were obtained on the basis of a few approximations resulting from the conditions imposed on the special solution concerning its pH and its concentration c as compared to the concentration (1/2)#ici, of the test solution. Thus, in the summ #iciui, experimentally determined as mentioned above, the products cHuH and cOHuOH are also included.Since we are generally interested in the value of the total concentration S of the free cations (anions) from the test solution excepting those of water, we shall define the following quantity:

T= 1c1u1- cHuH-c0u0H = clul ions &num; H+, oH- (Vl) Its value can be immediately calculated from the experimentally found value 'cIi after a simple determination of the test solution pH. So, the diffusion potential value ED, and thus the variation of the p.d.U with the test solution composition, will result mainly from the contribution of the ions other than H+ and OH- present in the test solution, if S # cH,cOH (when # # # #iciui, experimentally determined), or, on the contrary, will be due to the H+ and OH- ions if the concentration of one of these is higher or equal to the total concentration S (when one can disregard the total contribution of the other ions as compared with that of cHuH or cOHuOH, a fact that limits-in aqueous solutions-the possibility of determining a total concentration S value smaller than 1 0-8Eq/l). In the intermediate cases, one has to consider the contributions of all the ions existing in the solution to the value Fcjui experimentally determined.

In this invention the method for obtaining the value of the sum S from the value T calculated as mentioned above, is based on the relation:

T= c1u1=2 St' S (u+ ±uJ (Vl') ions *H+, (iH whereu,u+ and u represent the weighted mean mobilities of all ions, of all cations and of all anions respectively, excepting those of H+ and OH-, the conc. corresponding to the mobility u1 being given by the ratio between the concentration of the species land the total concentration of all cations (without H+) and/or anions (without OH-), i.e., c/2S, c+,/S or c~ /S, so that the following relations are valid: :

T ciuj =+ ions+H+,CH- tr++F 2S = S 2 c+,u+, c,u, cations + H- anions + CH (VII) i = (VII) S S Indeed, using the relations (Vl) to write the concentration cell (IV), one gets:: U = const + B log (2 uS + cH uH + cOHuOH) = = const + B log [S(u+ + u) + cHuH + cOHuOH] (V') The value of S (the total concentration of the free cations or anions in the test solution, without that of the H+ or OH- ions respectively) may be obtained by measuring this p.d. if the weighted mean mobility is known or can be estimated (i.e., the sum of the weighted mean mobilities of the cations and anions, u+ + u~), the other factors that are included in this expression having values which can be calculated and/or experimentally determined as we have already mentioned. The following situations are set forth as illustrative of the way of obtaining the value S.

In the case of solutions containing only one electrolyte of a known nature, e.g. NaBr, z+ + U = uNa + UB, (the values for uNa and us, can be found in the tables), the value S can be easily calculated with the help of relation (VI') S = T/(UNa + uBr) from the value T calculated by the relation (VI), using the experimental values of pH and of fciu determined from the measured value U related to the calibration straight line of the experimental device for the given conditions.The result thus obtained has the precision of direct potentiometric determinations to the extent to which the real values of the mobilities of these ions in the liquid junctions of the given experimental device correspond to those in the tables. For this reason, the value of the sum S can be more correctly determined from the value Fciu obtained as we have mentioned above, with the help of one more calibration curve #iciui = S (uNa + uBr) + cHuH + cOHuOH, experimentally plotted for solutions having the same pH as the test solution but with different concentrations S of that electrolyte, taking care that for each solution the condition (1/2)fc c c remains valid.This second calibration curve is also a straight line in the range of concentrations of interest for the method (S < 1 0-3Eq/l) because in this concentration range the ionic mobilities become practically constant (they do not depend on the ionic strength of the solution, i.e. on the electrolyte concentration). This method of determination provides more accurate values for S because it implicitly uses for the individual mobilities uNa and uBr the real values (not table ones) within the liquid junctions of the given experimental device, and this is more important for the case in which S > 10-3Eq/l, when the calibration curve begins to deviate from a straight line because the ionic mobilities begin to depend on the concentration.Evidently, the calibration straight line U function of log cju; and the second calibration curve can be drawn on a single functional diagram if on the logarithmic axis one writes near the values ivcju; the corresponding values of S obtained from the second calibration curve.

