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{{Short description|Method in analytical chemistry}}
The '''Standard addition''' method, often used in [[Chemistry:Analytical chemistry|analytical chemistry]], quantifies the analyte present in an unknown. This method is useful for analyzing complex samples where a matrix effect interferes with the analyte signal. In comparison to the [[Biology:Calibration curve|calibration curve]] method, the standard addition method has the advantage of the matrices of the unknown and standards being nearly identical.<ref name=":0">{{Cite journal |last=Bader |first=Morris |date=1980 |title=A systematic approach to standard addition methods in instrumental analysis |url=https://pubs.acs.org/doi/abs/10.1021/ed057p703 |journal=Journal of Chemical Education |language=en |volume=57 |issue=10 |pages=703 |doi=10.1021/ed057p703 |issn=0021-9584}}</ref> This minimizes the potential bias arising from the matrix effect when determining the concentration.

== Variations ==
Standard addition involves adding known amounts of analyte to an unknown sample, a process known as ''spiking''. By increasing the number of spikes, the analyst can extrapolate for the analyte concentration in the unknown that has not been spiked.<ref name=":1">{{Cite book |last=Skoog |first=Douglas A. |title=Principles of Instrumental Analysis |last2=Holler |first2=James F. |last3=Crouch |first3=Stanley R. |publisher=Cengage Learning |year=2016 |isbn=978-1-305-57721-3 |edition=6th |location=Boston, MA, USA |pages=13–14}}</ref> There are multiple approaches to the standard addition. The following section summarize each approach.

=== Single standard addition used in polarography ===
In classic [[Physics:Polarography|polarography]], the standard addition method involves creating two samples – one sample without any spikes, and another one with spikes. By comparing the current measured from two samples, the amount of analyte in the unknown is determined.<ref name=":0" /> This approach was the first reported use of standard addition, and was introduced by a German mining chemist, Hans Hohn, in 1937.<ref>{{Cite book |last=Hohn |first=Hans |title=Chemische Analysen mit dem Polarographen |publisher=SpringerVerlag |year=1937 |location=Berlin, Germany |pages=51}}</ref> In his polarography practical book, titled ''Chemische Analysen mit dem Polargraphen,'' Hohn referred this method as ''Eizhusatzes'', which translates to "calibration addition" in English. Later in the German literature, this method was called as ''Standardzugabe'', meaning "standard addition" in English.

Modern polarography typically involves using three solutions: the standard solution, the unknown solution, and a mixture of the standard and unknown solution. By measuring any two of these solutions, the unknown concentration is calculated.<ref name=":0" />

As polarographic standard addition involves using only one solution with the standard added – the two-level design, polarographers always refer to the method as singular, standard addition.<ref name=":2">{{Cite book |last=Harvey |first=Charles E. |title=Spectrochemical Procedures |publisher=Applied Research Laboratories |year=1950 |edition=1st |location=Glendale}}</ref>

=== Successive addition of standards in constant sample and total volume ===
Outside the field of polarography, Harvey's book ''Spectrochemical Procedures'' was the next earliest reference book to mention standard addition.<ref name=":2" /> Harvey's approach, which involves the successive addition of standards, closely resembles the most commonly used method of standard addition today.

To apply this method, analysts prepare multiple solutions containing equal amounts of unknown and spike them with varying concentrations of the analyte. The amount of unknown and the total volume are the same across the standards and the only difference between the standards is the amount of analyte spiked. This leads to a linear relationship between the analyte signal and the amount of analyte added, allowing for the determination of the unknown's concentration by extrapolating the zero analyte signal. One disadvantage of this approach is that it requires sufficient amount of the unknown.<ref name=":1" /> When working with limiting amount of sample, an analyst might need to make a single addition, but it is generally considered a best practice to make at least two additions whenever possible.<ref name=":3">{{Cite book |last=Robinson |first=James W. |title=Introduction to Spectroscopy |last2=Skelly Frame |first2=Eileen M. |last3=Frame II |first3=George M. |publisher=Marcel Dekker |year=2005 |isbn=0-203-99730-1 |edition=6th |location=New York |pages=84–87}}</ref>

Note that this is not limited to liquid samples. In [[Physics:Atomic absorption spectroscopy|atomic absorption spectroscopy]], for example, standard additions are often used with solid as the sample.<ref>{{Cite journal |last=Fan |first=Xiaoyu |last2=Li |first2=Qing |last3=Lin |first3=Ping |last4=Jin |first4=Zhonggan |last5=Chen |first5=Meizi |last6=Yi |first6=Zu |date=2022 |title=A standard addition method to quantify serum lithium by inductively coupled plasma mass spectrometry |url=https://pubmed.ncbi.nlm.nih.gov/34719967/ |journal=Ann Clin Biochem |volume=59 |issue=3 |pages=166–170}}</ref>

