Anal. Chem. 1988, 60, 1351-1354
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CORRESPONDENCE Kinetic Response of an Ammonia-Selective Electrode Evaluated for Quantitation of Ammonia Sir: Studies of the kinetics of potentiometric ion-selective electrodes (ISE’s) have tended to focus on mechanisms of response and mathematical descriptions of kinetic behavior (1-4). There have been few if any attempts to exploit the kinetic responses of ISEs for quantitation of analytes; rather, quantitative applications are invariably based on measurements made after the electrode is at or near steady state. This approach is quite satisfactory for rapidly responding electrodes and for situations in which rapid sample throughput is not necessary. However, for slowly responding electrodes and for situations in which fast sample throughput is desirable, it could be advantageous to make use of the higher speed of kinetic methods if that higher speed could be achieved without the loss of reliability normally inherent in steady-state methods. The initial-rate and fixed-time kinetic methods in common use (5) have not been attractive for applications with ISE’s because they tend to have much larger error coefficients than steady-state (equilibrium) methods (6).However, in recent years a general approach to kinetic determinations has been developed (7-9) that combines the high speed of kinetic methods with the lower error coefficients of steady-state methods. Simply stated, the method uses signals measured during the early part of the kinetic response to predict the signal that would be measured if the process were monitored to steady state. Accordingly, effects of variables that affect the kinetic response but do not affect the steady-state signal are reduced substantially. This paper describes a fmt attempt to adapt this “predictive kinetic” method to the kinetic response of an ion-selective electrode. An ammonia-selective electrode was chosen as a model for this study because the response characteristics were known (10) to be in a convenient time range. Because the study was intended as a “proof-of-principle”, a first-order model was used in the curve-fitting process, although it was known from previous studies (1-4) that this model would not likely be either exactly correct or generally applicable. However, as results will show, the model was reasonably satisfactory for the ammonia-selective electrode and was an expedient way to evaluate the concept. EXPERIMENTAL SECTION An Orion 95-10 ammonia-selective electrode was used with an Orion 601A pH and millivolt meter (Orion Research, Cambridge, MA). The output of the meter was amplified by a factor of 100 with an operational amplifier circuit (follower and two XI0 gain stapes). The output from the amplifier circuit was monitored with a microcomputer (AT&T PC6300) through a commercially available interface (Lab Master, Scientific Products Corp., Cleveland, OH). Data were transferred to a supermicrocomputer (11) (MASSCOMP MCS-510 workstation, Massachusetts Computer Corp., Westford, MA) for processing. The program used is analogous to that described earlier (7, 11) for first-order processes. All solutions were prepared in distilled deionized water. Working solutions of ammonia were prepared fresh in 0.72 M sodium hydroxide just prior to each set of experiments. Three types of experiments are described. In the first and second sets, 0003-2700/88/0360-1351$01.50/0
the electrode was equilibrated in 0.1 and 0.003 M ammonia, respectively, between samples; in the third set, the electrode was equilibrated between samples in different randomly selected concentrations of ammonia between 0.0001 and 0.1 M. The electrode was rinsed with water and wiped lightly with tissue as it was transferred from the equilibration solution to each sample. All samples were monitored to steady state so that computed values of steady-state potentials could be compared with measured values.
