Unknown samples

Before determining the amount of Na2C03 in an unknown sample, a student decides to check her procedure by analyzing a sample known to contain 98.76% w/w Na2C03. Five replicate determinations of the %w/w Na2C03 in the standard were made with the following results... 

A potentiometric titration is used to determine if an unknown sample is pure Na2G03, a mixture of Na2G03 and NaHG03, pure Na3P04, or a mixture of Na3P04 and Na2HP04. 

This example can be used in reverse to show the usefulness of looking for such isotopes. Suppose there were an unknown sample that had two molecular ion peaks in the ratio of 3 1 that were two mass units apart then it could reasonably be deduced that it was highly likely the unknown contained chlorine. In this case, the isotope ratio has been used to identify a chlorine-containing compound. This use of mass spectrometry is widespread in general analysis of materials, and it... 

Analysis for Poly(Ethylene Oxide). Another special analytical method takes advantage of the fact that poly(ethylene oxide) forms a water-insoluble association compound with poly(acryhc acid). This reaction can be used in the analysis of the concentration of poly(ethylene oxide) in a dilute aqueous solution. Ereshly prepared poly(acryhc acid) is added to a solution of unknown poly(ethylene oxide) concentration. A precipitate forms, and its concentration can be measured turbidimetricaHy. Using appropriate caUbration standards, the precipitate concentration can then be converted to concentration of poly(ethylene oxide). The optimum resin concentration in the unknown sample is 0.2—0.4 ppm. Therefore, it is necessary to dilute more concentrated solutions to this range before analysis (97). Low concentrations of poly(ethylene oxide) in water may also be determined by viscometry (98) or by complexation with KI and then titration with Na2S202 (99). 

Sea.rch-Ma.tch. The computer identifies which crystalline phases (components) match the unknown pattern by using a file of known powder patterns maintained by the International Center for Diffraction Data (ICDD). The Powder Diffraction File contains interplanar t5 -spacings d = A/(2sin0)] and intensities of the diffraction maxima for each crystalline powder pattern submitted to the ICDD. Currendy there are about 65,000 patterns in the file. Current search—match programs can successfully identify up to seven components in an unknown pattern. A typical diffraction pattern of an unknown sample and the components identified by the computer search-match program is shown in Figure 15. 

Quantitative Phase Analysis. Once the identity of the components in a sample are known, it is possible to determine the quantitative composition of the sample. There are several different methods for doing a quantitative analysis, but the most rehable method is to use mixtures of known composition as standards. The computer can determine quantitatively the relative amounts of each component in the unknown sample. For accurate calculations of relative amounts in the unknown sample, it is necessary that the sample and standards have uniform distributions of crystaUites. Often the sample and standards are rotated during data collection to provide a more even distribution of crystaUites which diffract. 

The matrix (C) is called the generalized inverse of C. Having estimated the matrix K, one can then estimate the amounts of analytes in an unknown sample. If the number of sensors is equal to the number of analytes, iCis a square matrix. If K exists then... 

For many applications, quantitative band shape analysis is difficult to apply. Bands may be numerous or may overlap, the optical transmission properties of the film or host matrix may distort features, and features may be indistinct. If one can prepare samples of known properties and collect the FTIR spectra, then it is possible to produce a calibration matrix that can be used to assist in predicting these properties in unknown samples. Statistical, chemometric techniques, such as PLS (partial least-squares) and PCR (principle components of regression), may be applied to this matrix. Chemometric methods permit much larger segments of the spectra to be comprehended in developing an analysis model than is usually the case for simple band shape analyses. 

Due to the convoluted mass and depth scales present in an RBS spectrum, it may not be possible to accurately describe an unknown sample using a single RBS spectrum. For example. Figure 4a is an RBS spectrum acquired at a backscattering angle of 160° from a sample implanted with 2.50 x 10 atoms/cm of As at a depth of approximately 140 nm. If this were a totally unknown sample it would not be possible to determine positively the mass and depth of the implanted species from this spectrum alone, since the peak in the RBS spectrum also could have been caused by a heavier element at greater depth, such as Sb at 450 nm, or Mo at 330 nm, or by a... 

Ion implantation is often used to produce reliable standards for quantification of SIMS analyses. Ion implantation allows the introducdon of a known amount of an element into a solid sample. A sample with a major component composition similar to that of the unknown sample may be implanted to produce an accurate standard. The accuracy of quandfication using this implantation method can be as good as 2%. 

The most accurate - and most popular - method of quantifying matrix effects is to analyze the unknown sample with a similar sample of known composition. The relationship between measured intensity and the content of each sample is, usually, defined by the relative sensitivity factor (RSF) ... 

The procedure commonly used to quantify EDX spectra was originally outlined by Castaing [4.109], although for the general situation of investigating bulk materials. To a good approximation it can be assumed that the concentration Csp of an element present in an unknown sample is related to the concentration Cst of the same element in a standard specimen by... 

Because of the complex nature of the discharge conditions, GD-OES is a comparative analytical method and standard reference materials must be used to establish a unique relationship between the measured line intensities and the elemental concentration. In quantitative bulk analysis, which has been developed to very high standards, calibration is performed with a set of calibration samples of composition similar to the unknown samples. Normally, a major element is used as reference and the internal standard method is applied. This approach is not generally applicable in depth-profile analysis, because the different layers encountered in a depth profile of ten comprise widely different types of material which means that a common reference element is not available. 

