Calculations from equations

Frost-Kalkwarf equation calculated from molecular structures, normal bp and... 

The regression equation, calculated from the standard solutions in each collection, is employed to determine quantitatively the drug concentration present in individual plasma samples. 

Table I shows a series of simple linear regression equations calculated from the data plotted in Figure 1. For the samples heated alone total lysine correlated ( r =0.55 ) badly with FDNB lysine and overestimated it at all levels of heating.

TABLE 3.4 Constants for the Van der Waals and Redlich-Kwong Equations Calculated From the Listed Values of the Critical Constants... 

From Si-0 asymmetric stretching frequency and Sohn et al. equation. Calculated from FU (1) and total aluminium by chemical analysis. 

TABLE 1 summarizes the data set for two chemical groups simple alcohols and simple ketones. TABLE 2 contains regression equations calculated from the data in TABLE 1. The geometric mean functional regression method was employed wherever possible but where the slope of the regression is near zero this technique could not be used (Sokal and Rohlf 1981). 

The fugacity coefficient is a function of temperature, total pressure, and composition of the vapor phase it can be calculated from volumetric data for the vapor mixture. For a mixture containing m components, such data are often expressed in the form of an equation of state explicit in the pressure... 

For a real vapor mixture, there is a deviation from the ideal enthalpy that can be calculated from an equation of state. The enthalpy of the real vapor is given by... 

Equilibrium constants,, for all possible dimerization reactions are calculated from the metastable, bound, and chemical contributions to the second virial coefficients, B , as given by Equations (6) and (7). The equilibrium constants, K calculated using Equation (3-15). 

The constants in Equation (5) are not the same as those in Equation (4). Using this saturation pressure, the pure-liquid reference fugacity at zero pressure is then calculated from the equation... 

Rmin is calculated from the binary form of the Underwood equation applied to the key components ... 

If the composition of the waste stream is known, then the theoretical oxygen demand can be calculated from the appropriate stoichiometric equations. As a first level of approximation, we can assume that this theoretical oxygen demand would be equal to the COD. Then, experience with domestic sewage indicates that the average ratio of COD to BOD will be on the order 1.5 to 2. The following example will help to clarify these relationships. 

The Cpg of real gas is calculated using the equation derived from the Lee and Kesler model ... 

The downhole density of oil (at reservoir conditions) can be calculated from the surface density using the equation ... 

Equation 11-30 may be integrated to obtain the profile of a meniscus against a vertical plate the integrated form is given in Ref. 53. Calculate the meniscus profile for water at 20°C for (a) the case where water wets the plate and (b) the case where the contact angle is 40°. For (b) obtain from your plot the value of h, and compare with that calculated from Eq. 11-28. [Hint Obtain from 11-15.]... 

Smith [113] studied the adsorption of n-pentane on mercury, determining both the surface tension change and the ellipsometric film thickness as a function of the equilibrium pentane pressure. F could then be calculated from the Gibbs equation in the form of Eq. ni-106, and from t. The agreement was excellent. Ellipsometry has also been used to determine the surface compositions of solutions [114,115], as well polymer adsorption at the solution-air interface [116]. 

A 1.5% by weight aqueous surfactant solution has a surface tension of 53.8 dyn/cm (or mN/m) at 20°C. (a) Calculate a, the area of surface containing one molecule. State any assumptions that must be made to make the calculation from the preceding data, (b) The additional information is now supplied that a 1.7% solution has a surface tension of 53.6 dyn/cm. If the surface-adsorbed film obeys the equation of state ir(o - 00) = kT, calculate from the combined data a value of 00, the actual area of a molecule. 

Calculated from various theoretical equations some of the sources are themselves compilations rather than original. 

Dye adsorption from solution may be used to estimate the surface area of a powdered solid. Suppose that if 3.0 g of a bone charcoal is equilibrated with 100 ml of initially 10 Af methylene blue, the final dye concentration is 0.3 x 10 Af, while if 6.0 g of bone charcoal had been used, the final concentration would have been 0.1 x Qr M. Assuming that the dye adsorption obeys the Langmuir equation, calculate the specific surface area of the bone charcoal in square meters per gram. Assume that the molecular area of methylene blue is 197 A. ... 

Interestingly, a general thermodynamic relationship allows the surface area of a porous system (without ink bottles) to be calculated from porosimetry data, note Section XVII-16B. The equation is [45]... 

Figure A2.3.4 compares PIpkT- 1, calculated from the CS equation of state for hard spheres, as a fiinction of...

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