To determine the value of the sum S one can also use the standard addition method, determining and T + AT for the test solution of concentration S and for the solution resulting after the known AS addition. If the concentrations S and S + AS are smaller than 10-3Eq/l, the sum of the mobilities uNa + uBr in the two solutions has practically the same value so that T + AT S + AS T S and consequently:: S AS AT (cell) In the case of solutions containing a mixture of two or more electrolytes of a known nature and in known proportions one can calculate the weighted mean mobility u because the weights ci/2S are known and the values of the mobilities ui may be taken from tables, so that S = #/2u. As in the above discussed case, better results can be achieved by using the method of the two calibration curves U vs log zciu and cjUi vs S, or its further development, i.e., the method which uses only one calibration graph U function of S, obtained by condensing the two above mentioned calibration curves; of course the different values S correspond to different mixtures of the respective electrolytes but with the same proportions between the electrolytes, in order to maintain the ratio c/2S unchanged. One can use in this case too, the method of standard addition of the same mixture of electrolytes in the same proportions when the relation S = TAS/liT remains valid.

If in these cases the sum S of the total cationic (anionic) concentration (without the water ions) can be determined with the precision of direct potentiometric methods, in the case of an unknown solution it can be only approximated, because the component ions of the solution are unknown and so are their mobilities; or even if the qualitative composition of the solution is known, the ratios ci/2S of the respective ions are unknown.Fortunately, the weighted mean mobility can still be estimated quite precisely, thus making possible a good approximation of the value S, because-with the exception of the ions H+ and OH--the mobilities of most ions (especially inorganic) are very close to one another being generally in the range of 4o-8o #-1cmȆq-1 at T = 25 C and high dilutions (1/2#ici < 10-3Eq/l).

Thus, in this case too, the method of obtaining the value S involves the determination of test solution pH in order to eliminate the contribution of the H+ and OH- ions from the value Fc,u, (experimentally obtained as already mentioned), and calculating in this way the value T. Further, the value of the sum S can be well approximated by estimating the value of the weighted mean mobility. Indeed, u lies somewhere within the interval Urn < U < UM, where Urn and UM represent the lowest and the highest mobilities respectively, of the ionic species (except for H+ and OH-) existing in the test solution.

From the relation (Vi') results: # > 2S > # (IX) um um The method of the present invention chooses as estimated value 2Se for the sum 2S of the concentrations of all the ions existing in the solution, except for the ions H+ and OH-, the following value::

corresponding to which the real value S is placed in the interval Se(1 - es) < S < Se(1 + es) (X') where es represents the maximum error that can occur when the real sum S is approximated by this procedure and which has the expression UM m Urn (X) j= UM+Urn Thus, in the case of a test solution containing ions with the extreme values of mobility i.e., 80 and 40 Q~'cm2Eq-', es would have the value 80 - 40 es = = 0.33 80 - 40 i.e. the application of the relation (X) leads to a value Se = z/1 o7 that approximates the sum S of the concentrations of all the cations (except for tkat of the H+ ions), or the sum of the concentrations of all the anions (excepting the OH- ones) with a maximum error of i33%, an error that is reached only if all the prevailing concentrations correspond to ions that all have mobilities either of about 80 or of about 40 #-1cmȆq-1. Of course, such a composition of the test solution is rarely encountered in practice, so that usually the error made by estimating the value S by Se becomes acceptable, i.e., 10-15%, which is close to the current errors in direct potentiometry.Therefore, knowing the qualitative composition of the test solution-as we have supposed and as is generally the cases and taking the values Urn and UM from the tables for the selected working temperature (250C), the maximum possible error can be immediately calculated by the relation (X"), so that one can establish the maximum interval within which the total concentration S#[Se(1#es)] can be found. Evidently, the error is smaller when the values Um and uM belong to a more restricted interval.Thus, for a test solution containing ions with mobilities between 50 and 60 Q~'cm2Eq~', the maximum possible error is of + 17% and can be reached only when the values of the mobilities of all the ions whose concentrations prevail are either 50 or 70, #-1cmȆq-l; of course in this case the real value of S is situated within the interval Se(1 # 0.17). But in most cases, the real error is much smaller than es; it is smallest when the test solution contains ions that have practically the same mobility and when the concentrations of these ions are the only ones significantly different from zero.In the case of qualitatively unknown solutions um and a must be taken as the extreme values from the tables, so that at 250C and concentrations below 1 0-3Eq/l, the sum of the cation (anion) concentrations may be approximated by: Sess/100 (Xl) the real value of S being situated inthe interval Se (1 + 0.33).

