Environ. Sci. Technol. 1988, 22,590-592
NOTES Gran’s Titrations and Ion Balances: Some Analytical Control Limits for Precipitation and Surface Waters Neil R. McQuaker” and Douglas K. Sandberg Environmental Laboratory, Ministry of Environment, 3650 Wesbrook Mall, Vancouver, British Columbia, Canada V6S 2L2
Analytical results provided by weakly buffered samples are used to define control limits for cation-anion balances when the combined cation plus anion concentration is below 700 pequiv/L. Application of the control limits can help identify when measurement processes are out of control. For acidic precipitation, an important component of the ion balance is free acidity, and in many applications, the determination of whether or not the free acidity exists principally as strong acidity becomes important. Use of Gran’s titration in making this determination is discussed. The deviation from unity of the rate of change of [H+] with respect to the addition of titrant is used as a control limit that monitors the presence of interference.
Introduction Use of an ion balance (anion - cation difference) has long been recognized as an important quality control check in the analysis of water samples ( I ) . When control limits for the ion difference are available, they can be used to help identify when one or more of the laboratory measurement processes is out of control. Control limits for weakly buffered samples have evidently not appeared in the literature, and in this work analytical data provided by precipitation and surface waters of low alkalinity are used to determine typical values. The samples used were collected from some 30 sites that were approximately equally distributed between precipitation and surface water monitoring sites located in British Columbia. Procedures for sample collection and preservation appear elsewhere (2). All chemical analyses were carried out over a 6 month period at the Environmental Laboratory, Ministry of Environment, with routine procedures (3). For acidic precipitation, an important component of the ion balance will be free acidity, and in order to assess the environmental impact of acidic precipitation it becomes important to know whether or not the free acidity exists principally as strong acidity. Recently, it has been suggested that the ratio -A[H+]/ACB provided by Gran’s titration could be used to make this determination (4);ACB is the moles liter-l of strong base required to produce a concentration change of A[H+]. In this approach, the deviation from unity of the rate of change of [H+] with respect to the addition of titrant becomes a control limit that monitors the presence of interference. Application of this approach to British Columbia precipitation samples is discussed. Results and Discussion Ion Balance. It was assumed that the major ions present in the samples are those appearing in Table I. Alkalinity was determined from Gran’s titration, free acidity was determined from sample pH, and the balance of the ions was determined by either ion chromatography 590
Environ. Sci. Technol., Vol. 22, No. 5, 1988
Table I. Parameters Used in the Ion Balance
cations Ca2+ Mgz+
Na’
anions
so:-
NO; c1-
cations
anions
K+ NH,’ free acidity
Falkalinity
or inductively coupled plasma emission spectroscopy (Ca2+ and Mg2+only). Detection limits for each of the parameters appearing in Table I are typically 1pequiv/L or less (3),and participation in a series of interlaboratory comparison studies has suggested that the various analytical techniques used are free from significant measurement bias (5). Data from 233 samples provided the results shown in Table I1 for standard deviations of the anion - cation difference (A - C) associated with mean anion + cation concentrations (A + C ) below 700 pequiv/L. The results are plotted, by using a least-squares linear regression fit, in Figure 1. They provide a “linear” relationship similar to that observed by earlier workers ( I ) at much higher ion concentrations (approximately 100 times higher) and are compatible with the expectation that the standard deviation will increase with increasing concentration. When the results of Figure 1 are applied to individual samples, we expect that approximately 5 % of the observed ion differences, A - C, will exceed plus or minus two standard deviations (f2 SD) and approximately 0.3% will exceed h 3 SD. The 5% that exceed h2 SD should be flagged and all analytical results critically examined before the individual analyses for a particular sample are accepted or rejected. If a deviation of f3 SD is exceeded (when major ions other than those of Table I are absent), then the measurement process for one or more analyses can be considered to be out of control. A summary of criteria for acceptable ion balances based on two standard deviations appears in Table 111. It should perhaps be noted that the 2 SD and 3 SD control limits, which can be identified from Figure 1 (and Table 111), are for samples collected in British Columbia and analyzed with the procedures employed by the Environmental Laboratory, Ministry of Environment. Samples collected in a different geographical area and analyzed at a different laboratory may provide slightly different control limits. This may be particularly true at low-ion concentrations (approximately 20-50 pequiv/L) where analytical detection limits and sample composition become limiting factors. If we consider “duplicate” ion (i.e., cation-anion) analyses to be analogous to duplicate analyses of an individual analyte and if we designate the extrapolated standard deviation at zero concentration as So,then the “effective detection limit” for ion concentration may be estimated to be ( 2 4 5 X 1.645)S0(6). This provides a result of 17 pequiv/L when we use the Sovalue of 3.65 pequiv/L ob-
0013-936X/88/0922-0590$01.50/0
@ 1988 American Chemical Society
Table 11. Standard Deviation of Ion Difference as a Function of Ion Concentration'
ion concentration, pequiv/L no. of results mean ion concn (A + C) SD (A - C)
40-70
70-100
100-150
150-200
200-300
300-500
500-700
55 55 5.0
50 85 5.3
31 120 7.6
34 170 9.0
20 230 10.7
20 390 15.0
23 590 20.5
'(A + C) = anion + cation concentration; (A - C)
= anion - cation difference.
