A Dye in Effluent: When Dilution Changes the Answer
An environmental laboratory measures a colored dye in treated effluent by UV-Vis at 520 nm in a 1 cm cell. The calibration is 0.5–10.0 mg/L in deionized water, slope 0.102 AU per mg/L, intercept 0.003, r² = 0.9999. The undiluted sample gives absorbance 2.45. A 1:10 dilution gives 0.302, and a 1:100 dilution gives 0.041. The permit limit is 25 mg/L. A 5.0 mg/L spike into the 1:10 diluted sample gives 88% recovery. A cuvette mismatch test shows a 0.008 AU difference between the two cells. The sample contains suspended solids and is strongly colored; the analyst filtered a portion through 0.45 µm and did not refilter the diluted aliquots. The lab must decide which dilution to report and whether the result exceeds the permit limit.
1. Evaluate the three absorbance values against the calibration range and explain why they do not agree. Which result is most defensible and why?
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The undiluted absorbance of 2.45 is far above the calibration top: 10 mg/L corresponds to only about 1.02 AU. Reporting from that value requires extrapolation, and at high absorbance stray light and detector nonlinearity usually depress the signal, so the undiluted result is a lower bound. The 1:10 dilution gives 0.302 AU, which corresponds to about 2.93 mg/L in the diluted solution, or about 29.3 mg/L in the original. That is within the calibration range, but the 88% spike recovery shows matrix suppression, so it is probably biased low. The 1:100 dilution gives 0.041 AU, only about 0.038 AU above the intercept and below the lowest calibration standard; it is too close to the quantitation limit to be reliable.
The 1:10 result is the most defensible of the three because it lies in the calibrated range, but it is not defensible as a final report without standard addition. The cuvette mismatch of 0.008 AU is about 2.6% of 0.302, minor but correctable by using one matched cell. The three values point to matrix effects and extrapolation, not to a homogeneous sample that can be reported from any dilution.
2. Design a standard-addition experiment and specify how to handle filtration, cuvette, and spike recovery.
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Use the filtered sample and choose a dilution that puts the unspiked absorbance in the middle of the calibration range, for example 1:5 or 1:10. Prepare at least five solutions: sample alone and sample plus added dye at 2, 5, 10, and 20 mg/L, all in the same matrix and at the same dilution. Measure in a single matched cuvette, or correct with a blank, and plot absorbance against added concentration. The x-intercept gives the original concentration; check that the addition plot is linear and that the slope agrees with the aqueous calibration slope.
Filter one portion and use the same filtrate for all additions; test whether the filter adsorbs dye by filtering a standard and comparing it with an unfiltered standard. Include a 5 mg/L spike recovery in the same matrix and require 95–105% before accepting the result. If recovery remains low, the matrix suppresses the signal and standard addition is the appropriate calibration. Record filtration, dilution, and cuvette details.
3. The standard-addition result is 31.5 mg/L with an expanded uncertainty of ±3.2 mg/L (k=2). What should be reported against the 25 mg/L limit, and what does the uncertainty mean for compliance?
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Report 31.5 mg/L with an expanded uncertainty of ±3.2 mg/L (k=2), together with the standard-addition procedure, dilution, filtration, spike recovery, and cuvette handling. The lower bound of the interval is 28.3 mg/L, which is still above 25 mg/L. Under a decision rule that compares the lower confidence bound with the limit, the result supports an exceedance with about 95% confidence, provided the uncertainty estimate is valid and the sample is representative.
The laboratory should also state whether the permit applies to dissolved or total dye. Filtration through 0.45 µm may remove dye associated with particles and could underreport a total parameter; if the permit is total, a separate unfiltered digestion or dispersion step is needed. If a future result were, for example, 26 ± 3 mg/L, the interval would cross 25 mg/L and the laboratory could not declare exceedance without a defined decision rule. Here the lower bound is above the limit, so report the exceedance and retain the raw data.