The method of this invention avoids the disadvantages of the mentioned conductometric, cryoscopic and ebullioscopic methods, because it permits estimation of the value of the total concentration S of all free cations or anions (excepting H+ and OH-) from the test solution, in the range of high dilution (10-6 - 10-3Eq/l) by means of two direct potentiometric measurements: the first one for the determination of the value #iciui from the experimental value U of the concentration cell with transport (IV); the second to determine the value cHuH + cOWuOW from the measured value of the test solution pH; from these two experimentally determined values, one can get

T = z CjUi, ions + H+,OH and further one can determine, (by calculus, from the calibration curves, or by standard addition) the value S as precisely as in the case of any direct potentiometric method, for solutions containing a single known electrolyte or more known electrolytes in known proportions; and one can approximate (using eqs.(X)) the value of S with a precision close to that of direct potentiometry in the case of solutions with unknown composition (qualitatively known or completely unknown).

The invention is illustrated in the following Examples taken in conjunction with the accompanying drawings in which: Figs. 1, 2, 3 and 4 represent four respective C-electrodes (ES), according to the invention, that of Fig. 3 being preferred; and Figs. 5, 6 and 7 illustrate three respective concentration cells according to the invention, Fig. 7 being preferred.

EXAMPLE 1 The C-electrode (ES) in fig. 1 consists of a reference electrode (R) of the second species M/MX/Xn- electrode type, immersed in a special solution (4) that fulfils the conditions mentioned earlier and is contained in an L-shaped vessel that has at its lower end a closure capable of making a liquid junction (5), situated at the end of a ground joint (8). The electrode potential gR of the reference electrode (R) depends on the nature of the metal M and of MX (1), as well as on the concentration, of the common anion xn- of the solution (2), but for a given electrode and for given temperature and pressure, this potential is constant if the composition of the solution (2) does not change.The reference electrode (R) is put into electrochemical contact with the special solution (4) through a liquid junction (3), having a diffusion potential EDR. The liquid junctions (3) and (5) can be achieved by means of glass or ceramic frits, a free capillary tube or a capillary tube filled with porous material (e.g. asbestos fibre), an agar stopper impregnated with a solution of electrolyte, a solution film limited by ground joints, etc. The external electrical contact of the C-electrode (ES) is represented by a wire (6) that constitutes the electrical contact of the reference electrode (R). The electrode potential g5 of the C-electrode (ES) is g5 = g, + EDR and is constant in the case of a given C-electrode and given temperature and pressure.But when it comes into contact with the test solution through the liquid junction (5), the p.d. g that appears will depend only on the concentrations and mobilities of the ions from the test solution according to eqs.

(Il-Il''').

The above comments in fact apply to all of Figs. 1 to 4, in which like reference numerals denote like items. In Fig. 3, which represents a preferred C-electrode (ES), and in Fig. 4, (7) is a filling hole for the C-electrode through which it is filled with the special solution (4).

In the case of the C-electrode presented in Fig. 1 the reference electrode (R)-a calomel (1) electrode with a solution (2) of KCI (0.1 Eq/))is immersed in a solution (4) of LiCl having a concentration c = 0.1 Eq/l, the junction (3) between the two solutions being made of a capillary tube filled with asbestos fibre, and the junction (5) from the end of the exterior compartment of the Celectrode being of the glass frit type welded on the end of the ground joint (8). Thus this electrode can be written in the following form: Hg/Hg2CIz/KCi (0.1 )//LiCl (0.1) gR + EDR = EXAMPLE 2 This is a C-electrode as shown in Fig. 2.It is made of a reference saturated calomel (1), (2) electrode (R) immersed in a solution (4) of KCH3COO (0.1 Eq/l), the junctions (3) and (5) being solution films which moisten the respective ground glass stoppers; it can be expressed as follows: Hg/Hg2ClKCl(satWKCH3C00(0. 1 ) 9R + EDR = QS EXAMPLE 3 The C-electrode of Fig. 3 is easily obtained from a commercially available double junction reference electrode, the only operation needed being the filling of the exterior compartment with the special solution (4), through the filling hole (7). For this reason this is the preferred C-electrode. In our example, the reference electrode (R) is an Ag/AgCI electrode ( 1 ) immersed in a saturated solution (2) of KCI, put into contact with the special solution (4) of LiCI (0.1 Eq/l) through the junction (3) of porous ceramic. The terminal junction (5) is a film of the special solution (4) between the ground glass joint surfaces; by pushing the internal compartment, the special solution (4) can be removed from the external compartment, which is normally maintained closed by means of a spring (not presented in Fig. 3).This C-electrode can be written as follows: Ag/AgCl/KCl(sat)//LiCl (0.1) 9R + EDR = QS Evidently, the C-electrode can have other structural forms, and can use some other reference (R) electrodes than those mentioned, other filling solutions (2), other junction types (3) and (5), and any other special solution (4), made of other electrolytes and mixtures of electrolytes with different concentrations, but taking into account the mentioned conditions therefor.

