A Calibrating Signals

Signals are measured using equipment or instruments that must be properly calibrated if Sjneas is to be free of determinate errors. Calibration is accomplished against a standard, adjusting S eas until it agrees with the standard s known signal. Several common examples of calibration are discussed here. 

A 10-mL volumetric pipet was calibrated following the procedure just outlined, using a balance calibrated with brass weights having a density of 8.40 g/cm. At 25 °C the pipet was found to dispense 9.9736 g of water. What is the actual volume dispensed by the pipet  

If the buoyancy correction is ignored, the pipet s volume is reported as 

The American Chemical Society s Committee on Environmental Improvement defines standardization as the process of determining the relationship between the measured signal and the amount of analyte. A method is considered standardized when the value of k in equation 5.1 or 5.2 is known. 

A reagent of known purity that can be used to make a solution of known concentration. 

---

Thermistors have been used in another attempt to avoid heating of thermocouple wires. Unfortunately, these devices are liable to be limited in the temperature ranges within which they can be used to obtain resu lts(22). Bosisio et al developed an alternative approach in which the material properties %iere monitored by a calibrated signal at a second, lower frequency. Changes in this second signal could then be used to provide an indication of temperature. Such a system may well find seme applications, though it is liable to be expensive. 

Examples of calibration curves for the method of standard additions. In (a) the signal is plotted versus the volume of the added standard, and in (b) the signal is plotted versus the concentration of the added standard after dilution. 

A fifth spectrophotometric method for the quantitative determination of the concentration of Pb + in blood uses a multiple-point standard addition based on equation 5.6. The original blood sample has a volume of 1.00 mb, and the standard used for spiking the sample has a concentration of 1560 ppb Pb +. All samples were diluted to 5.00 mb before measuring the signal. A calibration curve of Sjpike versus Vj is described by... 

A calibration curve shows us the relationship between the measured signal and the analyte s concentration in a series of standards. The most useful calibration curve is a straight line since the method s sensitivity is the same for all concentrations of analyte. The equation for a linear calibration curve is... 

The following data were recorded during the preparation of a calibration curve, where S eas and s are the mean and standard deviation, respectively, for three replicate measurements of the signal. 

A sample is to be analyzed following the protocol shown in Figure 15.2, using a method with a detection limit of 0.05 ppm. The relationship between the analytical signal and the concentration of the analyte, as determined from a calibration curve is... 

Other instrumental advantages include its high sensitivity and a linear mass scale to m/z 10,000 at full sensitivity. The linearity of the mass scale means that it is necessary to calibrate the spectrometer using a single or sometimes two known mass standards. Some calibration is necessary because the start of the mass scale is subject to some instrumental zero offset. The digitized accumulation of spectra provides a better signal-to-noise ratio than can be obtained from one spectrum alone. 

Back-calculation is achieved by equating the individual calibration signal y i) with y, using Eq. (2.19), and calculating 100 X(y )Anominai [%]. The estimated standard deviation on X(y ), Sx, is transformed to a coefficient of variation by calculation of either CV = 100 /Xnominai or CV =... 

Option (Valid) presents a graph of relative standard deviation (c.o.v.) versus concentration, with the relative residuals superimposed. This gives a clear overview of the performance to be expected from a linear calibration Signal = A + B Concentration, both in terms of (relative) precision and of accuracy, because only a well-behaved analytical method will show most of the residuals to be inside a narrow trumpet -like curve this trumpet is wide at low concentrations and should narrow down to c.o.v. = 5% and rel. CL = 10%, or thereabouts, at medium to high concentrations. Residuals that are not randomly distributed about the horizontal axis point either to the presence of outliers, nonlinearity, or errors in the preparation of standards. 

Inject a calibration standard solution corresponding to a level at or below the estimated LOQ and obtain a signal-to-noise ratio of at least 9 1. 

In isotope dilution inductively coupled plasma-mass spectrometry (ID-ICP-MS) the spike, the unspiked and a spiked sample are measured by ICP-MS in order to determine the isotope ratio. Using this technique, more precise and accurate results can be obtained than by using a calibration graph or by standard addition. This is due to elimination of various systematic errors. Isotopes behave identically in most chemical and physical processes. Signal suppression and enhancement due to the matrix in ICP-MS affects both isotopes equally. The same holds for most long-term instrumental fluctuations and drift. Accuracy and precision obtained with ID-ICP-QMS are better than with other ICP-QMS calibration... 

Whereas the use of conventional fast atom bombardment (FAB) in the analysis of polymer/additive extracts has been reported (see Section 6.2.4), the need for a glycerol (or other polar) matrix might render FAB-MS analysis of a dissolved polymer/additive system rather unattractive (high chemical background, high level of matrix-, solvent- and polymer-related ions, complicated spectra). Yet, in selected cases the method has proved quite successful. Lay and Miller [53] have developed an alternative method to the use of sample extraction, cleanup, followed by GC in the quantitative analysis of PVC/DEHP with plasticiser levels as typically found in consumer products (ca. 30 %). The method relied on addition of the internal standard didecylphthalate (DDP) to a THF solution of the PVC sample with FAB-MS quantitation based on the relative signal levels of the [MH]+ ions of DEHP and DDP obtained from full-scan spectra, and on the use of a calibration curve (intensity ratio m/z 391/447 vs. mg DEHP/mg DDP). No FAB-matrix was added. No ions associated with the bulk of the PVC polymer were observed. It was... 

A quantitative correlation between the charges under the current and mass intensity signals can be carried out as suggested by Heitbaum and Wolter [11]. The magnitude of the mass intensity response depends not only on the electrochemical properties of the system under study but also on the permeability of the electrode to the volatile products in addition to mass spectrometer parameters. A calibration of the actual experimental setup is therefore necessary. The proportionality between mass intensity (MI), and faradaic current (/) can be formulated as follows ... 

---