Interpretation of Non-Ideal Calibrations of Ion-Selective Electrodes Derek Mldgley Central Electricity Research Laboratories, Kelvin A venue, Leatherhead, Surrey, KT22 IS€, United Kingdom
Procedures are developed for analyrlng non-Nernstlan responses of ion-selective electrodes arising from the followlng causes: (I) the presence of determlnand In reagents added to a sample solution, (il) the presence of lnterferlng species, (Ill) the solubility of the material of the electrode itself. Secondary effects due to the actlon of complexlng agents or the establishment of steady-state rather than equlllbrium condltlons are also consldered. The theory Is rlgorously developed for several types of solld-state electrode, and is tentatively applied to liquid membrane electrodes also. Applicatlon of the correct procedure results In a llnear graph wlth an intercept that can be used to calculate the reagent blank and/or the level of interference and a slope with a value characterlstlcof the type of non-Ideal behavior, provlded that the electrode is operatlng reversibly and has a mechanlsm conformlng to the models discussed. Practical examples are taken, involvlng glass, llquld lon-exchange, and solid-state electrodes.
minand concentration, that can give rise to an electrode response independently of the analytical and membranederived determinand concentrations. Any determinand introduced as an impurity appears as b,, the reagent blank determinand concentration. Each interferent, whether introduced in a reagent or present in the original sample, gives a term b,, which is the product of the interferent concentration and a selectivity coefficient. “Interferent” refers to substances that have a direct effect on the electrode and not to those that mask the determinand.
Few ion-selective electrodes are sufficiently sensitive to give an ideal, Nernstian, calibration at the concentrations found in highly pure power station waters, but they may still be used a t these concentrations, provided they behave in a reproducible way, e.g., for the determination of chloride (1-3). Before a non-ideal calibration is accepted, the system should be checked for possible causes of non-ideality, such as an interferent that may be removed or masked, or determinand introduced with a reagent. Theoretical values of emf are calculated for hypothetical electrodes that do not give ideal calibration curves and ways are devised of treating emf data graphically so that the non-ideal behavior can be interpreted. The causes of nonideality considered are the presence of determinand in reagents added to the solution, the presence of interfering species, and the solubility equilibria of the material of the electrode itself. Secondary effects due to the action of complexing agents and the establishment of steady-state rather than equilibrium conditions are also considered. The theory is developed rigorously for solid-state electrodes and tentatively applied to liquid membrane electrodes. The different causes of non-Nernstian calibrations also have implications for the limits and criteria of detection of ionselective electrodes ( 4 ) . Definitions and Symbols. The analytical determinand concentration, c , is the nominal concentration of a standard solution or the true concentration in a sample solution, corrected for any dilution caused by the addition of reagents. The membrane-derived determinand concentration, s, is the concentration of determinand arising from dissolution of the materials comprised in the electrode itself. If the dissolution products are not uniformly distributed throughout the solution, this concentration refers only to the solution adjacent to the electrode surface, Le., that part of the solution to which the electrode is actually responding. The additional determinand concentration, b = b, + Bb,, includes all the other factors, expressed in terms of deter-
E = E o + k log c
CALCULATION OF THEORETICAL RESPONSES OF ELECTRODES It is assumed that concentrations can be used instead of activities, since when measurements are made in a medium of constant ionic strength, the activity coefficients can be included in the Eo term of Equation 1. Even without a constant ionic medium, however, we are concerned with very dilute solutions in which activity Coefficients are close to unity. An electrode responding ideally to a single determinand obeys Equation 1, where E is the emf, Eo the standard potential of the electrode, k = (RT In (10))/nF is a constant at a given temperature, and c is the concentration of determinand in the solution. Any deviation of the response from Equation 1depends on both the mechanism of the electrode and the composition of the solution containing the determinand. The theoretical responses shown in Figure 1 were calculated as described below. The electrodes were cation-responsive and each univalent electrode had a standard electrode potential of 337.15 mV and a sensitivity of 59.16 mV per tenfold change in concentration. The parameters (solubility products, interference levels, and reagent blanks) governing each calibration were chosen so that the electrode potential at zero added determinand was 0.0 mV in each case, corresponding to an apparent concentration of 2 x mol/L. Exactly corresponding responses could be calculated for anion-sensitive electrodes, but the sensitivities and standard potentials would be negative. Deviations Occurring Well above the Intrinsic Limit of the Electrode. Such deviations are due to the presence of reagent blank determinand and/or interfering substances. The electrode obeys Equation 2
E = E o + k log
(C
+ b)