The cells of Figs. 5, 6 and 7 in which like reference numerals denote like items, mainly consist of a central compartment (9) in which is the test solution (S), a glass electrode (H) for pH measurement, a reference electrode (R), and a magnet (M) for stirring the test solution (S), the central compartment (9) being in electrochemical contact via respective liquid junctions with a C-electrode and a second electrode-which can be a C-electrode as in Figs. 5 and 7 where it is marked (ES I) and (ES 11), or a reference electrode (R II) as in Fig. 6. More generally, the electrochemical cell has three compartments filled with solutions, separated one from another by electrochemical junctions. The central compartment (9) contains the test solution (S) and the other mentioned components.As for the side compartments, one at least must be a C-electrode while the second one may be either a C-electrode or a reference electrode. If two C-electrodes are used, it is advantageous that their slopes should have opposite signs.

The whole electrochemical system is maintained at the working temperature selected by means of a thermostating liquid (10) contained in a thermostat bath (T), under which a magnetic stirrer (A) is placed. The cell also has a mV-pH-meter (U), with an input impedance > 1 012Q, for measuring the p.d. of the cell and the pH of the test solution respectively. Irrespective of whether the cell has two C electrodes, (Figs. 5 and 7), or a single C-electrode and a reference electrode (Fig. 6), two reference electrodes (R I) and (R II) are necessary for measuring the p.d. U of the cell.To measure the pH of the test solution, when two C-electrodes (ES I) and (ES II) are used as in Figs. 5 and 7, a third reference electrode (R') is necessary, while when only one C-electrode is used as in Fig. 6, the reference electrode (R II) may also serve for pH measurements. Using identical reference electrodes, the difference between their electrode potentials g,, - g,,, is zero or negligible, even if the two reference electrodes have some dissymmetries between them, a fact that has to be experimentally tested when selecting the reference electrodes.

The component parts of the C-electrodes in Figs. 5 to 7 have the same references as in Figs. 1-4 but with addition of "I" or "II" to show whether they belong to the first or to the second electrode of the cell. This can be written for the Figs. 5 and 7 as follows: ES l//test solution (S)//ES II 951 + ED = 91; g11 = DII + gSII (lV') that can be developed to obtain: Rl//special solution l(c)//test solution(S)//special solution lI(c)//RII

having a p.d. of the form::

(the difference g,, -- g,,, is zero, because RI and RI are supposed to be identical) while for the case of Fig. 6 one gets: Rl//special solution I (c)//test solution (S)//RII

with a p.d. in the form:

which also depends linearly on the logarithm of the sum of the concentration-mobility products of all the free ions in the test solution, but with a slope given only by the single C-electrode (ESI).

The diffusion potentials from the interior of the C-electrodes, DR, and DR"equations (V") (V"')-have by definition very small values, when the solutions (2) are e.g. of KCI with UKNUCI so that the difference EDRXI remains small enough(in the range of 0.2 mV) to be neglected-especially if the concentrations of the special solutions (4 1) and (411) are equal (cl = c" = c) and the concentration of the solution (2) of KCI is much higher than c (a saturated solution of KCI has 4.2 Eq/l compared to c = 0.1 Eq/l) as in the preferred cell which has two C-electrodes as in the example illustrated in Fig. 7.However, if desired, these potentials can be approximated by calculus (for instance using the Henderson formula) because the solutions (2) and (4) have known compositions.

The slopes bI, bII and the intercepts aI, aII as well as their differences bI - bII and aI - aII can be calculated by using the eqs. (III') and (III"), but they also depend on the particular form of the liquid junctions of the cell (VI) so that their experimental determination is necessary (once only, for given temperature and pressure and a given cell), as mentioned above, by plotting U vs log #ixiui for different test solutions (S1, S2,...) with known compositions.At the same time, one determines in fact as intercept #DRI - #DRII + aI - aII, i.e., the difference #DRI - #DRIl (negligible) is taken into consideration too, in all the subsequent determinations, so that the relation (V) written in its most general form

is perfectly valid; the slope B could be due either to both C-electrodes in the form b1 - b11, as in the relation (V") and in the examples of Figs. 5 and 7, or to just one C-electrode, as in the relation (V"') valid for the cell from Fig. 6.

