Standards external

The most commonly employed standardization method uses one or more external standards containing known concentrations of analyte. These standards are identified as external standards because they are prepared and analyzed separately from the samples. 

A quantitative determination using a single external standard was described at the beginning of this section, with k given by equation 5.3. Once standardized, the concentration of analyte, Ca, is given as 

A standard solution containing a known amount of analyte, prepared separately from samples containing the analyte. 

A spectrophotometric method for the quantitative determination of Pb + levels in blood yields an Sjtand of 0.474 for a standard whose concentration of lead is 1.75 ppb. How many parts per billion of Pb + occur in a sample of blood if Ssamp is 0.361  

Equation 5.3 allows us to calculate the value of k for this method using the data for the standard 

Of course, we still have the problem of selecting a compound that doesn t interfere with the spectrum and that has a suitable relaxation time but we don t need to worry about its volatility. What would be really good is a standard that doesn t interfere with the sample at all. Something that has no relaxation 

Automated sample injection systems and multiport injection valves (HPLC) have good reproducibility so that a series of injections can be made with a 

The mixture is then analysed and the amount of the components in the sample calculated using the peak area data for the standard mixture. Therefore, if the recorded peak area for the component in a sample mixture is v4mjx then the amount of component x is 

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A calibration curve prepared using several external standards. 

Colorplate i shows an example of a set of external standards and their corresponding normal calibration curve. 

Adjusting the matrix of an external standard so that it is the same as the matrix of the samples to be analyzed. 

An external standardization allows a related series of samples to be analyzed using a single calibration curve. This is an important advantage in laboratories where many samples are to be analyzed or when the need for a rapid throughput of samples is critical. Not surprisingly, many of the most commonly encountered quantitative analytical methods are based on an external standardization. 

Since a standard additions calibration curve is constructed in the sample, it cannot be extended to the analysis of another sample. Each sample, therefore, requires its own standard additions calibration curve. This is a serious drawback to the routine application of the method of standard additions, particularly in laboratories that must handle many samples or that require a quick turnaround time. For example, suppose you need to analyze ten samples using a three-point calibration curve. For a normal calibration curve using external standards, only 13 solutions need to be analyzed (3 standards and 10 samples). Using the method of standard additions, however, requires the analysis of 30 solutions, since each of the 10 samples must be analyzed three times (once before spiking and two times after adding successive spikes). 

The method of standard additions can be used to check the validity of an external standardization when matrix matching is not feasible. To do this, a normal calibration curve of Sjtand versus Cs is constructed, and the value of k is determined from its slope. A standard additions calibration curve is then constructed using equation 5.6, plotting the data as shown in Figure 5.7(b). The slope of this standard additions calibration curve gives an independent determination of k. If the two values of k are identical, then any difference between the sample s matrix and that of the external standards can be ignored. When the values of k are different, a proportional determinate error is introduced if the normal calibration curve is used. 

The successful application of an external standardization or the method of standard additions, depends on the analyst s ability to handle samples and standards repro-ducibly. When a procedure cannot be controlled to the extent that all samples and standards are treated equally, the accuracy and precision of the standardization may suffer. For example, if an analyte is present in a volatile solvent, its concentration will increase if some solvent is lost to evaporation. Suppose that you have a sample and a standard with identical concentrations of analyte and identical signals. If both experience the same loss of solvent their concentrations of analyte and signals will continue to be identical. In effect, we can ignore changes in concentration due to evaporation provided that the samples and standards experience an equivalent loss of solvent. If an identical standard and sample experience different losses of solvent. 

A multiple-point standardization presents a more difficult problem. Consider the data in Table 5.1 for a multiple-point external standardization. What is the best estimate of the relationship between Smeas and Cs It is tempting to treat this data as five separate single-point standardizations, determining k for each standard and reporting the mean value. Despite its simplicity, this is not an appropriate way to treat a multiple-point standardization. 

Data for Hypothetical Multiple-Point External Standardization... 

Using the Regression Equation Once the regression equation is known, we can use it to determine the concentration of analyte in a sample. When using a normal calibration curve with external standards or an internal standards calibration curve, we measure an average signal for our sample, Yx, and use it to calculate the value of X... 

The equation for a normal calibration curve using external standards is... 

An analytical method is standardized by determining its sensitivity. There are several approaches to standardization, including the use of external standards, the method of standard addition. 

Standardization—External standards, standard additions, and internal standards are a common feature of many quantitative analyses. Suggested experiments using these standardization methods are found in later chapters. A good project experiment for introducing external standardization, standard additions, and the importance of the sample s matrix is to explore the effect of pH on the quantitative analysis of an acid-base indicator. Using bromothymol blue as an example, external standards can be prepared in a pH 9 buffer and used to analyze samples buffered to different pHs in the range of 6-10. Results can be compared with those obtained using a standard addition. 

The following standardization data were provided for a series of external standards of Cd + that had been buffered to a pH of 4.6. " ... 

The generalized standard addition method (GSAM) extends the analysis of mixtures to situations in which matrix effects prevent the determination of 8x and 8y using external standards.When adding a known concentration of analyte to a solution containing an unknown concentration of analyte, the concentrations usually are not additive (see question 9 in Chapter 5). Conservation of mass, however, is always obeyed. Equation 10.11 can be written in terms of moles, n, by using the relationship... 

