1002 Analyst, October, 1980 Com mu nica t ion Material f o r publication as a Communication must be on a n urgent matter and be of obvious scientijic importance. Rapidity of Publication i s enhanced i f diagrams are omitted, but tables and formulae can be included. Communications should not be simple claims for priority: this facility f o r rapid publication is intended f o r brief descriptions of work that has progressed to a stage at which i t i s likely to be valuable to workers faced with similar probl,sms. A fuller paper may be offered subsequently, i f justijied by later work. Manuscripts are not subjected to the usual examination by referees and inclusion of a Communication i s at the Editor's discretion. Limit of Detection in Analysis with Ion-selective Electrodes Keywords : Ion-selective electrodes ; potentiornetry ; limit of detection In an earlier paper1 approximations were used in deriving some of the equations [ ( 8 ) , (10) and (12)] expressing C,, the criterion of detection, and C,, the limit of detection, and these equations were restricted to electrodes whose responses were limited by the solubility products of isovalent ( 1 : 1) salts. In this paper, exact and general solutions are derived within the same treatment as before.Retaining the earlier notation1 [C = analytical determinand concentration, s = concentration of determinand dissolved from electrode, b, = reagent blank determinand, b , = ith interference effect, K = solubility product, uB = standard deviation of the blank (mv), Q = 2.330,, L = 4.650~1, the following derivations ensue for an electrode incorporating a salt A,B and responding to ion A.Response Not Limited by Solubility Product There is no change and equation (6) in the earlier paper' is exact and general in application, i.e., where b = b , + Cb6, C, = - l ) b Response Limited by Solubility Product Only In this instance b, = Xbd = 0 and the solubility product is given by (1) The e.m.f. can be expressed as follows: E = EO+ Klog [ K / ( ;.s>"]'" At C = 0, the blank e.m.f. is given by [ (;)"I l / ( Z + Y ) EB = EO + k log K At the criterion of detection, C = C,, s = s, and the e.m.f. is Hence,COMMUNICATION and 1003 Y/X V/(X+V) lo&/* = [ KlP( E) ] Sg'/" Substituting in equation (1) and solving for C, we obtain Equation (2) replaces equations (8), (14) and (16) in the earlier paper1 and also covers other stoicheiometries.The equation for the limit of detection, C,, is exactly analogous with L substituted for Q. Response Limited by Solubility Product and Interference As b, = 0, Zb, = b # 0 and the solubility product is still defined as in equation ( l ) , the e.m.f. can be expressed as follows: E = E O + k log { b + KllX/ (:.s)"") At C = 0, the blank e.m.f. is given by E , = E O + k l o g At the criterion of detection, C = C,, s = s, and the e.m.f. is E, = EO + k 1og{b + X1/X/(~*sQ)'/x} Now, Q = jE, - E,I, and hence Solving for s,, we obtain Hence, from equation (l), the criterion of detection is given by Equation (3) not only replaces equation (10) in the earlier paper1 but also extends the treat- The equation for the limit of detection, C,, is ment to electrodes based on non-isovalent salts. exactly analogous with L substituted for Q.1004 COMMUNICATION Analyst, VoZ.105 Response Limited by Solubility Product and Reagent :Blank Determinand In this case Xbd = 0 and b, # 0. The solubility product equation for a salt A,B, in an electrode responsive to ion A is . . (4) K = (C + b, + s)X [";..IU .. . . . . At C = 0, s = so and the e.m.f. of the blank is EB = Ea + k log { K / [ At the criterion of detection, C = C,, s = sQ and the e.m.f. is EQ = Eo + k log { K / [ Y;*S~]')"~ Hence, SQ = so 10-"Q/Uk From equation (4), the criterion of detection is K1/X For x = y = 1, equation (4) with C = 0 can be solved analytically to give so, which can be substi- tuted in equation ( 5 ) .For other stoicheiometries, so is best found by an iterative method, although for x = 2, y = 1 and x = 1, y = 2, so can be determined explicitly in terms of hyperbolic functions. Equations (2), (3) and (5) do not involve any approximations and are, therefore, more accurate than the earlier equations,l as shown in Table I. The newly calculated values agree more closely The equation for the limit of detection, C,, is exactly analogous to equation ( 5 ) . TABLE I CRITERIA AND LIMITS OF DETECTION FOR UNIVALENT ELECTRODES WITH uB = 1.0 mV Code* 7 B 106b,/mol 1-l . . . . .. 0 1O6Zb,/rnol 1-1 . . . . .. 0 10'2K . . .. . . . . 4 Equation used . . .. * . (2) 107CQ/mol 1-1- Graphical . . . . . . 3.63 This calculation . . . . 3.63 Previous calculation* .. . . 3.47 Graphical . . . . . . 7.41 This calculation . . . . 7.28 Previous calculation* . . . . 7.28 * See Table I11 in the earlier paper.' 107cL/mo1 1-1- C 0 1 1 (3) 3.43 3.49 4.28 6.76 6.81 8.23 D 1.5 0 1 (5) 2 29 2 33 199 4.79 4.79 4.03 v E 0 0 4 x 10-6 (3) 5.25 5.22 6.21 9.66 10.04 10.05October, 1980 COMMUNICATION 1005 with the graphical values, especially for electrodes C and D, for which the earlier treatment involved the greatest approximations. All of the discussion in the earlier paper is applicable to the more accurate equations developed here. It may also be noted that simple expressions exist for the limit and criterion of detection in the special cases where the e.m.f. can be measured with sufficient precision to allow limiting linear calibrations to be used.2 This work was carried out at the Central Electricity Research Laboratories and is published with the permission of the Central Electricity Generating Board. References 1. 2. Midgley, D., Analyst, 1979, 104, 248. Midgley, D., Analyst, 1980, 105, 417. Central Electricity Research Laboratories, Kelvin Avenue, Leatherhead, Surrey, KT22 7SE Received July 22nd, 1980 Derek Midgley