where b is the additional determinand concentration. A theoretically calculated calibration curve (A) with b = 2 X lo4 mol/L is shown in Figure 1. This type of behavior can be found with every kind of electrode. Deviations Due to the Solubility of the Electrode. These deviations are to be expected for electrodes with crystalline membranes capable of reaching a rapid reversible solubility equilibrium with the solution immediately adjacent to it. Response of Isovalent Crystal Membrane without Interference. In this case, the electrode responds to deANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
*
1211
chloride electrode in solutions of low chloride concentration which were flowing a t such a rate that the solution in the vicinity of the electrode was not saturated with silver chloride. Applying this theory to Equation 4, we obtain Equation 7
E=E"
1 -7
0
1
I -6 0
-6 5
-5 5
lO.(C)
Figure 1. Non-Nernstian Calibration curves for univalent electrodes. ( A )b = 2 X mol/L, interference or reagent blank determinand, no solubility effect: ( B ) K = 4 X lo-'' moI2/L2,solubility effect only: (C) b, = rnol/L, K = lo-'* mol'/L', solubility effect with interference: (D) b r = 1.5 X lo-' mol/L, K = lo-'* moI2/L2,solubility effect, with reagent blank: ( E ) K = 4 X lo-'* moI3/L3,non-isovalent (2:l)solubility
+ hlog
(;+/;
+ K')
(7)
where K' = K (Di/D,)'i3 and D, and D, are the diffusion coefficients in the solution of the determinand and its counterion in the crystal and to a very good approximation (D,/D,)2i3is constant. Equation 7 can therefore be treated in all subsequent calculations in the same way as Equation 4. Similarly, Equations 5 and 6 will have analogues with K replaced by K'. Response of Non-Isovalent Cr-ystal Membranes. The calculation of the response in this case is illustrated for 2:l stoichiometry. If the determinand is univalent, its concentration is determined by the solubility equilibrium Equation 8 and the response obeys Equation 9. (C
+ s ) *S- = K 2
+ s) = E o + h l o g d m '
effect: (N)Ideal Nernstian response
E = E o + h log (c
terminand dissolved from its own surface as well as to that originally present in solution; no interference effects occur. The total concentration of determinand is (c + s), where c is the original concentration and s derives from the electrode, and is governed by the solubility product, K , of the crystal such that
A theoretically calculated calibration (E) is shown in Figure 1 for K = 4 X lo-'' mo13/L3. The concentration of a divalent determinand is given by the solubility equilibrium Equation 10 and the corresponding electrode response by Equation 11.
(e
+ s)s = K
(3)
Equation 3 can be solved for s and the emf of the electrode shown to be
E = Eo
+ h log (C + S ) (4)
A theoretically calculated curve (B)with K = 4 X lo-'' moI2/L2 is shown in Figure 1. Response of Isovalent Crystal Membrane w i t h I n terference. The total concentration of determinand is derived from Equation 3 as before, but the interference effect, Zb,, causes the response to follow Equation 5. It is assumed that the interference does not arise from competitive precipitation (see below) and that the solubility of the membrane material is not affected, e.g., a redox interference.
+ h log [% +J + K + Z b i ] ~
E
= Eo
(5)
A theoretically calculated curve (C) with Bb, = lo4 mol/L and K = 10-l' mol2/L2is shown in Figure 1. Response of Isovalent Crystal Membrane w i t h Reagent B l a n k Determinand. The presence of determinand, b,, from a reagent blank produces a response analogous to Equation 4.
E
=
Eo
+ h log
[bpi" A theoretically calculated curve (D)with b, = 1.5 X lo4 mol/L and K = 10-l' mol2/L2is shown in Figure 1. Solubility Effects i n Flowing Solutions. Bystritskii, Bardin, and Aleskovskii (5) calculated the emf of a silver-silver 1212
ANALYTICAL CHEMISTRY, VOL.
49, NO. 8,JULY 1977
+ s) ( 2 S ) * = K E = E , + h log (e
(9)
(10)
(3
The responses of non-isovalent electrodes cannot be analyzed by all the techniques used below-only by Equations 23 and 32. When the non-isovalent compound is used in conjunction with a more soluble isovalent one which is in direct equilibrium with the determinand, e.g., solid-state membrane electrodes for chloride, bromide, and iodide with membranes comprising the silver halide mixed with silver sulfide, the electrode response will be determined by the properties of the isovalent salt and the effects of interferences and reagent blank determinand on the calibration can be calculated as before. Interference from Competitive Precipitation. The interference of bromide with a silver-silver chloride electrode is typical of this case. Bromide will not affect the electrode unless condition 12 is fulfilled, but then the bromide concentration alone and not the chloride concentration will determine the potential. In practice the transition may be less clearly defined because of adsorption or the formation of a mixed precipitate. Equations 4-7 describe the non-ideal responses only if condition 1 2 is not met.
->-
KAgBr
CCl
KAgCl
Effect of a Complexing Agent on a n Isovalent Crystal Electrode. If the electrode contains crystals of composition AB with a solubility product K and is immersed in a solution containing a substance X which forms a complex AX with a stability constant 3( = [AX]/([A] [XI), more of AB will be dissolved than in the absence of X. The effect on the potential depends on whether the electrode responds to A or B. Electrode Responding to the Uncomplexed Component of t h e Membrane. As [B] = c + s and [A] = s - [AX], the solubility equilibrium is governed by Equation 13.
K = (C +
S) (S -
[AX] ) = (C +
S)S -
KP[X]
(13)
Provided [XI >> [AX], p[X] is virtually constant and we can write Equation 14 which is identical in form to Equation 3. (c
+ s)s = K"
(14)
where K" = K ( l + @[XI). The potential can be written, analogously to Equation 4.
