Reference substance plot

Several useful methods are available for extrapolating equilibrium data for a given system to various temperatures and pressures. One convenient method is by use of a reference substance plot. Here, the adsorption equilibrium partial pressure of the adsorbate is plotted against a pure substance vapor pressure, preferably that of the adsorbate. If logarithmic coordinates are used on both axes, lines of constant adsorbent loading, isosteres, are linear for most substances. Therefore, only two datum points are required to establish each isostere. 

Figure 6.1-2 Reference-substance plot for vapor pressure correlation.

Figure 6.1-3 Reference-substance plot temperature scale for water on abscissa.

Relative saluration. Relatiiie saturation, also called r ladmJitmudiiyi expressed as a percentage is defined as lOOp // , where is the vapor pressure at the dry-bulb temperature of the mixture. For any vapor, the graphical representation of conditions of constant relative saturation can easily be constructed on a vapor-pressure-temperature chart, as in Fig. lAa, by dividing the ordinates of the vapor-pressure curve into appropriate intervals. Thus the curve for 50 percent relative saturation shows a vapor partial pressure equal to one-half the equilibrium vapor pressure at any temperature. A reference-substance plot, such as Fig, 7.2, could also be used for this. 

Prepare a logarithmic reference-substance plot of the vapor pressure of acetone over a temperature range of 10 C to its critical temperature, 235"C, with water as reference substance. With the help of the plot, determine (vapor pressure of acetone at 65 C, (b) the temperature at which acetone has a vapor pressure of 500 torr, and (c) the latent heat of vaporization of acetone at 40 C (accepted value 536.1 kN m/kg). 

Flgrae 113 Reference-substance plot of equilibrium adsorption of acetone on an activated carbon. [Data of Josefemtz and Othmer, Ind. Eng. Chem., 40, 739 (1948).]... 

In another type of reference plot the temperature of a property of compound A is plotted vs the temperature of the reference substance at equal vapor pressures values. 

By use of Othmer plots of reference substances, large tables of thermodynamic data can be expressed as simple correlations which are extremely accurate and easy to use. The real power of these correlations is the abiUty to interpolate and extrapolate the correlations beyond the experimental values with considerable accuracy. Mathematically stated... 

Experimental Methods In Differential thermal analysis (DTA) the sample and an inert reference substance, undergoing no thermal transition in the temperature range under study are heated at the same rate. The temperature difference between sample and reference is measured and plotted as a function of sample temperature. The temperature difference is finite only when heat is being evolved or absorbed because of exothermic or endothermic activity in the sample, or when the heat capacity of the sample changes abruptly. As the temperature difference is directly proportional to the heat capacity so the curves are similar to specific heat curves, but are inverted because, by convention, heat evolution is registered as an upward peak and heat absorption as a downward peak. 

Briefly, the method involves determining the capacity factors (retention time corrected for an unretained substance) for a suitable set of reference substances (having known K(k values) using RP-HPLC. The relationship between the capacity factors and Kol for the reference or calibration compounds is determined from regression analysis of a log-log plot of the two properties. The capacity factors of compounds having unknown Koc values then are determined using the identical experimental conditions, and Koc values then are calculated from the regression expression. 

Another measurement principle is the DSC, after Boersma [8]. In this case, no compensation heating is used and a temperature difference is allowed between sample crucible and reference crucible (Figure 4.5). This temperature difference is recorded and plotted as a function of time or temperature. The instrument must be calibrated in order to identify the relation between heat release rate and temperature difference. Usually this calibration is by using the melting enthalpy of reference substances. This allows both a temperature calibration and a calorimetric calibration. In fact, the DSC after Boersma works following the isoperibolic operating mode (see Section 4.2.2). Nevertheless, the sample size is so small (3 to 20 mg) that it is close to ideal flux. 

It is also possible to get straight-line correlations with Duhring plots, which are plots of the temperature at which a substance has a certain vapor pressure versus the temperature at which a reference substance has the same vapor pressure. The principles of the preparation and use of these charts are identical to those of the Cox chart. 

As explained in Appendix M, you can estimate the values of the coefficients in Eq. (3.32) by the method of least squares. We look at another way, a graphical method. Over very wide temperature intervals experimental data will not prove to be exactly linear as indicated by Eq. (3.31), but have a slight tendency to curve. This curvature can be straightened out by using a special plot known as a Cox chart. The In or logic of the vapor pressure of a compound is plotted against a special nonlinear temperature scale constructed from the vapor-pressure data for water (called a reference substance). 

The external standard method is the technique used most frequently to gather quantitative information from a chromatogram. In this case, a pure reference substance (ideally the same compound as the one to be determined in the sample) is injected in increasing concentrations and the peak areas or peak heights obtained are plotted versus the concentration (calibration curve ->Chemo-metrics). These calibration curves should show a constant slope (linear curves), and the intercept should be as close to zero as possible. Since the calibration curves usually show nonlinear behavior and flatten off at higher concentrations (.see Section 12.2.6), the quantification should be carried out only within the linear part of the curve. 

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