Uncertainty weighing

The weighing operations are present in the dry-base correction factor (three) and in the sample metal content (one). Two contributions for the associated uncertainty, weighing, were studied ... 

Recording a measurement provides information about both its magnitude and uncertainty. For example, if we weigh a sample on a balance and record its mass as 1.2637 g, we assume that all digits, except the last, are known exactly. We assume that the last digit has an uncertainty of at least 1, giving an absolute uncertainty of ... 

Suppose the weight of the can is 61 1 grams and the weight of the can plus water is 406 1 grams. Calculate the weight of the water and the maximum uncertainty in the weight caused by the uncertainties in each of the two weighings. 

This solution is widely employed, particularly for the titration of organic adds. Barium carbonate is insoluble, so that a clear solution is a carbonate-free strong alkali. The relative molecular mass of Ba(0H)2,8H20 is 315.50, but a standard solution cannot be prepared by direct weighing owing to the uncertainty of the... 

The standard uncertainty arising from random effects is typically measured from precision studies and is quantified in terms of the standard deviation of a set of measured values. For example, consider a set of replicate weighings performed in order to determine the random error associated with a weighing. If the true mass of the object being weighed is 10 g exactly, then the values obtained might be as follows ... 

Rogers presented a comprehensive theory of the weighing method including an uncertainty analysis. 

The overall assessment factor is the product of a number of assessment factors accounting for uncertainties related to various extrapolation steps (inter- and intraspecies, route-to-route, subchro-nic-to-chronic, LOAEL-to-NOAEL, namre and severity of effect, and database-deficiency). However, the higher the number of extrapolation steps, the higher the level of conservatism. Since the different assessment factors are not always independent of each other, straightforward multiplication may lead to unreasonably high factors, and discussion are and weighing of individual factors are essential to establish a reliable and justifiable overall assessment factor. Some aspects to consider in the final qualitative discussion are ... 

Usually, some lines of evidence will not be suitable for direct incorporation into quantitative analysis. Semiquantitative or qualitative methods will then be needed to weigh the different lines of evidence, including the quantitative assessment, and integrate them for decision making. Methods for assessing weight of evidence were outside the scope of the workshop that developed this book but are discussed by Suter et al. (2000) and were recently the focus of another workshop (Chapman et al. 2002). Whatever method is used for weighing different lines of evidence, it will be important to characterize uncertainties in each line of evidence and show their effect on the overall assessment outcome. 

Answers (i) Viscosity ieads to incomplete drainage of the pipette (ii) In any weighing there is an uncertainty of 0.05 mg which in relation to 2 mg is 2.5% (iii) The degree of moisture absorption is uncertain (iv) Poor recovery of the analyte (v) Poor recovery of the analyte (vi) Loss of meniscus making reading of the burette inaccurate... 

Figure 4.22. Pareto chart of the contributions to the uncertainty of the quantitative NMR analysis of Profenofos. The effects are a (intra), the intralaboratory precision P(std), the purity of the proton standard w, weighings of unknown and standard MW, the molecular weights of unknown and standard. (Data kindly supplied by T Saed Al-Deen.)...

Weighing on an appropriate balance is usually a very accurate procedure, and therefore is often a candidate for the insignificance test. Uncertainty components of weighing on a modern electronic balance are given in table 6.1. 

It is worthwhile to discuss the components of the standard uncertainty of a volume measurement here. The repeatability may be independently assessed by a series of fill-and-weigh experiments with water at a controlled temperature (and therefore density) using a balance so that the uncertainty of weighing is small compared with the variation in volume. Although this may be instructive, if the whole analysis is repeated, say, ten times, then the repeatability of the use of the pipette, or any other volume measurement is part of the repeatability of the overall measurement. This shows the benefit, in terms of reaching the final estimate of measurement uncertainty more quickly, of lumping together uncertainty components. 

Spreadsheet 6.1. Data from 10 fill-and-weigh experiments of a 10-mL pipette. The masses have been converted to volumes, and the uncertainty calculation assumes the components of weighing and the volume calculation are negligible. 

Uncertainties always combine according to equations like 6.28 even if the quantities are subtracted (i.e., the squares of the uncertainties are always added). This is why a calculation that eventuates in the subtraction of two large numbers of nearly equal magnitude (e.g., weighing the captain of the ship by weighing the ship with the captain on board and subtracting the mass of the ship when the captain is not on board), is notoriously beset by large uncertainty. 

To prepare a calibration solution of 1 pmol L 1 ofCd+2 from a CRM of pure Cd metal, a mass of Cd is weighed into a flask, dissolved, and made up to the mark. The atomic weight of cadmium is 112.411 g mol 1 with uc = 0.008 g mol 1. Thus, 1.12411 g of pure cadmium metal dissolved in hydrochloric acid and made up to 1.00 L will have an amount concentration of 1.00 x 10 2 mol L 1. An aliquot of 0.100 mL of this solution made up to 1.00 L should create the desired solution of amount concentration 1.00 pmol Lr1. Until a proper estimate of the measurement uncertainty is made the significant fig-... 

A very important advantage of PLS is that it supports errors in both the X- and Y-blocks. Questions on whether the y-values (the concentrations of the analyte in the standards) can be wrong may appear exotic but the real fact is that nowadays we have such powerful instruments, so precise and so sensitive that the statement that there are no errors in the concentrations can be discussed. As Brereton pointed out [18], the standards are, most of the time, prepared by weighing and/or diluting and the quality of the volumetric hardware (pipettes, flasks, etc.) has not improved as dramatically as the electronics, accessories and, in general, instruments. Therefore, the concentration of the analyte may have a non-negligible uncertainty. This is of special concern for trace and ultra-trace analyses. Thus, MLR cannot cope with such uncertainties, but PLS can because it performs a sort of averaging i.e. factors) which can remove most... 

Ultimately, decision makers must have access to the best possible scientific analyses with full knowledge of all of the incumbent uncertainties to make the best possible public health judgments in the context of all of the legal, social, political, technological, and economic imperatives that must be weighed. 

In a gravimetric analysis, plan to have enough precipitate for a low relative uncertainty. If weighing precision is 0.3 mg, a 100-mg precipitate has a relative weighing error of 0.3% and a 300-mg precipitate has an uncertainty of 0.1 %. 

Any measurement is only as good as the skill of the person doing the work and the reliability of the equipment being used. You ve probably noticed, for instance, that you get slightly different readings when you weigh yourself on a bathroom scale and on a scale at the doctor s office, so there s always some uncertainty about your real weight. The same is true in chemistry—there is always some uncertainty in the value of a measurement. 

---