The sensitivity accuracy and reproducibility of the method of this invention are improved the greater the slope B. When using only one C-electrode, as in Fig. 6, the slope B is given by the slope of this electrode itself and thus according to eq. (Ill") it increases when (u+/z+) - (uJlzI) increases, i.e.

when the mobilities of the cation and anion of the special solution (4) are more different one from another (this is one of the conditions imposed on the special solution). When using two C-lectrodes, as in the examples illustrated in Figs. 5 and 7, the slope B = bI - bII can be increased by appropriate selection of the component electrolytes of the two special solutions (4), so that b1 and b11 should have opposite signs, when the absolute value of the slope B will be higher than the value of each slope taken separately, i.e. the reading will be amplified.That is why the preferred embodiment of the cell has two C-electrodes (ESI) and (ESII) in which the corresponding special solutions (4I) and (4II) have mobilities of the cation and anion which differ greatly with the mobility of the cation of one equal to the mobility of the anion of the other and vice versa, i.e. u+,I = u-,II and u-,I = u+,II so that (u+ + u-)I = (u+ + u-)II = u+ + u-.Under these circumstances, considering the relations (III') and (III"), the slopes bI and bII as well as the values aI and aII are practically equal and have opposite signs so that the overall slope is B = bI - bII # 2 bI # 2 bII and aI - aII # 2 aI # 2 aII respectively, (because in the preferred embodiment of the invention the concentrations of the two special solutions (4) are equal = = c11 = c).For this reason, in the preferred form of cell, the special solutions of the two C-electrodes (Figs. 5 and 7) are: LiCI 0.1 Eq/I in (4.1) and KCH3COO 0.1 Eq/l in (4.11), whose mobilities at c = 0.1 M are presented in the following table

U (1cm2 Eq1) Temperature (u, + CI-II ( C) Li+ Cl K+ GH3COO- ~ - \i+ |z-| 18 25,7 55,8 55,l 26,2 81,5 81,3 -30,1 28,9 25 30,5 64,2 63,5 30,6 94,7 94 33,7 32.9 In the case of a concentration cell with a single C-electrode, as in Fig. 6, the diffusion potential from the half-cell II, corresponding to the junction between the test solution (S) and the reference electrode (R II), can be considered both as a diffusion potential between the reference electrode (R li) and a certain solution (i.e. the test solution), thus denoted by #DRII and # O by definition (because UK # UCI), and as a diffusion potential #DII between the test solution and the electrode ESII reduced now only to the reference electrode (RII) by the fact that the special solution (4 II) is just the KCl solution (2 II) within the reference electrode (RIl). We have denoted this diffusion potential by ED(Rlll. Regarding this potential from the point of view of the second aspect, i.e. corresponding to a C-electrode with special solution (4II) made of KCl (identical with the solution (2 II)) its value is close to zero because according to the eq. (III") its slope is practically zero, bII # o, because uK # uCI, so that the value a", given by the relation (III'), is practically zero too, and therefore #D(R)II # O. This fact suggests the idea-scientifically new-that a reference electrode is a particular case of C-electrode, i.e. a C-electrode with a slope practically equal to zero. (This is a consequence of the fact that one of the conditions imposed on the special solution is not fulfilled, namely the one which states that u+ and u~ should have values significantly differring from each other, a condition whose necessity thus becomes more evident). As a consequence, a "reference" electrode filled with solution (2) of an electrolyte having the mobilities of the component ions u+ and u~ significantly differing loses its reference electrode characteristic (its electrode potential will depend on the solution in which it is immersed), becoming a C-electrode. This means that a C-electrode can be realized (as is illustrated in fig. 4) even from a normal reference electrode with a single compartment, by using as filling solution (2) a solution with an anion xn- common with that of the combination MX, but having the mobility of the cation u+ significantly different from Ux (for instance by using for filling, in the case of an electrode of Ag/AgCI or Hg/Hg2CI2, a solution of LiCI instead of the solution of KCI).Thus the C-electrode represented in fig. 4 can be written in the form: Ag/AgCI/LiCI (0.1) g11=g5 Although such a C-electrode could seem advantageous because of its simple construction and because the diffusion potential EDR from its interior is cut out, its use to determine the sum zciuj brings no additional advantages, especially because its filling solution is more rapidly contaminated with the ions of the test solution.