Direct analysis with the fluoride lon-selective electrode requires addition of total ionic strength adjustor buffer solution (TISAB) to the standard and to unknown samples Some advantages of this addition are that it provides a constant background ion strength, ties up interfenng cations such as aluminum or iron, which form a complex with fluoride ions, and maintains the pH between 5 0 and 5 5 According to the manufacturer s claim, reproducibility of direct electrode measurement IS 2 0%, and the accuracy for fluonde ion measurement is 0 2% [27]... 

HT 2 column with two Styragel HT 6E columns. While such a combination does not provide the highest resolution analysis, it is the best scouting tool for unknown samples. The best column combination can then be chosen for the routine analysis of the polymer. 

This definition outlines in very broad terms the scope of analytical chemistry. When a completely unknown sample is presented to an analyst, the first requirement is usually to ascertain what substances are present in it. This fundamental problem may sometimes be encountered in the modified form of deciding what impurities are present in a given sample, or perhaps of confirming that certain specified impurities are absent. The solution of such problems lies within the province of qualitative analysis and is outside the scope of the present volume. 

Running a blank determination. This consists in carrying out a separate determination, the sample being omitted, under exactly the same experimental conditions as are employed in the actual analysis of the sample. The object is to find out the effect of the impurities introduced through the reagents and vessels, or to determine the excess of standard solution necessary to establish the end-point under the conditions met with in the titration of the unknown sample. A large blank correction is undesirable, because the exact value then becomes uncertain and the precision of the analysis is reduced. 

Running a control determination. This consists in carrying out a determination under as nearly as possible identical experimental conditions upon a quantity of a standard substance which contains the same weight of the constituent as is contained in the unknown sample. The weight of the constituent in the unknown can then be calculated from the relation ... 

Determine the concentration of Mo in unknown samples supplied and containing less than 50 fig Mo per 10 mL use the calibration curve, and subject the unknown to the same treatment as the standard solutions. 

The unknown solution (which should contain between 0.5 and 2.0mg phenol L 1) is treated in the manner described above, and by reference to the calibration curve the absorbance reading will determine the phenol content of the unknown sample. 

We may now deal with some of the procedures employed in quantitative spectrographic analysis. In the comparison sample method, the spectrum of an unknown sample is compared with the spectra of a range of samples of known composition (e.g. those supplied by the US Bureau of Standards) with respect to a particular component or components. The spectra of the unknown and of the various standards are photographed on the same plate under the same conditions. The concentrations of the desired constituent can then be estimated by comparing the blackening of the lines of the particular constituent with the same lines on the standards visual or photometric comparison of blackening may be used. 

Prepare a calibration curve for each element (see Section 21.16) and use this to evaluate the concentration of any unknown sample (see Note). 

We will explore the two major families of chemometric quantitative calibration techniques that are most commonly employed the Multiple Linear Regression (MLR) techniques, and the Factor-Based Techniques. Within each family, we will review the various methods commonly employed, learn how to develop and test calibrations, and how to use the calibrations to estimate, or predict, the properties of unknown samples. We will consider the advantages and limitations of each method as well as some of the tricks and pitfalls associated with their use. While our emphasis will be on quantitative analysis, we will also touch on how these techniques are used for qualitative analysis, classification, and discriminative analysis. 

Use the Information to learn how to make accurate predictions about unknown samples. 

The data in the training set are used to derive the calibration which we use on the spectra of unknown samples (i.e. samples of unknown composition) to predict the concentrations in those samples. In order for the calibration to be valid, the data in the training set which is used to find the calibration must meet certain requirements. Basically, the training set must contain data which, as a group, are representative, in all ways, of the unknown samples on which the analysis will be used. A statistician would express this requirement by saying, "The training set must be a statistically valid sample of the population... 

This requirement is pretty easy to accept. It makes sense that, if we are going to generate a calibration, we must construct a training set that exhibits all the forms of variation that we expect to encounter in the unknown samples. We certainly would not expect a calibration to produce accurate results if an unknown sample contained a spectral peak that was never present in any of the calibration samples. 

The data in the validation set are used to challenge the calibration. We treat the validation samples as if they are unknowns. We use the calibration developed with the training set to predict (or estimate) the concentrations of the components in the validation samples. We then compare these predicted concentrations to the actual concentrations as determined by an independent referee method (these are also called the expected concentrations). In this way, we can assess the expected performance of the calibration on actual unknowns. To the extent that the validation samples are a good representation of all the unknown samples we will encounter, this validation step will provide a reliable estimate of the calibration s performance on the unknowns. But if we encounter unknowns that are significantly different from the validation samples, we are likely to be surprised by the actual performance of the calibration (and such surprises are seldom pleasant). 

When we measure the spectrum of an unknown sample, we assemble it into an absorbance matrix. If we are measuring a single unknown sample, our unknown absorbance matrix will have only one column (for MLR or PCR) or one row (for PLS). If we measure the spectra of a number of unknown samples, we can assemble them together into a single unknown absorbance matrix just as we assemble training or validation spectra. 

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