Percent Analyte Calculations

As with gravimetric analysis, the weight of the sample (the denominator in Equation (4.33)) is determined by direct measurement in the laboratory or by weighing by difference. The weight of the analyte in the sample is determined from the titration data via a stoichiometry calculation. As discussed previously, we calculate moles of substance titrated (in this case, the analyte) as in Equation (4.21)  

The weight of the analyte is then calculated by multiplying by its formula weight (grams per mole)  

If normality and equivalents are used, we calculate equivalents of analyte as in Equation (4.25) (again, the substance titrated is the analyte)  

The weight of the analyte (the numerator in Equation (4.33)) can then be calculated by multiplying the equivalents of substance titrated by the equivalent weight (grams per equivalent)  

In the analysis of a sample for KH2P04 content, a sample weighing 0.3994 g required 18.28 mL of 0.1011 M KOH for titration. The equation below represents the reaction involved. What is the percent KH2P04 in this sample  

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In the calculation of the percent analyte when using a back titration, the following appears in the numerator ... 

Since the sensory data collected involved degree of sample difference from a reference, it was felt that the analytical data should be analyzed in a similar manner. In cases where some peaks making up a multicomponent mixture are known to be specific to that mixture, this is a relatively simple matter. In such cases, the peak areas of the known components can be compared to a reference and average percent difference calculated. However, if it is not possible to pick out peaks that are clearly specific to a single multicomponent mixture, a more sophisticated technique such as factor analysis is required. There are circumstances where all peaks are common to each multicomponent mixture, i.e. qualitatively similar but quantitatively different. Also there are cases where peaks are found only in one of the multicomponent mixtures, but it is not clear to which mixture they belong. In these cases factor analysis is required to extract patterns that are characteristic of the specific multicomponent mixtures. Analytical concentrations of each of the multicomponent mixtures are then calculated as a set of factor scores where each score is directly proportional to the actual concentration of each multicomponent mixture. 

The confirmation of a compound s identity is only one half of the overall confirmation procedure quantitative confirmation is the other half. Compound concentrations calculated from analyses on two columns or two detectors must be in agreement. The EPA recommends a 40 percent difference (calculated as the RPD shown in Equation 1, Table 2.2) as a threshold value for making decisions on the presence or absence of a compound (EPA, 1996a). This means that the concentrations obtained from two columns or two detectors that agree within 40 percent indicate the presence of an analyte, provided that the retention time confirmation criterion has been also met. 

We observe from numerical simulations an exponential decrease of the survival probability Sf(t) in the potential well, at the bottom of which we initialize the process. Moreover, we find that the mean crossing time assumes the scaled form (114) with scaling exponent p being approximately constant in the range 1 < a // 1.6, followed by an increase before the apparent divergence at a = 2, that leads back to the exponential form of the Brownian case, Eq. (113). An analytic calculation in the Cauchy limit a = 1 reproduces, consistently with the constant flux approximation commonly applied in the Brownian case, the scaling Tc 1/D, and, within a few percent error, the numerical value of the mean crossing time Tc. 

In a manner similar to that used to derive Equation 5.22, we can list the steps in arriving at a general expression for calculating the percent analyte A in a sample determined by titrating a known weight of sample with a standard solution of titrant T ... 

How to calculate weight and percent analyted from molarities, volumes, and reaction ratios (Key equations 5.5, 5.17-5.22, 5.27), p. 160... 

Considerable work has already been done on such systems in temperature ranges for which the condensed-phase component appears in the gas phase in only small amounts, so that the analytical calculations can be simplified accordingly. Only very limited data are available in regions (the concentration of the condensed-phase component in the gas phase is sufficiently large—several percent) for which such simplifications may result in large errors, thereby necessitating solution of the general equilibrium equations. 

The dimensions of the sides of the parallelepiped are conveniently taken as the difference between extreme atomic points along the inertial axes plus the largest atomic radius. An analytical calculation of molecular volume is also possible [12], although differences between the various methods of calculation usually do not exceed a few percent for non-strained molecules. 

When chemists believe that they have synthesized a new compound, a sample is generally sent to an analytical laboratory where its percent composition is determined. This experimentally determined percent composition is then compared with the percent composition calculated from the formula of the expected compound. In this way, chemists can see if fhe compound obtained could be the one expected. 

Spike Recoveries One of the most important quality assessment tools is the recovery of a known addition, or spike, of analyte to a method blank, field blank, or sample. To determine a spike recovery, the blank or sample is split into two portions, and a known amount of a standard solution of the analyte is added to one portion. The concentration of the analyte is determined for both the spiked, F, and unspiked portions, I, and the percent recovery, %R, is calculated as... 