Table 111. Criteria for Acceptable Ion Balances'
ion concn (A + C), pequiv/L
ion diff (A - C), pequiv/L
20-50 50-200 200-700
8-10 10-19 19-49
(A - C)/(A
+ C)
0.40-0.20 0.20-0.10 0.10-0.07
"Based on two standard deviations; i.e., A - C = 2[0.0290(A + C)
+ 3.651.
0
0 05
7
16
06
07
Slope Value
1 08
'
1 09
'
1 10
-S[H+]/C,
Figure 2. Strong acidity/free acidity ratio versus the slope value
-A[H+] l A C s .
3
i
i
:@L 1 i
j
'
F
0
i ,-
*"
I
-
100 200 300 400 500 600 ion C o n c e n t r a t i o n A - C ( p e q 1)
700
Figure 1. Standard deviation of the ion difference, A - C, versus the ion concentration, A f C. The curve is the least-squares linear fit y = 0 . 0 2 9 0 ~ 3.65;r = 0.996.
+
tained from Figure 1 and suggests that, in our laboratory, ion balances are meaningful for only those samples where the ion concentration exceeds approximately 20 pequiv/L. Even so, an ion concentration of 20 pequiv/L is extremely dilute and will include essentially all weakly buffered samples, including precipitation. This compares with the earlier work ( I ) where the ion concentration requirement for a meaningful ion balance was approximately 500 pequiv/L (So = 106.5 pequiv/L). The 500 pequiv/L concentration cannot include weakly buffered samples, and the So ratio of 106.5:3.6 is a measure of the enhanced detection limits (i.e., 1-2 orders of magnitude) that currently make this possible. Gran's Titration. Gran's titration curves may be generated by plotting (V, + V)[H+]versus V where V, is the original sample volume and V is the volume of titrant added. In the absence of interference, the intersection of the linear portion of the curve with the volume axis establishes the equivalence point V, for strong acidity. The minimum requirement commonly used for establishing linearity is four successive data points with a correlation
coefficient of at least 0.9995 (7,8). Recently, it has been pointed out that even though the curve is "linear", interference due to the dissociation of weak acids as the titration proceeds may be present (2, 9). When dissociation of weak acids is absent, the slope value -A[Hf]/AC~,which measures the rate of change of [H+] with respect to the addition of titrant, is expected to be unity. This suggests using a slope requirement, in addition to the linearity requirement, as a further analytical control limit. When V , >> V, the initial titration point ([H'], zero) and the extrapolated end point (zero, V,) may be used to approximate the slope (i.e., -A[H+]/ACB N [H+]/(NV,/V,) = free acidity/Gran's acidity). Reference samples of 50 pequiv/L strong acidity (H,SO, in distilled water) provided a slope value of 1.00 f 0.10 where the deviation is expressed as 2 SD. This result was obtained from 23 successive replicate analyses carried out on separate analytical runs. The titrations were carried out with 0.01-mL incremental additions of 0.01 N NaOH (7). Results provided by 70 acidic precipitation samples for the slope value -A[H+]/ACB obtained from free acidity/ Gran's acidity ratios are summarized in Table IV as a function of free acidity. The interval 15-80 pequiv/L free acidity shows a mean slope value of 0.95 f 0.14 (which compares with the reference value of 1.00 f 0.10). The observed deviation of the mean slope value from unity tends to suggest that some dissociation of weak acids may be occurring as Gran's titrations proceed. A graphical illustration of the effect of dissociation on the slope values appears in Figure 2. Here, slope values for mixtures of a weak acid of pK, 4.76 (acetic acid) and a strong acid,