E = E o + k log
[ +d5>]
Electrode Responding to the Complex-Forming Component of the Membrane. As [A] + [AX] = c + s and [B] = s, the solubility equilibrium in this case is given by Equation 16,
+ s - [AX] )S = K
(16) which also reduces by expansion of [AX] etc. as above to Equation 14. The potential can be written as Equation 17, (C
E = E o + k log-
K"
(17)
S
where s is given by
+ k log K"
-
k log
1-i:+/
+ S)S = (C*)'
KD-' = KL
(211
Equation 21 is analogous to Equation 3 for an isovalent crystal membrane electrode, and Equation 4, with the substitution of KL for K , will describe the electrode potential in the absence of additional determinand. The effect of a masking agent should also be similar. If reagent blank determinand is present, an equation similar to Equation 6 with the substitution of KL = (c*)~/KDfor K describes the electrode potential. The poor selectivities of liquid membrane electrodes make them prone to interferences by (i) impurities in the water or the reagents, (ii) ions present in the reagents themselves, (iii) hydrogen or hydroxide ions produced by autoprotolysis of the water. It may, therefore, be rare to find a case where the contribution from interferences is negligible. In the presence of an interferent, the emf takes the form of Equation 22,
E
= Eo
+k
log [C + a,
+ s + R ( b ,- a,)]
(22) where R is the electrode selectivity coefficient for the interferent, b, is the original concentration of interferent and (b, - a,) the concentration after exchange, i.e., a, mol/L of interferent enter the membrane phase and a, mol/L of determinand leave it, concentrations referring to the aqueous phase. If more than one interferent is present, Equation 22 becomes
E = E o + k log [C + Ca, + s + Z R , ( b , - a , ) ] when R,, b,, a, refer to the ith interferent.
Equation 17 can be rewritten
E = Eo
(C
+ K"
i(18)
Multiple Complex System. Equations 15 and 18 can be written for any series of complexes, AX,, mononuclear in A, including protonated complexes, H,AX,, if the pH is constant. If polynuclear complexes, A,X,, are formed, equations such as 15 and 18 cannot be written, as there are no explicit solutions for s. Application to Liquid Ion-Exchange Electrodes. No distinction is made between exchangers dissolved in organic solvents and those immobilized on polymer matrices, as the mechanism should be the same, although the distribution coefficients may differ. Isovalent Liquid Ion-Exchange Electrodes. It is assumed that the membrane contains the equally charged ionic species A and B, that the electrode responds to A and that co-ion uptake is negligible. Concentrations in the exchanger phase are denoted by C*. The distribution of species between the membrane and solution phases follows Equation 19.
When the electrode is immersed in a solution of A a t a concentration, c, both A and B will be extracted from the membrane, so that CB = s, the concentration of dissolved exchanger, and C A = c s. From Equation 19,
+
where c* is the original concentration of exchanger in the membrane phase and s* the decrease in concentration of exchanger in the membrane phase as a result of dissolution in the aqueous phase. For any practical electrode, the distribution of exchanger overwhelmingly favors the membrane phase and therefore c* >> s* provided the membrane phase is in equilibrium with only a small volume of aqueous solution. Equation 20 can then be rewritten
s and a, cannot be determined algebraically and the analysis of this condition does not lend itself to an easy solution. In practice, liquid ion-exchange systems may take so long to reach equilibrium in the presence of an interferent that the practical limit of detection is set by kinetic rather than thermodynamic factors. Non-Isovalent Liquid Ion-Exchange Electrodes. By making the same assumptions as in Equations 20 and 21, but corresponding to a stoichiometry of 2:1, it can be shown that the electrode potential obeys Equations 9 or 11, with the substitution of an appropriate KL for K; KL = ((c*)'/2) KD-' and KL = 4(c*)' KD-' for univalent and divalent determinands, respectively (cf. Equation 21). Neutral Carrier Membranes. In neutral carrier membrane electrodes, an extractive, as opposed to an ion-exchange, mechanism means that the limiting solubility cannot be described by an equation analogous to the solubility product and therefore the equations and functions derived above do not apply in this case.
ANALYSIS OF NON-IDEAL CALIBRATION CURVES It is assumed in the following sections that measurements in a concentration range where the calibration is linear have established the values of the standard potential, Eo, and the slope, k. The appropriateness of the following mathematical treatments depends on the extent to which the deviation is caused by the solubility product of the material of which the electrode is constituted. Deviations to Which the Solubility Product Makes a Negligible Contribution. Equation 2 can be transformed into Equation 23 E
10
-E, k
=c+b
(23)
A plot of the left-hand side of the equation vs. c will intercept the ordinate at b and have a slope of unity (curve A in Figure 2). The same transform applied to Equations 4, 5, and 6 , Le., to electrodes for which the solubility product is significantly ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
1213
I
I
I 1
’
1
1 IO’C
mol
1
I-’
Flgure 2. Plots for identifying deviations with negligible solubility effect. Annotation as in Figure 1
large, gives Equations 24a-24c, respectively Figure 3. Plots for identifying deviations with predominant solubility effect. Annotation as in Figure 1
E -E,
10
-+K
2
E-E,
loh
C
=
2 + bi
+
,/:>
(24b)
+
If K >> c2/4 or K >> (c2 b,2)/4 (Equation 24c), the square root terms in Equations 24a-24c can be expanded by means of the binomial theorem and written, neglecting all but the first term, as Equations 25a-25c E -E, -
10
c 2
c2 8-
-
c
rfl+-+-
E -E,
c2
zero, whether Eo is accurately known or not, and thus some useful information can be gained by plotting 10Eikvs. c when Eo is unknown. As a special case, the limiting linear portion of Equation 25a intercepts the abscissa at c = -2&, whether loiE- Eo)/k or loEik is plotted. By comparing the negative intercept with the value of the solubility product of the electrode material, it is possible to infer whether an electrode is responding as described by Equation 4, even if Eo is unknown and the procedure described below cannot be used. Solubility-Induced Deviations. The following functions can also be applied in circumstances where K is replaced by K’ (Equation 7)) K” (Equation 141, or K L (Equation 21). Functions of the Analytical Determinand Concentration. Equation 24a can be transformed into Equation 26 E -E,
cz
(lo--;)
C2
= -4 + K
(26)
A plot of the left-hand side of the equation vs. c2 will have a slope of 0.25 and an intercept of K (curve B , Figure 3). For comparison, Equations 23, 25b, and 25c have been similarly transformed to give Equations 27-29.