EXAMPLE 4 The concentration cell illustrated in Fig. 5 consists of two Celectrodes (ESI) and (ESII) of the type shown in Fig. 1, having as special solution (41) an aqueous solution (0.1 Eq/l) of LiCI and as special solution (411) an aqueous solution (0.1 Eq/l) of KCH3COO brought to the pH of the distilled water (5.7) which has been used to prepare the solution by adding HCH3COO in order to compensate for the hydrolysis of this electrolyte, so that c,+ = CCHBCOO-- = 0.1 Eq/l. The C-electrodes are put into contact with the test solution (S) through the glass frits (51) and (511) with porosity G4.The concentration cell thus obtained can be written as follows: Hg/Hg2Cl2/KCl(0.1)//LiCl(0.1)//test solution (S)//KCH3COO(0.1)// KCl(0.1)//Hg2Cl2/Hg Measuring the p.d. of this cell between the wires (6I) and (6II) by means of the apparatus (U), and the pH of the test solution by means of the electrodes (H) and (R'), (the test solution being stirred during the determination of the pH), one can determine from the relations (V) and (VI) the values

respectively, if one has previously determined experimentally the intercept and the slope from the relation (V), by performing the same measurements for (test) solutions with known compositions, as mentioned above.

EXAMPLE 5 In Fig. 6 the concentration cell has only one C-electrode, similar to the one in Fig. 2, the second electrode being a saturated calomel electrode; in this case the central compartment is made of a simple Berzelius glass in which the three electrodes (C-reference and pH) are immersed. The concentration cell thus obtained can be written as follows: Hg/Hg,CldKCl(sat.)//LiCI(O. 1 )//test solution (S)/oKCl(sat)/ Hg2CI2/Hg Evidently, the slope B obtained with this device was about half that obtained in the case of Example 4.

This cell is simpler than that of the previous Example, because reference electrodes such as that of Fig.

6 can be found in commerce.

EXAMPLE 6 A cell as illustrated in Fig. 7, which is the simplest and most elegant and hence the preferred embodiment, is made up by pouring the test solution (S) into a lab glass (9) which is then put in the thermostatic bath; into the test solution are introduced two C-electrodes (ESI) and (ESII) of the type shown in Fig. 3, whose exterior compartments are filled with a solution of LiCI (0.1 Eq/l) and with a solution of KCH3COO (0.1 Eq/l) respectively, thus obtaining the concentration cell Ag/AgCl/KCl(sat)//LiCl(0. 1 )//test sol.(S)//KCH3COO(0. 1 )//KCl(sat)/ AgOVAg whose p.d. is measured with the millivoltmeter U.Into the same glass container are introduced a reference electrode (R') and a glass electrode (H) for measuring the pH of the test solution-subjected during this time to magnetic stirring via (M) and (A). Determining the slope and the intercept of the calibration straight line corresponding to the concentration cell thus obtained, we have all the elements for calculating by the presented methods both

and for further calculating and determining from the calibration curve T function of S or by the method of standard addition, the total concentration (S) of the cations (anions) from the test solution, excepting the H+ and OH ones, in the case of solutions containing only one electrolyte or a mixture of known electrolytes in known proportions, or for approximating the value of S by calculus from the value T by means of eqs. (X).

Evidently, the concentration cell (IV) can be realised in many other ways than those illustrated in the Examples and the Figures which are not of a limitating character, by using other types of Celectrode, containing other reference electrodes, other special solutions and other types of junction (3) and (5), other ways of positioning the constituent elements of the cell and other methods and procedures of calculus, etc.

The present invention thus provides a) an electrode with a Nernstian response to the sum of the concentration-mobility products of all the free ions existing in a test solution in which it is immersed, without selectively differentiating between the various ions; b) a method of determining the sum ecru, for all the free ions of the test solution, irrespective of their nature, based on the simple measuring of a p.d.U; c) a method of determining the sum of the products ,u, -- c,u, -- = T by a simple supplementary measurement of the test solution pH; d) a cell for the application of the above mentioned methods, based on the use of at least one such electrode; e) some calculation or approximation procedures for obtaining the sum of the concentrations of all the cations (without H+) or of all the anions (without OH-) in the concentration range of 10-8 -- 10-3E4/1.