Table IV. Slope Values and Ion Ratios as a Function of Free Acidity
free acidity, pequiv/L no. of results mean slope (-A[H']/AC,) mean ion ratio (C/A)
15-20
20-30
30-80
15-80
20 0.94 f 0.12 0.97 f 0.11
30 0.97 f 0.15 0.96 f 0.19
20 0.96 f 0.15 0.95 f 0.19
70 0.95 f 0.14 0.96 f 0.17
Environ. Sci. Technol., Vol. 22, No. 5 , 1988 591
containing 50 pequiv/L total acidity, are plotted versus the strong aciditylfree acidity ratio. The results show that if a 15% interference (Le., a strong aciditylfree acidity ratio of 0.85) is admitted, then the control limit for the slope is 0,890. When the 85% strong acidity criteria is maintained, the control limit will tend toward higherllower values as the pKa value and/or total acidity decreases/increases. For example, at pKa 4.76, the control limit shifts from 0.850 to 0.925 as the total acidity shifts from 80 to 15 pequiv/L. Application of these results to the mean slope values appearing in Table IV suggests that, within the limits of analytical precision, interference is not a significant factor for British Columbia precipitation samples. This conclusion is supported by mean cationlanion ratios, C/A (see Table IV), which give no evidence of the anion deficit expected if significant concentrations of partially dissociated weak acids were present. Even so, the small deviation of the mean slope values from unity does suggest marginal interference and is compatible with recent reports that the majority of precipitation samples are expected to contain weak organic acids (9). Within this context, the use of the slope value (or free acidity/Gran’s acidity ratio) to monitor the presence of interference becomes important, and the principal appeal of Gran’s titration is that it can be used (together with the ion balance) to help confirm whether or not the free acidity exists principally as strong acidity. Registry No. HzO, 7732-18-5.
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Environ. Scl. Technol., Vol. 22. No. 5, 1988
Literature Cited Greenberg, A. E.; Navone, R. J.-Am. Water Works Assoc. 1958, 50, 1365. McQuaker, N. R. Precipitation and Surface Water: Recommended Methods f o r Sampling and Site Selection; Federal-Provincial Research and Monitoring Co-ordinating Committee for the Long Range Transport of Acid Pollutants; Environment Canada: Ottawa, Ontario, 1983. McQuaker, N. R.; Sandberg, D. K.; Keene, W. C.; Galloway, J. N. Atmos. Environ. 1986, 20, 1507. McQuaker, N. R. A Laboratory Manual for the Chemical Analysis of Ambient Air, Emissions, Precipitation, Soil and Vegetation; Ministry of Environment, Province of British Columbia: Victoria, 1983. Aspila, K. I.; Todd, S. LRTAP Intercomparison Studies L l - L l 2 Major Ions, Nutrients and Physical Properties o f Water; Environment Canada: Ottawa, Ontario, 1983-1986. King, D. E. Analytical Reproducibility; Ministry of Environment, Province of Ontario: Toronto, 1976. McQuaker, N. R.; Kluckner, P. D.; Sandberg, D. K. Enuiron. Sci. Technol. 1983, 17, 431. McQuaker, N. R. Measurement of Acidity and Alkalinity; Federal-Provincial Research and Monitoring Co-ordinating Committee for the Long Range Transport of Acid Pollutants; Environment Canada: Ottawa, Ontario, 1986. Keene, W. C.; Galloway, J. N. Atmos. Environ. 1985, 19, 199.
Received for review July 15,1986. Revised manuscript received April 6, 1987. Accepted December 11, 1987.
