Determination of experimental error

Measurement-determination error has been discussed in Sect. 2.1.4. 

Design of Experiments in Chemical Engineering. Zivorad R. Lazic Copyright 2004 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim ISBN 3-527-31142-4 

The error square average of a trial has the well-known form  

An increase in S2 or S values characterizes larger dispersion of trials outcomes around the average (y ). In accord with expression (1.69), we may estimate the deviation of the average yu from the real value of a trial (yu) with significance level (a)  

Determine confidence interval where the value of trial yu will lie with 95% confidence. Use values from Example 2.6 (yu=31.2 n=5). By analogy with Sect. 2.1.4, expression (2.27) or expression (2.128) become  

---

The mathematical requirements for unique determination of the two slopes mi and ni2 are satisfied by these two measurements, provided that the second equation is not a linear combination of the first. In practice, however, because of experimental error, this is a minimum requirement and may be expected to yield the least reliable solution set for the system, just as establishing the slope of a straight line through the origin by one experimental point may be expected to yield the least reliable slope, inferior in this respect to the slope obtained from 2, 3, or p experimental points. In univariate problems, accepted practice dictates that we... 

Berthelot showed that the mean compressibility between 1 and 2 atm. does not differ appreciably from that between 0 and 1 atm. in the case of permanent gases, and either may be used within the limits of experimental error. But in the case of easily liquefiable gases the two coefficients are different. According to Berthelot and Guye the value of aJ can be determined from that of aj by means of a small additive correction derived from the critical data, and the linear extrapolation then applied Gray and Burt consider, however, that this method may lead to inaccuracies, and consider that the true form of the isothermal can only be satisfactorily ascertained by the experimental determination of a large number of points, followed by graphical extrapolation. 

Many other distances determined to within 0.1 or 0.2 A could be tabulated, but the limit of experimental error is so large as to make a comparison with these values no test of the radii. 

In many analyses, fhe compound(s) of inferesf are found as par of a complex mixfure and fhe role of fhe chromatographic technique is to provide separation of fhe components of that mixture to allow their identification or quantitative determination. From a qualitative perspective, the main limitation of chromatography in isolation is its inability to provide an unequivocal identification of the components of a mixture even if they can be completely separated from each other. Identification is based on the comparison of the retention characteristics, simplistically the retention time, of an unknown with those of reference materials determined under identical experimental conditions. There are, however, so many compounds in existence that even if the retention characteristics of an unknown and a reference material are, within the limits of experimental error, identical, the analyst cannot say with absolute certainty that the two compounds are the same. Despite a range of chromatographic conditions being available to the analyst, it is not always possible to effect complete separation of all of the components of a mixture and this may prevent the precise and accurate quantitative determination of the analyte(s) of interest. 

Precise knowledge of the critical point is not required to determine k by this method because the scaling relation holds over a finite range of p at intermediate frequency. The exponent k has been evaluated for each of the experiments of Scanlan and Winter [122]. Within the limits of experimental error, the experiments indicate that k takes on a universal value. The average value from 30 experiments on the PDMS system with various stoichiometry, chain length, and concentration is k = 0.214 + 0.017. Exponent k has a value of about 0.2 for all the systems which we have studied so far. Colby et al. [38] reported a value of 0.24 for their polyester system. It seems to be insensitive to molecular detail. We expect the dynamic critical exponent k to be related to the other critical exponents. The frequency range of the above observations has to be explored further. 

Build search criteria that include information such as possible elements and the numbers of each element maximum and minimum number of double bond equivalency (DBE) maximum tolerance of experimental error in the determined exact mass. 

Deuterium exchange with DjO was used by Shuravlev and Kiselev (199) in the determination of surface hydroxyl groups of silica gel. Adsorption isotherms of HgO and DjO were determined gravi-metrically they agreed with each other within the limits of experimental error. 

The reader is cautioned that there is often a considerable divergence in the literature for values of rate constants [Buback et al., 1988, 2002], One needs to examine the experimental details of literature reports to choose appropriately the values to be used for any needed calculations. Apparently different values of a rate constant may be a consequence of experimental error, experimental conditions (e.g., differences in conversion, solvent viscosity), or method of calculation (e.g., different workers using different literature values of kd for calculating Rt, which is subsequently used to calculate kp/kXJ2 from an experimental determination of Rp). 

However, the ft values were probably incorrectly taken from Bowen s work.150 If the ft values obtained by this author are used, Pa = 0.42 and j3s = 0.057 (see Table VII), a better agreement between the calculated slope (=0.14) and the observed slope is obtained. The range of experimental error in determining the individual ft values as well as in obtaining a reliable slope from the competitive photooxygenation reaction appears to be fairly large. The difference between the calculated and the experimental slope, therefore, does not allow the abandonment of the energy-transfer mechanism. 

Kinetic gelation models [178] have been used to determine, within experimental error, the fraction of constrained and unconstrained double bonds over a wide range of conversions in the polymerization of ethylene glycol dimethacrylate. The amount of unconstrained and constrained functional groups was determined experimentally by solid state nuclear magnetic resonance spectroscopy. The rules for determining constraint in the model were that all pendant double bonds and all monomers in pools of six or less are constrained. Monomers in pools of seven or more are assumed to be unconstrained. Whether a site is constrained or not does not affect the reactivity only the analysis of the model is affected by the rules defining constraint. 

The determination of n from measurement of peff is the most familiar application of magnetic susceptibility measurements to inorganic chemists. To the extent that the spin-only formula is valid, it is possible to obtain the oxidation state of the central atom in a complex. Thus an iron complex with a peff of 5.9B.M. certainly contains Fe(III) (high-spin d5) and not Fe(II). The diamagnetism of AgO rules out its formulation as silver(II) oxide, because Ag2+ has an odd number of electrons (d9) and should be paramagnetic it contains Ag(I) and Ag(III), in equal amounts. There are, however, a number of pitfalls, especially if reliance is placed on a single measurement at room temperature. The Curie law is rarely obeyed within the limits of experimental error. This means that the measured peff is somewhat temperature-dependent. A number of factors can be responsible for deviations from ideal Curie (or even Curie-Weiss) behaviour, and/or from the spin-only formula. 

The conformation of the polytetrafluoroethylene molecule in the low temperature form (Phase II) has been determined to be 2.159 CF2 units per turn of the helix within the limits of experimental error. This conformation is slightly untwisted from the previously assigned 13/6 = 2.167 value but is substantially different from that for the 25°C form (Phase IV) in which the conformation is 15/7 = 2.143. By comparison, the planar zig-zag is 2/1 = 2.000. 

The concentration of the FLUKA albumin, as determined in weighted samples of the product using the calibration line constructed with the NIST albumin, fluctuated around the weighted amount in the range of experimental error of the determination considered as the 95% tolerance limit. The data were evaluated using EXCEL 97. 

For the application of this test, the experimental error must be known. One way of determining the experimental error is to carry out a set of tests, conducted in identical conditions. The relationship between the error from model fitting and the experimental error estimate is given by Equation 90 ... 

The theoretical data was computed without adjustable parameters and provides a nearly quantitative simulation of the experimental data. By reasonable variation of electrostatic interaction potentials (within the limits of experimental error in determining electrostatic interaction and shape parameters), completely quantitative simulation can be obtained. 

Calculate the percentage of water in the hydrate. Determine the experimental error. Show all your work. 

---