(27) Plots of the left-hand sides of each equation vs. c are not truly linear (curves B-D in Figure 2) because of the c2/8& term, but at low values of c this term becomes negligible and the plots approach linearity. The slopes of these linear portions are 0.5 for Equations 25a and 25b, and >0.5 for Equation 25c. For b, = 2&, Equation 25c would have a slope of unity and could be distinguished from Equation 23 only with difficulty. For b, > however, the binomial expansion is not valid and the electrode potential approaches that of Equation 2, giving transform 23. Figure 2 shows the transforms for the theoretical calibration curves (A-D) in Figure 1. - Eo)ik vs. c is effectively the same as that A plot of derived by Gran (6) for potentiometric titrations, although without Gran’s arbitrary constants and with no need for a volume correction. The form loiE - E o ) / k was used so that Equations 24 and 25 could be written without arbitrary constants and developed easily into Equations 26-29. Differentiation between Equation 23 and the limiting linear portions of Equations 25a-25c depends on knowing Eo. The assignation of an arbitrary value to E,, as in Gran’s plot, does not affect the linearity of the plot, but the value of the slope no longer has a definite meaning. The level, b, of reagent blank determinand and/or interferent is given by the negative intercept on the abscissa when - E , ) / k is extrapolated to
a,
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ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
E-E,
(loA
+ -C24
-
(
f
)’
1-t-
=
biz
+ 2bifl + K
2;)
A plot of the left-hand side of Equation 28 vs. c2 will be linear with an intercept on the ordinate, I , given by Equation 30 and a slope S given by Equation 31, (curve C, Figure 4). The curves in Figure 3 are transforms of the theoretically generated calibration curves (A-D) in Figure 1.
+ 2bifl + K S = 0.25 (1 + I = bi2
(30)
Equations 30 and 31 can be solved simultaneously to give bi and K. A curved plot is obtained if solubility effects are negligible (Equation 27 and curve A in Figure 3) or if the solubility effect is complicated by the presence of reagent blank determinand (Equation 29 and curve D in Figure 3). If there are no deviations from a Nernstian response, the plot gives a straight line through the origin with a slope of 0.25. Functions of the Apparent Determinand ConcenE o ) / k , the tration. All the Equations 23-29 contain apparent determinand concentration calculated from the Nernst equation, on the left-hand side only, while the right-hand sides contain the analytical determinand concentration c. Parthasarathy, Buffle, and Monnier (7) have shown that for an electrode based on a crystal of formula A,B, and responsive to A. E -E, 10 - ~ = b , + bj
’
It should be noted that m and n represent the stoichiometry of the crystal and not necessarily the ionic charges, as stated by Parthasarath et al. If there are no interferences, b, = 0 and a plot of 10‘’ E o ) / k - c vs. E a ) / k ) - m / nwill be linear with a slope of ( r n / r ~ ) K land / ~ intercept b,. If there is an interference effect, bi, the above plot is curved but a plot of 10@ E o ) / k - c vs. E o ) / k - b,)-m/” is linear with slope (m/n)K’/”and intercept b’ = b, b,. Without foreknowledge of b,, such a plot is not strictly possible but an estimate of b may be obtained from the intercept of the plot of Eo)/k - c) vs. - Eo)/k)-m/n; this estimate is used in the second plot, from which, iteratively, that value of b, can be obtained that gives a straight line, and hence an accurate value of b, b, from the intercept on the ordinate. An overestimate of b, leads to a convex plot and an underestimate to a concave plot. Although such plots would -be useful with perfect experi- c may be high, because mental data, the error in it is often the difference between two very similar quantities, and the plots may be very scattered and difficult to interpret. Parthasarathy et al. (7), obtained a good plot with a silver chloride membrane electrode, but plots of their fluoride results were too scattered to be helpful. Because of these experimental difficulties, the plots described earlier in this paper are more likely to yield useful information and they do not involve iterative procedures. Effect of Variation in Conditions of Measurement. More information about an electrode’s behavior can be obtained if it is calibrated in different conditions of, for example, temperature, background electrolyte, pH, or oxygen content. The effect on the electrode response of the parameter to be varied will differ according to the mechanism, e.g., temperature has no effect on the level of reagent blank determinand, but can change the solubility considerably, while its effect on interferences is generally unpredictable.
