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5.5: Compensating for the Reagent Blank

  • Page ID
    219815
  • Thus far in our discussion of strategies for standardizing analytical methods, we have assumed that a suitable reagent blank is available to correct for signals arising from sources other than the analyte. We did not, however ask an important question: “What constitutes an appropriate reagent blank?” Surprisingly, the answer is not immediately obvious.

    In one study, approximately 200 analytical chemists were asked to evaluate a data set consisting of a normal calibration curve, a separate analyte-free blank, and three samples with different sizes, but drawn from the same source [Cardone, M. J. Anal. Chem. 1986, 58, 433–438]. The first two columns in Table 5.5.1 shows a series of external standards and their corresponding signals. The normal calibration curve for the data is

    \[S_{std} = 0.0750 \times W_{std} + 0.1250 \nonumber\]

    where the y-intercept of 0.1250 is the calibration blank. A separate reagent blank gives the signal for an analyte-free sample.

    Table 5.5.1 : Data Used to Study the Blank in an Analytical Method
    \(W_{std}\) \(S_{std}\) \(\text{Sample Number}\) \(W_{samp}\) \(S_{samp}\)
    1.6667 0.2500 1 62.4746 0.8000
    5.0000 0.5000 2 82.7915 1.0000
    8.3333 0.7500 3 103.1085 1.2000
    11.6667 0.8413
    18.1600 1.4870 \(\text{reagent blank}\) 0.1000
    19.9333 1.6200
    \(S_{std} = 0.0750 \times W_{std} + 0.1250\)
    \(W_{std} \text{: weight of analyte used to prepare the external standard; diluted to a volume, } V\)
    \(W_{samp} \text{: weight of sample used to prepare sample as analyzed; diluted to a volume, } V\)

    In working up this data, the analytical chemists used at least four different approaches to correct the signals: (a) ignoring both the calibration blank, CB, and the reagent blank, RB, which clearly is incorrect; (b) using the calibration blank only; (c) using the reagent blank only; and (d) using both the calibration blank and the reagent blank. The first four rows of Table 5.5.2 shows the equations for calculating the analyte’s concentration using each approach, along with the reported concentrations for the analyte in each sample.

    Table 5.5.2 : Equations and Resulting Concentrations of Analyte for Different Approaches to Correcting for the Blank
    Concentration of Analyte in...
    Approach for Correcting the Signal Equation Sample 1 Sample 2 Sample 3
    ignore calibration and reagent blanks \(C_A = \frac {W_A} {W_{samp}} = \frac {S_{samp}} {k_A W_{samp}}\) 0.1707 0.1610 0.1552
    use calibration blank only \(C_A = \frac {W_A} {W_{samp}} = \frac {S_{samp} -CB} {k_A W_{samp}}\) 0.1441 0.1409 0.1390
    use reagent blank only \(C_A = \frac {W_A} {W_{samp}} = \frac {S_{samp} - RB} {k_A W_{samp}}\) 0.1494 0.1449 0.1422
    use both calibration and reagent blanks \(C_A = \frac {W_A} {W_{samp}} = \frac {S_{samp} -CB -RB} {k_A W_{samp}}\) 0.1227 0.1248 0.1266
    use total Youden blank \(C_A = \frac {W_A} {W_{samp}} = \frac {S_{samp} -TYB} {k_A W_{samp}}\) 0.1313 0.1313 0.1313

    \(C_A = \text{ concentration of analyte; } W_A = \text{ weight of analyte; } W_{samp} \text{ weight of sample; }\)

    \(k_A = \text{ slope of calibration curve (0.0750; slope of calibration equation); } CB = \text{ calibration blank (0.125; intercept of calibration equation); }\)

    \(RB = \text{ reagent blank (0.100); } TYB = \text{ total Youden blank (0.185; see text)}\)

    That all four methods give a different result for the analyte’s concentration underscores the importance of choosing a proper blank, but does not tell us which blank is correct. Because all four methods fail to predict the same concentration of analyte for each sample, none of these blank corrections properly accounts for an underlying constant source of determinate error.

    To correct for a constant method error, a blank must account for signals from any reagents and solvents used in the analysis and any bias that results from interactions between the analyte and the sample’s matrix. Both the calibration blank and the reagent blank compensate for signals from reagents and solvents. Any difference in their values is due to indeterminate errors in preparing and analyzing the standards.

    Because we are considering a matrix effect of sorts, you might think that the method of standard additions is one way to overcome this problem. Although the method of standard additions can compensate for proportional determinate errors, it cannot correct for a constant determinate error; see Ellison, S. L. R.; Thompson, M. T. “Standard additions: myth and reality,” Analyst, 2008, 133, 992–997.

    Unfortunately, neither a calibration blank nor a reagent blank can correct for a bias that results from an interaction between the analyte and the sample’s matrix. To be effective, the blank must include both the sample’s matrix and the analyte and, consequently, it must be determined using the sample itself. One approach is to measure the signal for samples of different size, and to determine the regression line for a plot of Ssamp versus the amount of sample. The resulting y-intercept gives the signal in the absence of sample, and is known as the total Youden blank [Cardone, M. J. Anal. Chem. 1986, 58, 438–445]. This is the true blank correction. The regression line for the three samples in Table 5.5.1 is

    \[S_{samp} = 0.009844 \times W_{samp} + 0.185 \nonumber\]

    giving a true blank correction of 0.185. As shown in Table 5.5.2 , using this value to correct Ssamp gives identical values for the concentration of analyte in all three samples.

    The use of the total Youden blank is not common in analytical work, with most chemists relying on a calibration blank when using a calibration curve and a reagent blank when using a single-point standardization. As long we can ignore any constant bias due to interactions between the analyte and the sample’s matrix, which is often the case, the accuracy of an analytical method will not suffer. It is a good idea, however, to check for constant sources of error before relying on either a calibration blank or a reagent blank.