Analytical balances uncertainties

The average accuracy of the data was 4.9% for volume, 2.5% for mass and 5.6% for the particulate matter levels. Future improvements in our technique of measurement of Ah will permit a decrease in the uncertainty of PMi0 levels to about 4%. Further decreases in the final error are limited by the quality of mass measurements. For example, a decrease of 0.001 g in the uncertainty of mass measurements will reduce the PM10 final error to a value as low as 0.5%. Thus, we are now focusing efforts in the improvement of our weighting procedure, particularly in what concerns ambient conditions for the operation of the analytical balance. 

Using information on the purity of the material used to prepare the spiked sample, and the accuracy and precision of the volumetric glassware and analytical balance used, the uncertainty in the concentration of Cl solvent red 24 in the sample, (CRM), was estimated as 0.05 mg l-1.1 The uncertainties associated with the concentration of quinizarin and Cl solvent yellow 124 were estimated as 0.025 mg 1 1 and 0.062 mg 1 1, respectively. The relevant values are ... 

Generally, the absolute uncertainty of a mass obtained with an analytical balance will be on the order of 0.0001 g. Thus the relative uncertainty of the denominator Sjj/D is... 

More accurate density measurements may be made by instruments that take advantage of the principle of Archimedes, where the apparent weight of an object immersed in a fluid is diminished by that of the fluid displaced. In the simplest version of this experiment, a sinker of known mass and volume is immersed in the fluid while suspended by a wire from an analytical balance. More sophisticated versions may use a magnet to suspend the sinker or measure the difference between two sinkers of similar mass and surface area but different volume. With care and good control of temperature and pressure, such instruments can achieve uncertainties of 0.02% or lower for both vapor and liquid densities. 

Single-pan analytical balance. There are a great variety of single-pan analytical balances, but most have a capacity of 80.-150. g with an uncertainty of +0.0001 g. Since the effects of chemical fumes are very critical at this level of uncertainty, these balances are usually kept in a balance room separate from the laboratory. These balances are very expensive and require tender loving care in their operation. Two basic types are shown in FIGURE C.4.a and C.4.b. 

The remainder of this chapter will be devoted to indeterminate errors, those fra- which we cannot assign a specific reason but which represent the very limits of our ability to observe and the limits of the instruments we employ. If an analytical balance can detect a change of 0.0001 g, each measurement will be uncertain at least to this extent. We term the uncertainty random because it is as likely to be negative as positive. The magnitude of the error is much more likely to be small the probability of occurrence of an error fells with the size of the uncertainty. 

Balances of interest in this book are often classified with respect to their resolution, i.e., the smallest mass difference that can be reliably measured. Generally, the better the resolution, the lower the maximum mass that can be reliably weighed. Thus, the term analytical balance is generally applied to a device that can measure up to a few hundred grams with an uncertainty of 0.1 mg a semi-microbalance can weigh up to a few tens of grams with an uncertainty of 0.01 mg a microbalance is limited to a few grams with an uncertainty of 0.001 mg and an ultramicrobalance can handle only very small loads but can provide uncertainties of as httle as 0.1 p.g. 

Weigh a clean dry weighing bottle mass of empty bottle mj = 9.8916 g, with an estimated uncertainty 8mj = 0.0005 g (an analytical balance. Section 2.3). 

For analytical balances and microbalances the contribution of the components to measurement uncertainty are very different. For the lower weighing range, repeatability is by far the most important. For precision balances and industrial scales, this is less prominent. But testing frequencies (see Sect. 29.1.6) are, via risk assessment, for these balances are largely determined by checking repeatability and sensitivity. 

Calibration errors should be ascertained with a certified test weight of substantially lower uncertainty than the calibration tolerance of the balance (insofar as this is possible or necessary in practice). In the finest analytical balances, the achievable calibration-error tolerance is dictated by the accuracy of the available mass standards. However, this limitation is not relevant at the level of 0.1 % to 0.01 % accuracy applicable to most laboratory work. 