In [[Physics:Atomic emission spectroscopy|atomic emission spectroscopy]], background signal cannot be resolved by standard addition. Thus, background signal must be subtracted from the unknown and standard intensities prior to extrapolating for the zero signal.<ref name=":3" />

As this approach involves varying amount of standards added, it is often referred in the plural form as ''standard additions''.<ref name=":2" />

== Example ==
Suppose an analyst is determining the concentration of silver in samples of waste solution in [[Engineering:Photographic film|photographic film]] by [[Physics:Atomic absorption spectroscopy|atomic absorption spectroscopy]]. Using the calibration curve method, the analyst can calibrate the [[Physics:Spectrometer|spectrometer]] with a pure silver [[Chemistry:Aqueous solution|aqueous solution]]s, and use the calibration graph to determine the amount of silver present in the waste samples. This method, however, assumes the pure aqueous solution of silver and a photographic waste sample have the same matrix and therefore the waste samples are free of matrix effect.
[[File:Standard_addition_example.png|thumb|354x354px|Spreadsheet for standard addition example on determining the silver concentration of photographic film waste. Please refer to the Limitation and Uncertainty of Standard Addition section for more information on how to calculate for the Error Analysis portion. The silver concentration in the test sample is the x-intercept of the plot. The dilution factor is multiplied by this initial concentration to determine the original concentration.]]
Matrix effects occur even with methods such as [[Chemistry:Inductively coupled plasma mass spectrometry|plasma spectrometry]], which have a reputation for being relatively free from interferences. As such, analyst would use standard additions in this case.

For standard additions, equal volumes of the sample solutions are taken, and all are separately spiked with varying amounts of the analyte – 0, 1, 2, 3, 4, 5 mL, where 0 mL addition is a pure test sample solution. All solutions are then diluted to the same volume of 25 mL, by using the same solvent as the one used to prepare the spiking solutions. Each prepared solution is then analyzed using an atomic absorption spectrometer. The resulting signals and corresponding spiked silver concentrations are plotted, with concentration on the x-axis and the signal on the y-axis. A [[Linear regression|regression line]] is calculated through [[Least squares|least squares]] analysis and the x-intercept of the line is determined by the ratio of the y-intercept and the slope of the regression line. This x-intercept represents the silver concentration of the test sample where there is no standard solution added.        

==Error==
While the standard addition method is effective in reducing the interference of most matrix effects on the analyte signal, it cannot correct for the ''translational'' matrix effects.<ref>{{Cite journal |last=Ellison |first=Stephen L. |last2=Thompson |first2=Michael |date=2008 |title=Standard additions: myth and reality |url=https://pubmed.ncbi.nlm.nih.gov/18645637/ |journal=The Analyst |volume=133 |issue=8 |pages=992–7}}</ref> These effects are caused by other substances present in the unknown sample that are often independent of the analyte concentration. They are commonly referred to as 'background' and can impact the intercept of the regression line without affecting the slope. This results in bias towards the unknown concentration. In other words, standard addition will not correct for these backgrounds or other spectral interferences.<ref name=":3" />

Analysts also needs to evaluate the precision of the determined unknown concentration by calculating for the standard deviation, <math>s_x
</math>. Lower <math>s_x
</math> indicates greater precision of the measurements. The value of <math>s_x
</math> is given by 

:<math>
s_x=\frac{s_y}{|m|}\sqrt{\frac{1}{n}+\frac{\bar{y}^2}{m^2\sum{(x_i-\bar{x})^2}}}
</math>

where the calculation involves the following variables:

* standard deviation of the residuals, <math>s_y</math> <math>=\sqrt{\frac{\sum{(y_i-mx_i-b)}^2}{n-2}}</math>
* absolute value of the slope of the least-squares line, <math>m</math>
* y-intercept of the linear curve, <math>b</math>
* number of standards, <math>n</math>
* average measurement of the standards, <math>\bar{y}</math>
* concentrations of the standards, <math>x_i</math>
* average concentration of the standards, <math>\bar{x}</math>

==See also==
* [[Biology:Standard curve|Standard curve]]
*[[Isotope dilution]]
* [[Chemistry:Internal standard|Internal standard]]

==References==
<references />
{{Analytical chemistry}}

[[Category:Analytical chemistry]]
[[Category:Laboratory techniques]]

{{Sourceattribution|Standard addition}}