Quantitative mass spectrometry, also used for pharmaceutical appHcations, involves the use of isotopicaHy labeled internal standards for method calibration and the calculation of percent recoveries (9). Maximum sensitivity is obtained when the mass spectrometer is set to monitor only a few ions, which are characteristic of the target compounds to be quantified, a procedure known as the selected ion monitoring mode (sim). When chlorinated species are to be detected, then two ions from the isotopic envelope can be monitored, and confirmation of the target compound can be based not only on the gc retention time and the mass, but on the ratio of the two ion abundances being close to the theoretically expected value. The spectrometer cycles through the ions in the shortest possible time. This avoids compromising the chromatographic resolution of the gc, because even after extraction the sample contains many compounds in addition to the analyte. To increase sensitivity, some methods use sample concentration techniques. 

For a problem for which we cannot obtain an analytical solution, you need to determine sensitivities numerically. You compute (1) the cost for the base case, that is, for a specified value of a parameter (2) change each parameter separately (one at a time) by some arbitrarily small value, such as plus 1 percent or 10 percent, and then calculate the new cost. You might repeat the procedure for minus 1 percent or 10 percent. The variation of the parameter, of course, can be made arbitrarily small to approximate a differential however, when the change approaches an infinitesimal value, the numerical error engendered may confound the calculations. 

PER) was modified in several respects. The diets were calculated on a 10 percent protein level rather than on an isonitrogenous basis. This was done because the nitrogen factors of the various blend components varied appreciably from the 6.25 nitrogen factor assumed in the AOAC procedure. A composite nitrogen factor for each blend was calculated from analytical results by dividing the total amino acid content by the nitrogen content. In this manner,... 

In each of these cases, the percent of the analyte is often calculated. The weight percent of an analyte in a sample is calculated using the definition of weight percent ... 

The weight of the precipitate after filtering and drying can then be measured free of any influence from the NaCl and converted back to the weight of the analyte with the use of a gravimetric factor (see the next section) and its percent in the sample calculated. Examples are given in Section 3.6.4. 

In the case in which the analyte participates in a chemical reaction, the product of which is weighed, the weight of this product must be converted to the weight of the analyte before the percent can be calculated. 

The ultimate goal of any titrimetric analysis is to determine the amount of the analyte in a sample. This involves the stoichiometry calculation mentioned in the Work the Data section of the analytical strategy flow chart in Figure 4.1. This amount of analyte is often expressed as a percentage, as it was for the gravimetric analysis examples in Chapter 3. This percentage is calculated via the basic equation for percent used previously for the gravimetric analysis examples ... 

It may be possible to evaluate the percent extracted by a separate experiment. A solution of the analyte in the original solvent may be prepared such that WOTig (before extraction) is known. Following this, an extraction is performed on this solution using a particular volume of extracting solvent (V ). This volume of extract is then analyzed quantitatively for the analyte by some appropriate analysis technique. Knowing the concentration of the analyte and the volume of extract converted to liters (L ), one can calculate the percent extracted ... 

The accuracy of an analysis can be determined by several procedures. One common method is to analyze a known sample, such as a standard solution or a quality control check standard solution that may be available commercially, or a laboratory-prepared standard solution made from a neat compound, and to compare the test results with the true values (values expected theoretically). Such samples must be subjected to all analytical steps, including sample extraction, digestion, or concentration, similar to regular samples. Alternatively, accuracy may be estimated from the recovery of a known standard solution spiked or added into the sample in which a known amount of the same substance that is to be tested is added to an aliquot of the sample, usually as a solution, prior to the analysis. The concentration of the analyte in the spiked solution of the sample is then measured. The percent spike recovery is then calculated. A correction for the bias in the analytical procedure can then be made, based on the percent spike recovery. However, in most routine analysis such bias correction is not required. Percent spike recovery may then be calculated as follows ... 

It is required for quantitative purity assays, and it must be established across the specified range of the analytical procedure. This can be done, by establishing the recovery rate over the range of the method. Alternatively, a method comparison between a validated method and a new method can be performed. Accuracy can be determined by spiking degraded, aggregated, pure or impure material into a known amount of sample. A theoretical recovery would then be calculated and the spike material analyzed using the chosen method. The actual recovery should then be compared to the theoretical recovery to calculate the accuracy of the method. Accuracy in this case would be reported as percent recovery. 

Calculation of mean for control standards at the end of analytical test series as percent of control standard at the beginning of the test series and assessment against the predefined acceptance criteria... 

As a further means of comparing the datasets produced by the two techniques, group means, standard deviation from mean, and percent relative standard deviation from mean were calculated for each measured element as a way of quantifying the amount of dispersion present in each analytical group (Table Ila and b). 

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