+
+
PRACTICAL EXAMPLES The plot of E o ) / k vs. c can be used with any electrode, but the application of the other functions depends on the mechanism, i.e., they are valid only for electrodes in which the mechanism includes a solubility product equilibrium or an analogous equilibrium reaction that can be expressed in similar terms, as with liquid ion-exchange electrodes. Ion-Selective Glass Electrodes. Electrodes of this type would be expected to give linear plots of E o ) / k vs. c, as there is no solubility product equilibrium in their mechanism.
Table I. Results of Plots of 10(E-Eo)/kvs. c for Fluoride Electrodes Additional determinand Electrode T, “C concn, mol/L Slope Beckman 39600a 25 5.4 x 10-7 1.03 Beckman 39650‘ 25 2.1 x 10-7 0.96 Orion 94-09Aa 25 1.6 x 10-7 0.95 Orion 96-09Ab 22 5.2 x 10-7 a Data from reference (7). E , set arbitrarily to zero, data from reference ( 4 ) . Applying the plot to the results of Goodfellow and Webber (8) for an ammonium-selective electrode and Goodfellow, Midgley, and Webber (9) for various sodium-selective electrodes shows this to be so, in accordance with the original explanations offered for the non-ideal calibrations obtained with these electrodes near their limits of detection. Gas-Sensing Membrane Electrodes. These “electrodes” are really electrochemical cells incorporating an ion-selective electrode, but the plots described here may not be applicable to a gas-sensing electrode as a whole, even if they apply to the component ion-selective electrode when it is used separately. The reason for this apparent contradiction lies in the other components of the gas-sensing electrode-the gaspermeable membrane and the equilibria prevailing in the internal filling solution. Midgley and Torrance (10) found reagent blank determinand when using an ammonia gas-sensing electrode, and Ed’k this was confirmed when their data were plotted as vs. c, but none of the plots fitted the results obtained with a carbon dioxide gas-sensing electrode (11). Even in this case, however, the failure of the plot of - Ed’k vs. c showed that a likely cause of the non-ideal calibration, i.e., absorption of carbon dioxide from the atmosphere, could not be the only source of error. Copper-SelectiveElectrodes. Electrodes based on copper selenide and copper sulfide have practical limits of response far above those predicted by the very small solubility produds of the constituent compounds. Plots of Midgley’s data (12, 13) as E o ) / k vs. c were linear with slopes in the range 0.97-0.99, confirming that the solubility product mechanism was not the limiting factor. Fluoride Electrode. The fluoride electrode has a Nernstian response below the level ( mol/L) predicted by the solubility product of the lanthanum fluoride crystal (14). Plots of 1 0 ‘ ~ vs. c are linear. The results in Table I for electrodes from different sources show that all the electrodes behaved as if there were a constant level of additional determinand in the solutions, although the level was peculiar to each electrode even when measurements were made in the same solutions; this was in contrast to silver chloride electrodes, which showed remarkably similar blanks in a variety of media (see below). Parthasarathy et al.’s plots were so scattered that a line could not confidently be drawn through them. Suggested explanations for the anomalously extended Nernstian response are as follows. (a) Single crystals of lanthanum fluoride have different solubility products from the amorphous precipitates used for most of the solubility measurements. (b) The kinetics of dissolution of the crystal are so slow that equilibrium is not reached in the time of analysis (usually 1-5 min.). (c) There is some adsorption effect at the surface. The plots do not confirm or disprove any of the above explanations, although they indicate that the solubility effect (a) was not the limiting factor in the conditions tested. The only known interferent with the fluoride electrode is the hydroxide ion. Its effects have not been studied at low ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
1215
I .o
0.5
I
Table 11. Low-Level Chloride Measurements
1.5 I
I
Medium
X 10'
X
10'
rl
- r2
source
2.8
3.1
0.999
0.9995
(3)
3.3
3.2
1.000
1.000
(I)
buffer 0.005 mol/L
3.0
2.9
1.000
1.000
(16)
W O , 0.01 mol/L
2.57
2.9
1.000
1.000
(5)
KNO. 0.01 mbl/L KNO,~
2.70
2.9
1.000
1,000
(5)
0.1 mol/L HNO, 0.1 mol/L
acetate
0,s
I O 104
F
I 5 mol
1-1
Flgure 4. Plots of lo'€- Eo)'k vs. c ( 0 )and (lo'€(A) for a silver-silver chloride electrode
Eo)'k-
~ 1 2vs. ) ~c2
a
Intercept o n abscissa of 10Elk vs. e .
K = 1.69
X
lo-'' mo12/LZat 25 "C and f is the activity coefficient.
r l refers to a plot of 10Eik vs. e , rz to a plot of E vs. c.
Presaturated with silver chloride.
