# Limit of Detection

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For every measurement you make on an instrument, there will be associated noise (aka background signal or background noise) which may limit the amount of an analyte that can be detected. As the amount of analyte decreases, the corresponding signal on the instrument will also decrease, and so at some point, the analyte signal will be not be differentiated from the noise. Any analyte will cause a signal, however due to the noise level, we can reach a point where a signal is no longer detectable by us. With ‘no signal’, we can’t say that there is no analyte, only that we have reached the detection limit for that analyte.

## Determination of Limit of Detection

The limit of detection (LOD) is the lowest concentration of analyte that we can detect in a method. This does not necessarily mean we can quantitate this signal, only detect it (recall that for quantitation via a calibration curve, a signal should fall between a higher and lower concentrated standard). One common method to find the LOD is to measure a number of replicates of an appropriate blank or low concentration standard, then find the standard deviation of these measurements. Using a blank allows us to find the background or baseline noise. Using a low concentration standard gives us a starting point of reference as to ‘how low can we go?’ for determining the LOD. In terms of calculations, the LOD is considered the concentration of analyte that gives an signal (true signal) that is, usually, 3× the standard deviation (s) of the mean (${\displaystyle {\bar {x}}}$) blank signal.

${\displaystyle LOD={\bar {x}}_{blank}\pm 3s_{blank}}$     Eq. 1[1]

Using 3s assures that we are using the 99% confidence level.

## Instrument Limits of Detection

For the lab analyses of water samples on this project, we are able to calculate the limit of detection for the ion chromatrograph (IC) (salts analysis) and the optical emission spectrometer (OES) (metals analysis) for each species. Each salt or metal has a different level of detection limit because of the instrument's selectivity towards that species.

### Current Limits of Detection for Salts

Species Limit of Detection (ppm) EPA MCL (ppm)[2]
fluoride (F-) 0.010 4
chloride (Cl-) 0.023 250
bromide (Br-) 0.004 n/a
nitrate (NO3-) 0.011 10
phosphate (PO43-) 0.077 n/a
sulfate (SO42-) 0.050 250

For project lab data tables, these are the current ion chromatographic analyses lower limits of detection. Any instrument values that are less than those above are denoted by '<LD'.

### Current Limits of Detection for Metals

Species Limit of Detection (ppm) EPA MCL (ppm)[2]
calcium (Ca) 0.18
magnesium (Mg) 0.55
iron (Fe) 0.082
manganese (Mn) 0.016
aluminum (Al) 0.082
strontium (Sr) 0.003
lead (Pb) 0.009 0.015
arsenic (As) 0.009 0.010
mercury (Hg) 0.010 0.002
chromium (Cr) 0.0006 0.1
barium (Ba) 0.002 2
cadmium (Cd) 0.0005 0.005

For project lab data tables, these are the current optical emission spectroscopic analyses lower limits of detection. Any instrument values that are less than those above are denoted by '<LD'.

See also: Limit of Quantitation

## References

1. Harris, D. C. Quantitative Chemical Analysis, 8th ed.; W.H. Freeman and Co: New York, 2010; p. 103.
2. The US Environmental Protection Agency's Maximum Contaminant Level for drinking water' in parts per million.

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