The invention has the following advantages: compared to electrodes with Nernstian response known so far, the electrode according to present invention has the advantage of being entirely unselective, the impossibility of differentiating the various ions being fundamental for the determination of the sum of the concentration-mobility products and of the sum of the concentrations of all the free ions existing in the solution -the method of determining the sum fciu, has the advantage that the measured p.d.U increases in absolute value when the concentration of the test solution decreases, instead of decreasing as in the conductometric method, which permits more accurate and reproducible determinations in the range of small concentrations, which in fact is the range of the highest interest (the lower limit of 1 OEq/l being a consequence of the presence of the water ions).

-the method of obtaining the sum fig, presents--as compared to the cryoscopic and the ebullioscopic methods in which the property measured also decreases with lowering of concentration-the advantage that the measured value is directly proportional only to the sum of the concentration-mobility products corresponding to the free ions of the test solution, i.e. uncharged particles (molecules) do not contribute to the property measured.

compared to the latter methods the experimental measurements involved by the invention can be performed more easily and rapidly with better accuracy, entailing simple immersion of electrodes in the test solution and reading of the p.d. of the cell, without any supplementary operation like replatination of electrodes, redetermination of the conductometric cell constant, etc.

-the determination of the value

involves only one supplementary determination, i.e. of the test solution pH.

-the cell for the application of these methods is easily assembled using standard equipment such as glass container, electrodes, mV-pH-meter, thermostatic bath and sometimes a magnetic stirrer.

-the value of S, determined by the proposed method from the value experimentally obtained is, in the case of solutions consisting of a known electrolyte or of a mixture of known electrolytes in known proportions, as precise as any determination of direct potentiometry. This determination can be done by applying the elaborated calculus formula, by using the calibration curve '1'function of S, or by the method of standard addition.

-the approximation of the value S by the proposed method for the case of solutions with unknown and variable composition, is evidently superior (from the point of view of its precision) compared with that of the mentioned prior methods, because instead of a semiquantitative evaluation of S the method provides an approximation which involves a maximum error of +33%, occurring very seldom and only in the case of solutions of highly improbable composition, the usual errors of approximation being about +10-15%.

compared to the specific analytic methods which are concerned with only one ion or group of ions, the proposed method for obtaining the value of S has the advantage of large savings of time and labour when the determination of the total ionic concentration of a solution is required, because the method determines rapidly and at once all the ions.

-the electrode and the above mentioned method permitting determination of the discontinuity points in the variation of the value fc,u, can replace conductometry in different applications (i.e.

conductometric titration, studies of reaction kinetics, determination of dissociation, association and stability constants, etc.) with the above mentioned advantages.

-the method is not limited in principle to aqueous solutions. To the extent to which the values of ionic mobilities in non-aqueous solutions are known, the method can be used for such solutions too, maybe at even more advanced sensitivity limits, because the H+ and OH- ions are absent.

Claims

1. An electrode for use in determining the total concentration of free ions in a test solution, the electrode having the property that the variation of its electrode potential with the logarithm of the sum of the free ion concentration-mobility products of electrolyte solution in electrochemical contact therewith is linear with an intercept and slope which are constant for a given temperature and pressure, and the electrode being unselective and not distinguishing between different free ions.

2. An electrode according to claim 1 comprising a reference electrode in electrochemical contact via a liquid junction with a special solution, and means for providing a further liquid junction between the said special solution and a test solution.

3. An electrode according to claim 2 wherein the mobility or mean weighted mobility of the cation(s) of the reference electrode solution is close to that of its anion(s).

4. An electrode according to claim 2 or 3 wherein the reference electrode is an electrode of the M/MX/X"- type immersed in a solution having a common anion with MX.

5. An electrode according to claim 4 wherein the reference electrode is an idg/Hg2CI2/CI- or Ag/AgCI/CI- electrode.

6. An electrode according to claim 4 or 5 wherein the solution of the reference electrode is a KCI solution.

7. An electrode according to claim 1 comprising an electrode of the M/MX/Xn- type immersed in a special solution having a common anion with MX, and means for providing a liquid junction between the special solution and a test solution, the mobility or mean weighted mobility of the cation(s) of the special solution differing substantially from that of its anion(s).

8. An Hg/Hg2CI2/Cr or Ag/AgCI/CI~ electrode according to claim 7.

9. An electrode according to any of claims 2 to 8 wherein the or each liquid junction provides free diffusion usion of the ions whilst preventing rapid mixing of the solutions separated thereby.

10. An electrode according to claim 9 wherein the or each liquid junction is provided by means selected independently from porous materials, complementary surfaces allowing for a film of solution therebetween, an ion-permeable gel, empty capillary tubes, and capillary tubes containing porous material.