(,olt~E&~'
Flgure 5. Plots of (IO'€ - Eo)'k - c) vs. (lo'€ - Eo)'k )- ' for chloride electrodes. (0)Chloridized silver wire, (x) Pungor electrode, (A) chloridized silver billet
fluoride concentrations but at the pH of the data analyzed here, the hydroxide concentration is high enough for interference to be considered at the fluoride levels tested. With the data available, the plots cannot resolve whether an interference or reagent blank determinand is the limiting factor in the conditions tested. Chloride Electrodes. Torrance ( I , 15) determined chloride in the presence of an ammonium acetate buffer with three different electrodes based on silver chloride: a chloridized silver wire, a chloridized silver billet (Beckman Instruments Inc.) and a Pungor-type membrane electrode with silver chloride crystals set in silicone rubber. The plot of lo(' - E o ) / k vs. c is linear with slope 0.93 and intercept 2 X mol/L whereas the plot of - Eo)i' - (c/2))' c2 is curved. The results for all three electrodes gave coincident plots in the case of each of the functions: those for the chloridized silver wire are shown in Figure 4. When the results were plotted as (10'' - E o ) / k - c) vs. - 'a)'-', the curves shown in Figure 5 were obtained. The scatter due to the error in calculating (10'' Eo)/k - c) ave less well defined straight lines than the plot of 10@vs. c and the slopes were about one tenth of the theoretically known values of KAga. None of the plots conform to what would have been expected if the solubility of silver chloride had been the dominant cause of the non-ideal response and so an interferent or reagent blank determinand must be present. Interference effects with this type of electrode are by competitive precipitation, except for redox interference, but the identical
'Jfi
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ANALYTICAL CHEMISTRY, VOL. 49, NO. 8 , JULY 1977
behavior of the Pungor electrode, which is not sensitive to redox potentials, disproves the latter possibility. The main source of additional determinand is therefore likely to be chloride ions introduced with the ammonium acetate buffer, since this was added in constant proportion to all chloride solutions. Electrodes based on silver chloride have been used by several investigators for determining small concentrations of chloride in flowing solutions. The standard potential was not determined by any of these investigators, as they used linear calibrations of E vs. c. In all cases a plot of vs. c was linear with an intercept on the abscissa close to the theoretical values of 2 m f for the ionic medium concerned (Table 11). This agreement indicates that the level of reagent blank determinand in these tests was insignificant compared with the chloride dissolved from the electrodes themselves, which in the case of Florence's results (3) was confirmed by radioactive tracer measurements. The plot of vs. c is therefore the limiting case for an effect due urely to the solubility product, i.e., the slope of the - 0' lk vs. c plot would be close to 0.5 and the intercept on the ordinate would be Examples of less clear-cut behavior can also be found. The results of Parthasarathy, Buffle, and Monnier (7),who used Beckman 39604 electrodes in 0.5 mol/L KNOB, gave linear plots of 10" Eo)/k vs. c with a slope of 0.82 and an intercept of 2.3 X lo-' mol L-' (cf. = 1.8 X mol/L). This is typical of intermediate behavior between the cases where solubility effects are dominant or negligible. Parthasarathy et al. plotted (10" Eo)/k - c) vs. (10'' - 'a)'')-' and obtained a slope of 3.0 X 10-l' mol'/L (cf., K / f = 3.1 X lo-'' mo1'/L2) in 0.5 mol/L NaN03. They interpreted their results in terms of a nitrate interference, for which there are no theoretical grounds, presumably as a result of neglecting activity coefficients and comparing the slope with the solubility product of silver chloride at infinite dilution (1.7 X lo-'' mo12/L2). Mascini and Liberti (17) made electrodes by impregnating a thermoplastic polymer with silver chloride. Plotting their results as - Eo)/k vs. c gave a straight line with slope 0.98 and an intercept of 2.4 X mol/L (cf., = 1.3 X mol/L); in this case the calibration is dominated by a high level of additional determinand. No reagents were added to the solutions and therefore the only source of reagent blank determinand was the water used for preparing the standard solutions. Interfering ions would not be expected to be present and the electrode should not be sensitive to redox potentials.
P
mf,
mf
mf
The interference level indicated by the plot for the solutions containing mol/L chloride was 4.7 X mol/L, representing a selectivity coefficient for chloride of 4.7. In solutions containing mol/L chloride, the plot indicated a selectivity coefficient of 1.7. This discrepancy between the two selectivity coefficients is much reduced if allowance is made for a postulated bicarbonate interference of 2.5 X mol/L. Plotting the results as E d / k ) 2vs. c2 gives a curve of very steep slope at the lowest acetate concentrations mol/L), which is typical of an effect not due primarily to solubility (cf. Figure 2). The points over the range 0-10-4 mol/L fit a straight line fairly well, but the slope is higher (0.3) than would be expected from a solubility effect alone.
