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5.5: Blank Corrections

Thus far in our discussion of strategies for standardizing analytical methods, we have assumed the use of a suitable reagent blank 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 of different size but drawn from the same source.12 The first two columns in Table 5.3 show a series of external standards and their corresponding signals. The normal calibration curve for the data is

\[S_\ce{std} = 0.0750 × W_\ce{std} + 0.1250\]

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

Table 5.3 Data Used to Study the Blank in an Analytical Method
Wstd Sstd Sample Number Wsamp Ssamp
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   reagent blank 0.1000
19.9333 1.6200      

Calibration equation: \(S_\ce{std} = 0.0750 × W_\ce{std} + 0.1250\)

Wstd: weight of analyte used to prepare the external standard; diluted to volume, V.
Wsamp: weight of sample used to prepare sample; diluted to volume, V.

In working up this data, the analytical chemists used at least four different approaches for correcting 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. Table 5.4 shows the equations for calculating the analyte’s concentration using each approach, along with the resulting concentration for the analyte in each sample.

Table 5.4 Equations and Resulting Concentrations of Analyte for Different Approaches to Correcting for the Blank
Approach for Correcting Signal Equation Concentration of Analyte in...
Sample 1 Sample 2 Sample 3
ignore calibration and reagent blank \[C_\ce{A} = \dfrac{W_\ce{A}}{W_\ce{samp}} = \dfrac{S_\ce{samp}}{k_\ce{A}W_\ce{samp}}\] 0.1707 0.1610 0.1552
use calibration blank only \[C_\ce{A} = \dfrac{W_\ce{A}}{W_\ce{samp}} = \dfrac{S_\ce{samp} - \ce{CB}}{k_\ce{A}W_\ce{samp}}\] 0.1441 0.1409 0.1390
use reagent blank only \[C_\ce{A} = \dfrac{W_\ce{A}}{W_\ce{samp}} = \dfrac{S_\ce{samp} - \ce{RB}}{k_\ce{A}W_\ce{samp}}\] 0.1494 0.1449 0.1422
use both calibration and reagent blank \[C_\ce{A} = \dfrac{W_\ce{A}}{W_\ce{samp}} = \dfrac{S_\ce{samp} - \ce{CB} - \ce{RB}}{k_\ce{A}W_\ce{samp}}\] 0.1227 0.1248 0.1261
use total Youden blank \[C_\ce{A} = \dfrac{W_\ce{A}}{W_\ce{samp}} = \dfrac{S_\ce{samp} - \ce{TYB}}{k_\ce{A}W_\ce{samp}}\] 0.1313 0.1313 0.1313

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, as well as any bias resulting 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.

Note

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 resulting 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, 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.13 This is the true blank correction. The regression line for the three samples in Table 5.3 is

\[S_\ce{samp} = 0.009844 × W_\ce{samp} + 0.185\]

giving a true blank correction of 0.185. As shown by the last row of Table 5.4, 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.