RESULTS AND DISCUSSION Response Curves. Figure 1 includes response curves for situations in which the electrode was equilibrated in 0.10 M ammonia (Figure 1A) and 0.003 M ammonia (Figure 1B) just prior to immersion in each test solution. In each case, the dotted (lighter) curves are experimental data and the solid (darker) curves represent best fits (nonlinear least squares) of the data to a first-order model. For these plots, all data throughout the range monitored were used in the fitting process in order to determine how closely the data could be forced to fit the first-order model. Although there are some small systematic deviations, the data fit the first-order model surprisingly well. In another set of experiments, the electrode was equilibrated in different ammonia concentrations selected randomly prior to measurements on each test solution. Response curves were similar to those shown in Figure 1, except that the starting points were different. Numerical averages for measured and computed values of steady-state potential are compared in Table I for each concentration. Agreement between measured and computed potential is very good a t the higher concentrations and is within 2 standard deviations a t most concentrations. The kinetic responses for two runs each in 0.03 and 0.01 M ammonia were erratic and did not yield useful results. Numerical results for conditions such as those in Figure 1were analogous to those in Table I. Average standard deviations were 2.2 and 0.9 mV, respectively, for measured values with the two sets of experiments and 1.3 and 0.9 mV, respectively, for computed values; differences between measured and computed values a t 1 X M were somewhat and 3 X larger (5-7 mV) than those in Table I when the electrode was equilibrated in 0.1 M ammonia between runs. Given that these results were obtained by fitting data well into the steady-state region, the good agreement between measured and computed values is not surprising. However, these results give levels of uncertainties against which results obtained for shorter fitting ranges can be compared. They also give good estimates of rate constants and half-lives for the different responses. Table I1 summarizes apparent first-order rate constants for the different concentrations for two of the three sets of experiments described above. Uncertainties in the rate constants are in the range 0.001-0.01 s-l, with some slightly (X4) larger and some substantially (X 10) smaller. It is clear from both Figure 1 and Table I1 that half-lives vary with concentration and with the prior history of the electrode. For the concentrations examined here, half-lives vary from 3 to 12.3 s for the electrode equilibrated 0 1988 American Chemical Society
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A
ANALYTICAL CHEMISTRY, VOL. 60, NO. 13, JULY 1, 1988 eo
20
1
a
b
20
-25 C
A
>
n
> E
u
E
v
-70
-40
8
E
u
-70
ammonia concn, M
W -115
f
-160
I
0
30
60
90
Time
(SI
120
150
Figure 1. Plots of potential vs time for several concentrations of ammonia. Concentrations(lo4 M) a-f: 1, 3, 10, 30, 100, 300, 1000. Electrode equilibrated In: A, 0.1 M; 9,0.003 M ammonia. Experimental data (..-); computed values (-).
so
C0"3
Figure 3. Computed potential vs logarilhm of concentration. Conditions are as in Figure 1B; fitting range 0-141 s.
F'
1000 300 100 30 10 3 1
steady-state potential, mV measd computed" value std dev value std dev -155' -125d -95.Bd -65.gb -38.7d -10.0b +16Ad
0.5 1.0 0.8 1.3 1.9 3.9 3.8 1.9
-154' -123' -95.Y -65.8' -38.6d -12.0d +15.2d
0.5 1.6 2.0 4.1 3.8 2.4
av OComputed over data range of 176 a. 'Average of six runs. ' Average of four runs. Average of three runs. e One run.
i
Table 11. Apparent First-Order Rate Constants for Different Equilibration Concentrations
ammonia concn, lo4 M
tL d/
-160 -160
-120
-so
E,
-40
0
40
(mV>
Figure 2. Comparison of computed and meawred potentials. Conditions are as in Flgure 1B; fitting range 0-72 s.
in 0.1 M ammonia and from 7 to 35 s for the electrode equilibrated in 0.003 M ammonia; they varied over similar ranges for the other set of experiments but cannot be tabulated so readily because of the random nature of the experiments. This dependence of rate constants on both concentration and prior history of the electrode would make it very difficult if not impossible to utilize initial-rate or fixed-time kinetic methods; however, this is exactly the type of situation the predictive kinetic method was designed to handle (7-9). Quantitative Comparisons. The feasibility of using the predictive kinetic method was evaluated by fitting data over different time ranges to the first-order model and by evaluating relationships between computed values of steady-state
1000 300 100 30 10 3 1
apparent rate constant, s-' for electrode eauilibrated in 0.1 M NH3 0.003 M NH3 0.23 0.15 0.11 0.08 0.07 0.056
0.10 0.08 0.06 0.036 0.025 0.020
potential and both concentration and measured values of potential. Comparison of Potentials. Figure 2 is a comparison of computed and measured Potentials for a 72-s data processing range for the second group of experiments. The upper line (a) in the figure is the least-squares line for all the concentrations, and the lower line (b) is the least-squares line for all concentrations except that at 1 X M. Least-squares statistics for the lower line are included as the first line of the middle group of data in Table 111; least-squares statistics for other situations are also included in the table. In most cases, slopes are near unity, intercepts are near zero, standard errors are a few millivolts, and correlation coefficients are greater than 0.99, suggesting reasonably good agreement between computed and measured values of equilibrium potential.
ANALYTICAL CHEMISTRY, VOL. 60, NO. 13, JULY 1, 1988
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Table 111. Comparisons of Computed and Measured Values of Equilibrium Potentials data range, s
'lope intercept*mV std error, corr coeff value std dev value std dev mV (r) 1.07 0.987 0.970 0.967 0.976
0.01 0.008 0.008 0.007 0.006
6.0 -3.2 -5.1 -5.4 -4.3
1.1 0.7 0.6 0.6 0.5
3.2 2.0 1.9 1.7 1.4
-
n
> E
Electrode Equilibrated with 0.1 M Ammonia 0-30 0-45 0-60 0-75 0-176
20
0.998 0.999 0.999 0.999 0.999
-40