11. An electrode according to any of claims 2 to 10 wherein the special solution is a solution of at least one strong electrolyte having a pH close to neutral and having the mobility or weighted mean mobility of its cation(s) significantly different from that of its anion(s).

12. An electrode according to claim 10 wherein the special solution has a pH of about 5.7.

1 3. An electrode according to claim 11 or 12 wherein the special solution is an aqueous solution of LiCI or KCHsCGO.

14. An electrode according to any of claims 2 to 1 3 wherein the concentration of electrolyte in the special solution is about 0.1 Eq/l.

15. An electrode according to any of claims 1 to 14 having means for emptying and filling the compartment containing the special solution.

1 6. An electrode according to claim 1 substantially as hereinbefore described with reference to Figure 1 of the accompanying drawings.

17. An electrode according to claim 1 substantially as hereinbefore described with reference to Figure 2 of the accompanying drawings.

18. An electrode according to claim 1 substantially as hereinbefore described with reference to Figure 3 of the accompanying drawings.

1 9. An electrode according to claim 1 substantially as hereinbefore described with reference to Figure 4 of the accompanying drawings.

20. An electrode according to claim 1 substantially as hereinbefore described in Example 1.

21. An electrode according to claim 1 substantially as hereinbefore described in Example 2.

22. An electrode according to claim 1 substantially as hereinbefore described in Example 3.

23. A cell for use in determining the total concentration of free ions in a test solution, the cell comprising the test solution in electrochemical contact via respective liquid junctions with a first electrode according to any one of claims 1 to 22 and a second electrode which is a reference electrode or another electrode according to any one of claims 1 to 19.

24. A cell according to claim 23 provided with means for measuring the potential difference of the cell.

25. A cell according to claim 23 or 24 including electrode means for use in measuring the pH of the test solution.

26. A cell according to any of claims 23 to 25 provided with means for maintaining the cell at a constant temperature.

27. A cell according to any of claims 23 to 26 provided with means for stirring the test solution.

28. A cell according to any of claims 23 to 27 wherein at least one of the said first and second electrodes is according to claim 2 or claim 7 and the ionic concentration of the or each special solution is substantially greater than that of the test solution.

29. A cell according to any of claims 23 to 28 wherein each of the said first and second electrodes is according to claim 2 or 7, the said slopes of electrode potential variation for the two said electrodes being of opposite sign.

30. A cell according to claim 29 wherein the special solutions of the two said electrodes are of the same concentration.

31. A cell according to claim 29 or 30 wherein the special solution of one said electrode is of LiCI and that of the other is of KCH3COO.

32. A cell for use in determining the total concentration of free ions in a test solution, the cell being substantially as hereinbefore described with reference to Fig. 5 of the accompanying drawings.

33. A cell for use in determining the total concentration of free ions in a test solution, the cell being substantially as hereinbefore described with reference to Fig. 6 of the accompanying drawings.

34. A cell for use in determining the total concentration of free ions in a test solution, the cell being substantially as hereinbefore described with reference to Fig. 7 of the accompanying drawings.

35. A cell for use in determining the total concentration of free ions in a test solution, the cell being substantially as hereinbefore described in Example 4.

36. A cell for use in determining the total concentration of free ions in a test solution, the cell being substantially as hereinbefore described in Example 5.

37. A cell for use in determining the total concentration of free ions in a test solution, the cell being substantially as hereinbefore described in Example 6.

38. A method of determining the sum of the concentration (c)-mobility (u) products of free ions in a solution, the method comprising measuring at a given temperature and pressure the potential difference U between the first and second electrodes of a cell according to any of claims 23 to 37 containing said solution as test solution and determining the said sum fclu, from the relation:

where A and B are constants at constant temperature and pressure and are determined by plotting U at the said given temperature and pressure against log 12cul for test solutions of known compositions.

39. A method according to claim 38 which includes measuring the pH of the said solution and determining the sum ff of the said products for the ions other than H+ and OH- by the relation

40. A method according to claim 38 or 39 wherein the total concentration in the test solution of free ions or of free ions other than H+ and OH- is calculated or approximated from the product sum obtained.

41. A method of determining potentiometrically the sum of the concentration-mobility products of free ions in a solution, the method being substantially as hereinbefore described.

42. A method of obtaining potentiometrically the concentration of free ions in a solution, the method being substantially as hereinbefore described.