ORIGINAL

Standard addition

The method of standard addition is a type of quantitative analysis approach often used in analytical chemistry whereby the standard is added directly to the aliquots of analyzed sample. This method is used in situations where sample matrix also contributes to the analytical signal, a situation known as the matrix effect, thus making it impossible to compare the analytical signal between sample and standard using the traditional calibration curve approach.

Applications[edit]

Standard addition is frequently used in chemical instrumental analysis such as atomic absorption spectroscopy and gas chromatography.

Suppose that the concentration of silver in samples of photographic waste is to be determined by atomic-absorption spectrometry. Using the calibration curve method, an analyst could calibrate the spectrometer with some aqueous solutions of a pure silver salt and use the resulting calibration graph in the determination of the silver in the test samples. This method is only valid, however, if a pure aqueous solution of silver, and a photographic waste sample containing the same concentration of silver, give the same absorbance values. In other words, in using pure solutions to establish the calibration graph it is assumed that there are no ‘matrix effects’, i.e. no reduction or enhancement of the silver absorbance signal by other components. In many areas of analysis such an assumption is frequently invalid. Matrix effects occur even with methods such as plasma spectrometry, which have a reputation for being relatively free from interferences. The method of standard additions is usually followed to eliminate matrix effects. Experimentally, equal volumes of the sample solution are taken, all but one are separately ‘spiked’ with known and different amounts of the analyte, and all are then diluted to the same volume. The instrument signals are then determined for all these solutions and the results plotted. As usual, the signal is plotted on the y-axis; in this case the x-axis is graduated in terms of the amounts of analyte added (either as an absolute weight or as a concentration). The (unweighted) regression line is calculated in the normal way, but space is provided for it to be extrapolated to the point on the x-axis at which y = 0. This negative intercept on the x-axis corresponds to the amount of the analyte in the test sample. This value is given by b/a, the ratio of the intercept and the slope of the regression line. Similarly in gas chromatography the following procedure is used: 1) The chromatogram of the unknown is recorded 2) a known amount of the analyte(s) of interest is added 3) the sample is analyzed again under the same conditions and the chromatogram is recorded. From the increase in the peak area (or peak height), the original concentration can be computed by extrapolation. The detector response must be a linear function of analyte concentration and yield no signal (other than background) at zero concentration of the analyte.

Procedure[edit]

A typical procedure involves preparing several solutions containing the same amount of unknown, but different amounts of standard. For example, five 25 mL volumetric flasks are each filled with 10 mL of the unknown. Then the standard is added in differing amounts, such as 0, 1, 2, 3, and 4 mL. The flasks are then diluted to the mark and mixed well.

The idea of this procedure is that the total concentration of the analyte is the sum of the unknown and the standard, and that the total concentration varies linearly. If the signal response is linear in this concentration range, then a plot similar to what is shown above is generated.

Error[edit]

The x-intercept gives the concentration of the unknown. Note this value is the diluted concentration. In the procedure section above, 10 mL of unknown was diluted to 25 mL. It is this diluted concentration that is found by the x-intercept. To find the original concentration of the unknown, one must back calculate that value. The error in the x-intercept is calculated as shown below.

is the standard deviation in the residuals
is the slope of the line
is the y-intercept of the line
is the number of standards
is the average measurement of the standards
are the concentrations of the standards
is the average concentration of the standards

References[edit]

^ Harris, Daniel C. (2003). Quantitative Chemical Analysis 6th Edition. New York: W.H. Freeman.
^
^

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Standard Addition -- Draft Article

Standard addition method, often used in Analytical Chemistry, quantifies the analyte present in the unknown. This method is useful for analyzing complex samples, where a matrix effect interferes with the analyte signal. In comparison to the calibration curve method, standard addition method has the advantage of the matrix of unknown and standards being nearly identical.^[1] This minimizes the potential bias arising from the matrix effect when determining the concentration.

Variations of Standard Addition

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.^[2] There are multiple approaches to the standard addition. The following section summarize each approach.

Single Standard Addition Used in Polarography

In classic 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.^[1] This approach was the very first reported use of standard addition, and was introduced by a German mining chemist, Hans Hohn, in 1937.^[3] 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: standard solution, unknown solution, and a mixture of the standard and unknown solution. By measuring any two of these solutions, the unknown concentration is calculated.^[1]

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.^[4]

Successive Addition of Standards in Constant Sample and Total Volume

In the field outside of polarography, the Harvey's book of Spectrochemical Procedures was the next earliest reference book to mention standard addition.^[4] 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.^[2] 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.^[5]

Note that this is not limited to liquid samples. In atomic absorption spectroscopy, for example, standard additions are often used with solid as the sample.^[6]

In 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.^[5]

As this approach involves varying amount of standards added, this method is often referred in plural form, standard additions.^[4]

Example of Standard Addition

Suppose an analyst is determining the concentration of silver in samples of waste solution in photographic film by atomic absorption spectroscopy. Using the calibration curve method, the analyst can calibrate the spectrometer with a pure silver aqueous solutions, 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.