105 c no1
1-1
FI ure 6. Plots of Eo)'k vs. c ( 0 , 0 )and (lo'€- E o ) ' k - c/2)* vs. c (A, A) for acetate liquid ion-exchange electrode in the presence mol/L chloride ( 0 ,A) and absence (0, A) of
P
Possible explanations for such a high level of additional determinand are (i) the membrane was not perfectly tight and the internal filing solution mol/L chloride) was diffusing through into the test solution, (ii) the membrane contained co-precipitated soluble chloride salts. A very low rate of seepage may give rise to a large effect on the electrode potential, as the electrode will respond to a local concentration adjacent to the surface of the membrane and it is in this area that the leaking inner solution would mix with the test solution. Plots of the same authors' data for similarly constructed bromide and iodide electrodes also indicated the presence of a high reagent blank. Marshall (18) made measurements with an Orion 94-17 electrode (Ag2S/AgC1polycrystalline membrane), no reagents bein added to the solution. A plot of his results at 25 "C as (lO('-Eo)/k - c / Z ) ~vs. c2 was linear with near theoretical slope (0.29) and an intercept (2 X lo-'' mo12/L2)that compared well with the solubility product for AgCl of 1.78 X lo-'' mo12/L2. The plot of locEvs. c was curved with a limitin slo e of -0.3. At 5 "C the result gave a linear plot of lo('vs. c with a slope of 1.03 and an intercept on the ordinate of 3.9 X lo4 mol/L. Thus at the lower temperature, where the solubility is smaller ( K = 2.6 X mo12/L2),the additional determinand, which should be the same at both temperatures, becomes the more significant factor. These examples show how the responses of electrodes composed of the same material vary according to the details of their construction and the experimental conditions in which they are used. Acetate Liquid Ion-Exchange Electrodes. Garbett and Torrance (19)produced a number of acetate electrodes. Plots of - Ed'k vs. c are shown in Figure 6 for a typical electrode in pure acetate solutions and in the presence of an interfering ion mol/L chloride). The plots are linear, although the results in pure acetate solutions are more scattered than was found with the glass or solid-state electrodes. The slopes of the plots are 1.06 for the solutions containing chloride ion, Le., typical of an interference effect, and 0.9 for the pure acetate solutions, which is far more typical of an interference than of a solubility effect. No attempt was made to exclude carbon dioxide during the experiments and the indicated interference level (2.5 X mol/L) could be due to bicarbonate ion. The possibility that a solubility effect was operating far from equilibrium in the flowing solution, Le., that the rate of dissolution of exchanger was virtually independent of the acetate concentration can be discounted, as no difference in emf was observed when the flow was stopped.
EJk
DISCUSSION The various function plots will help to indicate the causes of non-ideal calibrations of electrodes and therefore the actions that may be taken to improve an analytical procedure. If the non-ideality arises from the physicochemical properties of the material in the electrode itself, the analyst can do little about it, whereas he may be able to control the level of an interferent or of reagent blank determinand. Similarly, the plots help the electrochemist to separate accidental from fundamental effects in the study of electrode characteristics. The curves in Figure 1 show that electrodes that have Nernstian calibrations at high concentrations and indicate the same level of determinand (estimated by extrapolation of the Nernstian calibration) in a blank solution vary considerably in the region of non-ideal response, depending on the cause of the deviations from ideality. The practical examples show how plots of the various functions can characterize either an electrode or an analytical method. As an instance, Figure 4 shows that Torrance's ( I ) chloride calibration can be adequately expressed in the form low Eo)/k vs. c, which is as linear as Torrance's less rigorously derived plot of E vs. log (c + 1). This latter function is appropriate to a system where the blank is dominated by membrane solubility effects rather than by an impurity and is valid in this form only for the temperature and ionic strength of Torrance's experiments. In the case of several sets of results with chloride electrodes, the deviations from ideality are greater than can be accounted for by solubility effects alone. With the fluoride electrode, on the other hand, the solubility of the membrane material is not significant even at fluoride concentrations where this would have been predicted from solubility product data in the literature. Even if none of the plots can define the calibration of a particular electrode, that fact alone may be useful, by eliminating possible causes of non-ideal behavior, e.g., the calibration of the gas-sensing carbon dioxide electrode. The interpretation of the various function plots described in this paper is most meaningful when two conditions are fulfilled. (i) The calibration should be closely spaced on the concentration axis; graphs showing only decadic changes in concentration give little more than qualitative information about an electrode operating near the lower limits of its performance. (ii) The mean value of the points should be known with a good precision even if this means considerable replication at each concentration level.
LITERATURE CITED (1) K. Torrance, Ana/yst (London), 99, 203 (1974). (2) K. Tomlinson and K. Torrance, Analyst (London), 102, 1 (1977). (3) T. M. Florence, J. Hectroanal. Chem. Interfac. Nectrochem., 31, 77 (1971). (4) D. Midgley, unpublished work. (5) A. L. Bvstritskii. V. V. Bardin. and V. B. Aleskovskii. Z b . Anal. Kbim. 21, 393 (1966). (6)G. Gran, Analyst(London), 77, 661 (1952). (7) N. Parthasarathy, J. Buffle. and D. Monnier, Anal. Cblm. Acta, 68, 185 (1974). (8) G. I. Goodfellow and H. M. Webber, Ana/yst(London), 97, 95 (1972). '
ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, JULY 1977
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(9) G. I. Goodfellow, D. Midgley, and H.M. Webber, Analyst(London), 101, 848 (1976). D. Midgley and K. Torrance, Analyst(London), 97, 626 (1972). D. Midaley, Analyst (London), 100, 386 (1975). D. Midgley, Anai. Chim. Acta, 87, 7 (1976). D. Midgley, Anal. Chim. Acta, 87, 19 (1976). G. J. Moody and J. D. R. Thomas, “Selective Ion Sensitive Electrodes”, Merrow Publishing, Watford, England, 1971. (15) K. Torrance, unpublished work. (16) H. M. Webber and E. A. Wheeler, unpublished work. (10) (11) (12) (13) (14)
(17) M. Mascini and A. Liberti, Anal. Chlm. Acta, 47, 339 (1969). (18) G. B. Marshall, unpubllshed work. (19) K. Garbett and K. Torrance, unpublished work.