By definition, the last significant digit obtained from an instrument or a calculation has an associated uncertainty. Rounding leads to a nominal value, but it does not allow for expression of the inherent uncertainty. To do this, the uncertainties of each contributing factor, device, or instrument must be known and accounted for. For measuring devices such as analytical balances, Eppen-dorf pipets, and flasks, that value is either displayed on the device, supplied by the manufacturer, or determined empirically. Because these values are known, it is also possible to estimate the uncertainty (i.e., potential error) in any combined calculation. The only caveat is that the units must be the same. On an analytical balance, the imcertainty would be listed as 0.0001 g, whereas the rmcertainty on a volumetric flask would be reported as 0.12 mL. These are absolute uncertainties that cannot be combined as is, because the units do not match. To combine uncertainties, relative uncertainties must be used. These can be expressed as "1 part per. .." or as a percentage. That way, the units cancel and a relative imcertainty results, which may then be combined with other uncertainties expressed the same way (i.e., as unitless value). 

When analytical uncertainties are propagated through a mass balance model, is... 

Limit of detection (LOD) sounds like a term that is easily defined and measured. It presumably is the smallest concentration of analyte that can be determined to be actually present, even if the quantification has large uncertainty. The problem is the need to balance false positives (concluding the analyte is present, when it is not) and false negatives (concluding the analyte is absent, when it is really present). The International Union of Pure and Applied Chemistry (IUPAC) and ISO both shy away from the words limit of detection, arguing that this term implies a clearly defined cutoff above which the analyte is measured and below which it is not. The IUPAC and ISO prefer minimum detectable (true) value and minimum detectable value of the net state variable, which in analytical chemistry would become minimum detectable net concentration. Note that the LOD will depend on the matrix and therefore must be validated for any matrices likely to be encountered in the use of the method. These will, of course, be described in the method validation document. 

The comparisons may take place every time a measurement is made (e.g., calibration of an analytical measurement using a standard solution), periodically (e.g., calibration of the balance), or infrequently (e.g., validation of a method). The reference value is used to either calibrate the process or to check its calibration or validity. The number of steps in the chain of comparisons should be kept to a minimum as each additional step introduces additional errors and increases the overall uncertainty. Interlaboratory comparisons provide evidence of comparability and provide confidence in traceability claims they do not, however, provide traceability directly. 

Determination of amount of substance often requires measurements of different properties, for example sample mass, on a balance compared to a mass reference analyte identity by comparison to a reference, perhaps using a spectrometer and a database of known compounds and analyte quantitation by comparison to a different reference, perhaps a reference material. Each property of the result should be traceable, and each may contribute uncertainty to the reported result. Thus, claims of traceability of a result must include not only a description of the references and uncertainty budgets for comparison to them, but also a description of the scope of traceability. 

Because much of Wollaston s platinum was produced by this second process, we decided to purify a crude platinum sample by this method to see if the purity of the product was adversely affected. The analytical results are given in Table IV and indicate that the platinum purified by the second process did not differ in any important respects from that obtained by the first process. The slight decrease in platinum content (98.57% to 97.35%) is balanced by small increases in the levels of the metallic impurities. Given the inherent uncertainties in the sampling procedure, the compositional differences between the platinum produced by the two methods are insignificant. The relative proportions of... 

One can also use phreeqc to perform inverse mass balance modeling for the same calculations, phreeqc is capable of taking into account the analytical uncertainties. Here, we assume the analyses of snow and groundwater samples carry 6% errors. The input file is listed in Table 9.3. The readers are referred to the phreeqc manual for a detailed explanation of the input file (Parkhurst and Appelo, 1999). 

Most of the commonly used models compute a cation/anion equivalent balance, but even this information is seldom translated into error for any subsequent calculation. No codes currently incorporate known analytical precision into evaluation of the error and uncertainty of speciation, saturation index, or mass transfer calculations. Future codes such as INTERP (Appendix) or the expert system of Pearson and others described in this volume, should include an optimization routine which would calculate the propagation of these reported errors, and compute bounding values that clearly define the magnitude of uncertainty. 

The problem has 2 parts. In the first part the sample T-93 is speciated on the Macinnes, and unsealed conventions, respectively, using the measured pH. In the second part an attempt is made to resolve uncertainties in the carbonate system by assuming the brine is in equilibrium with calcite, on the Macinnes and unsealed conventions, respectively. Use of calcite equilibrium is preferable to alternate means of defining pH, such as through charge balance, owing to uncertainties in the analytical data. 

Typical values of these correction factors are a = 0.095 and /S = 1.032 (P. W. Percival, unpublished results from S.I.N.). However, in the end a finite systematic uncertainty is always introduced by this procedure this is balanced by the statistical and analytical advantages. ... 

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