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 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 solutions are 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 regression line is calculated through 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. The x-intercept is determined by the ratio of the y-intercept and the slope of the regression line.

Limitation and Uncertainty of Standard Addition

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.^[7] 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.^[5]

Analysts also needs to evaluate the precision of the determined unknown concentration by calculating for the standard deviation, $s_{x}$ . Lower $s_{x}$ indicates greater precision of the measurements. The calculation involves following variables:

standard deviation of the residuals, $s_{y}$ $={\sqrt {\frac {\sum {(y_{i}-mx_{i}-b)}^{2}}{n-2}}}$
absolute value of the slope of the least-squares line, $m$
y-intercept of the linear curve, $b$
number of standards, $n$
average measurement of the standards, ${\bar {y}}$
concentrations of the standards, $x_{i}$
average concentration of the standards, ${\bar {x}}$

$s_{x}={\frac {s_{y}}{|m|}}{\sqrt {{\frac {1}{n}}+{\frac {{\bar {y}}^{2}}{m^{2}\sum {(x_{i}-{\bar {x}})^{2}}}}}}$

References

^ ^a ^b ^c Bader, Morris (1980). "A systematic approach to standard addition methods in instrumental analysis". Journal of Chemical Education. 57 (10): 703. doi:10.1021/ed057p703. ISSN 0021-9584.
^ ^a ^b Skoog, Douglas A.; Holler, James F.; Crouch, Stanley R. (2016). Principles of Instrumental Analysis (6th ed.). Boston, MA, USA: Cengage Learning. pp. 13–14. ISBN 978-1-305-57721-3.
^ Hohn, Hans (1937). Chemische Analysen mit dem Polarographen. Berlin, Germany: SpringerVerlag. p. 51.
^ ^a ^b ^c Harvey, Charles E. (1950). Spectrochemical Procedures (1st ed.). Glendale: Applied Research Laboratories.
^ ^a ^b ^c Robinson, James W.; Skelly Frame, Eileen M.; Frame II, George M. (2005). Introduction to Spectroscopy (6th ed.). New York: Marcel Dekker. pp. 84–87. ISBN 0-203-99730-1.
^ Fan, Xiaoyu; Li, Qing; Lin, Ping; Jin, Zhonggan; Chen, Meizi; Yi, Zu (2022). "A standard addition method to quantify serum lithium by inductively coupled plasma mass spectrometry". Ann Clin Biochem. 59 (3): 166–170.
^ Ellison, Stephen L.; Thompson, Michael (2008). "Standard additions: myth and reality". The Royal Society of Chemistry. 133 (8): 992–7.

[:0-1] Bader, Morris (1980). "A systematic approach to standard addition methods in instrumental analysis". Journal of Chemical Education. 57 (10): 703. doi:10.1021/ed057p703. ISSN 0021-9584.

[:1-2] Skoog, Douglas A.; Holler, James F.; Crouch, Stanley R. (2016). Principles of Instrumental Analysis (6th ed.). Boston, MA, USA: Cengage Learning. pp. 13–14. ISBN 978-1-305-57721-3.

[3] Hohn, Hans (1937). Chemische Analysen mit dem Polarographen. Berlin, Germany: SpringerVerlag. p. 51.

[:2-4] Harvey, Charles E. (1950). Spectrochemical Procedures (1st ed.). Glendale: Applied Research Laboratories.

[:3-5] Robinson, James W.; Skelly Frame, Eileen M.; Frame II, George M. (2005). Introduction to Spectroscopy (6th ed.). New York: Marcel Dekker. pp. 84–87. ISBN 0-203-99730-1.

[6] Fan, Xiaoyu; Li, Qing; Lin, Ping; Jin, Zhonggan; Chen, Meizi; Yi, Zu (2022). "A standard addition method to quantify serum lithium by inductively coupled plasma mass spectrometry". Ann Clin Biochem. 59 (3): 166–170.

[7] Ellison, Stephen L.; Thompson, Michael (2008). "Standard additions: myth and reality". The Royal Society of Chemistry. 133 (8): 992–7.

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