RECEIVED for review Jgnuary 13, 1977. Accepted April 18, 1977. This work was carried out a t the Central Electricity Research Laboratories and is published by permission of the Central Electricity Generating Board.
Determination of Trace Acetylene in Oxygen with a Portable Acetylene Analyzer Marshall N. Cappelloni, Lowell G. Frederick, David R. Latshaw,” and John B. Wallace Air Products and Chemicals, Inc., P.O. Box 538, Allentown, Pennsylvania 18 105
The portable trace acetylene analyzer determines acotyJene concentrations in the 0.1 to 10 ppm range with an accuracy of *lo%. Acetylene in the sample gas is adsorbed and concentrated on a molecular sieve column. The column Is then desorbed by heating the molecular sieve and the released acetylene is purged by nitrogen through a modified Xlosvay solution. Upon contact with the Ilosvay solutlon, the acetylene reacts to form red copper acetyllde. The csncontratlsn of copper acetylide is determlned with a colorimeter and the concentration of acetylene in the gas sample Is determined by reference to a calibration curve. Use of two separate stock solutions that are mixed to form the Ilosvey solution when needed Increases the storage life of the Ilosvay solution and also enhances the portabllity of the analyzer.
Industries associated with the production and usage of oxygen are continuously aware of violent reactions that can be initiated if hydrocarbons are present in oxygen. One of the most feared situations is the presence of acetylene (1,2) in liquid oxygen (LOX). Acetylene presents a greater problem in LOX than other similar molecular weight hydrocarbons because it is much less soluble. A t -183 “C (-297 O F ) the solubility of acetylene in LOX is 5 ppm (3). At normal reboiler operating pressures of 8 to 10 psig, the solubility is slightly increased. Since acetylene has a low solubility in LOX, any acetylene in excess of the solubility limit will form solid acetylene crystals which will float on LOX. An interface between solid acetylene crystals and LOX is thus established. Therefore the need for monitoring acetylene in LOX is critical and the analysis for acetylene must be rapid and relatively accurate. A need existed for a portable instrument that could provide rapid and accurate analyses for acetylene in the 0.1to 10-ppm concentration range. The name of Ludwig Ilosvay is continuously brought into mind when speaking of trace acetylene analysis. However, Berthelot ( 4 ) is first credited with the method of precipitating copper acetylide with an ammoniacal solution of cuprous chloride. Ilosvay ( 5 ) in 1899 simplified and improved the method and his name has been carried with the acetylene absorbing solution ever since. The direct absorption of acetylene into Ilosvay solution is not sensitive enough for the acetylene concentration levels presently being determined in this paper. Because it is not possible to analyze directly for 1218
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acetylene concentrations in the low parts-per-million range with Ilosvay solution, scientists studied the possibility of concentrating the acetylene before it contacted the Ilosvay solution. Geissman, Kaufman, and Dollman (6) reported a satisfactory method for the determination of acetylene concentrations in the 1 to 15 ppm range. This method consisted of passing the gas sample containing acetylene through a cooled condensing coil in which the acetylene was condensed and thus concentrated. After gas sampling, the coil was warmed, and the concentrated acetylene was passed into a 300-mL gas-sample bottle where it was contacted with Ilosvay solution. Hughes and Gordon (7) adsorbed acetylene from a gas stream on a column of silica gel, 10 mm long and 2-mm diameter, cooled with dry ice to -78 “C. The gel was then warmed to room temperature and was treated with a solution of ammoniacal cuprous chloride. The presence and quantity of acetylene were indicated by the depth of color produced on the gel. The major problems encountered with their two methods were dry ice was not available at all analysis sites, and the methods did not have the precision and accuracy desired for the present test. The long term stability of Ilosvay reagent also has been a major problem. This is witnessed by the fact that numerous formulations exist for Ilovsay reagent (5-9). Additional information has been published on the formation of copper acetylides ( I 0) and on the copper-catalyzed oxidation of hydroxylamine (11). The present authors found the best stability by preparing the Ilosvay reagent in two parts. One solution consists of copper nitrate, ammonium hydroxide, and potassium chloride in water, while the other solution consists of hydroxylamine hydrochloride and gelatin in water. These individual solutions were stable for more than six months while stored in closed polyethylene bottles at temperatures between 0 and 30 “C. At an elevated temperature of 37 “C, the solution containing the gelatin was stable for three months.
EXPERIMENTAL Construction. A flow schematic of the acetylene analyzer is illustrated in Figure 1. The nitrogen flowmeter is capable of
measuring 10-50 cm3/min, and the oxygen flowmeter is capable of measuring 0.2-3 L/min. The connecting tubing is 0.32-cm 0.d. (7.1-mm wall) type 304 stainless steel, and it is connected by the use of stainless steel control valves and fittings. The sparger tube is 0.32-cm 0.d. (8.9-mm wall) type 316 stainless steel, and it is cut long enough to reach from the gas outlet to the bottom of the scrubber tube. The 30-cm long scrubber tube is constructed from