When possible, a quantitative analysis is best conducted using external standards. Unfortunately, matrix interferences are a frequent problem, particularly when using electrothermal atomization. Eor this reason the method of standard additions is often used. One limitation to this method of standardization, however, is the requirement that there be a linear relationship between absorbance and concentration. 

M HNO3. The concentration of Cu and Zn in the diluted supernatant is determined by atomic absorption spectroscopy using an air-acetylene flame and external standards. Copper is analyzed at a wavelength of 324.8 nm with a slit width of 0.5 nm, and zinc is analyzed at 213.9 nm with a slit width of 1.0 nm. Background correction is used for zinc. Results are reported as micrograms of Cu or Zn per gram of FFDT. 

What is the proper matrix for the external standards and the blank ... 

Standardizing the Method Equations 10.32 and 10.33 show that the intensity of fluorescent or phosphorescent emission is proportional to the concentration of the photoluminescent species, provided that the absorbance of radiation from the excitation source (A = ebC) is less than approximately 0.01. Quantitative methods are usually standardized using a set of external standards. Calibration curves are linear over as much as four to six orders of magnitude for fluorescence and two to four orders of magnitude for phosphorescence. Calibration curves become nonlinear for high concentrations of the photoluminescent species at which the intensity of emission is given by equation 10.31. Nonlinearity also may be observed at low concentrations due to the presence of fluorescent or phosphorescent contaminants. As discussed earlier, the quantum efficiency for emission is sensitive to temperature and sample matrix, both of which must be controlled if external standards are to be used. In addition, emission intensity depends on the molar absorptivity of the photoluminescent species, which is sensitive to the sample matrix. 

When possible, quantitative analyses are best conducted using external standards. Emission intensity, however, is affected significantly by many parameters, including the temperature of the excitation source and the efficiency of atomization. An increase in temperature of 10 K, for example, results in a 4% change in the fraction of Na atoms present in the 3p excited state. The method of internal standards can be used when variations in source parameters are difficult to control. In this case an internal standard is selected that has an emission line close to that of the analyte to compensate for changes in the temperature of the excitation source. In addition, the internal standard should be subject to the same chemical interferences to compensate for changes in atomization efficiency. To accurately compensate for these errors, the analyte and internal standard emission lines must be monitored simultaneously. The method of standard additions also can be used. 

Description of Method. Adding BaC to an acidified sample precipitates S04 a BaS04. The concentration of S04 may be determined either by turbidimetry or nephelometry using an incident source of radiation of 420 nm. External standards containing known concentrations of S04 are used to standardize the method. 

Samples of car exhaust are collected using a 4-L glass bottle evacuated to a level of less than 2 torr. A normal calibration curve using external standards of known Pco is used to determine the Pco in the exhaust samples. 

The %w/w lead in a lead-based paint Standard Reference Material and in unknown paint chips is determined by atomic absorption using external standards. 

Samples of urine are analyzed for riboflavin before and after taking a vitamin tablet containing riboflavin. Concentrations are determined using external standards or by the method of standard additions, fluorescence is monitored at 525 nm using an excitation wavelength of 280 nm. 

In the absence of Fe +, the membrane is colorless, but when immersed in a solution of Fe + and C, the membrane develops a red color as a result of the formation of a Fe +-bathophenanthroline complex. A calibration curve determined using a set of external standards with known molar concentrations of Fe + gave a standardization relationship of... 

Gluodenis describes the use of ICP to analyze samples containing Pb and Ni in brass. The analysis for Pb uses external standards prepared from brass samples containing known amounts of lead. Results are shown in the following table. ... 

Quantitative Analysis Using External Standards To determine the concentration of analyte in a sample, it is necessary to standardize the electrode. If the electrode s response obeys the Nernst equation. 

The concentration of Ca + in a water sample was determined by the method of external standards. The ionic strength of the samples and standards was maintained at a nearly constant level by making each solution 0.5 M in KNO3. The measured cell potentials for the external standards are shown in the following table. 

Electrochemical methods covered in this chapter include poten-tiometry, coulometry, and voltammetry. Potentiometric methods are based on the measurement of an electrochemical cell s potential when only a negligible current is allowed to flow, fn principle the Nernst equation can be used to calculate the concentration of species in the electrochemical cell by measuring its potential and solving the Nernst equation the presence of liquid junction potentials, however, necessitates the use of an external standardization or the use of standard additions. 

The purity of a sample of K3Fe(CN)6 was determined using linear-potential scan hydrodynamic voltammetry at a glassy carbon electrode using the method of external standards. The following data were obtained for a set of calibration standards. 

Calibration curves are usually constructed by analyzing a series of external standards and plotting the detector s signal as a function of their known concentrations. As long as the injection volume is identical for every standard and sample, calibration curves prepared in this fashion give both accurate and precise results. Unfortunately, even under the best of conditions, replicate injections may have volumes that differ by as much as 5% and often may be substantially worse. For this... 

For a single-point external standard (omitting the internal standard) the relationship between peak area, A2, and the concentration, C2, ofp-xylene is... 

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