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Method of Tangents

We shall proceed to show that the free energy of the segregated system is lower than the free energy of the homogeneous system in the miscibility gap region. We shall also demonstrate that the segregated system with the composition foimd by the method of tangents is in equilibrium. But first we have to find the amoimt of the two phases present, namely and Np. [Pg.229]


Finally, it should be obvious that the method of tangents can be equally well applied to the determination of a utilizing eqn. (29) in precisely the same way as eqn. (15). [Pg.359]

Furazolidone, furaltadone Alkaline hydrolysis 1-20 Use of method of tangents... [Pg.2427]

Values of cb for various molalities were calculated from density data of Chemical Engineers Han ook (McGraw-Hill Book Company, Inc., New York, 1950). Partial molal volumes Vb were calculated from these density data by the method of tangent intercepts described by Lewis and Randall (loc, cit.f p. 39). Relative viscosities m/mb are available for NaCl solutions at 18°C. in International Critical Tables (Vol. V, p. 15). The accompanying tabulation summarizes the results of the various calculations, and Fig. 5.6 compares the calculated results with the experimental data as reported in International Critical Tables (Vol. V, p. 67). [Pg.115]

The problem of large scatter in the values of sought variables due to sharp deceleration in convergence of the computation process was solved by LA. Shirkalin (Shirkalin, 1997) on the basis of factual transition from the affine scaling method to the general Newton method (the method of tangents) when approaching the extreme point. [Pg.51]

This equation is known as the Michaelis-Menton equation. A plot of rate r versus substrate concentration [S] (Figure 2.20) shows that the rate equation follows first-order kinetics fp = (k/kuAS] at low substrate concentrations and zero-order kinetics r = k ed. high substrate concentrations. The tangent to versus [S] plot drawn at [S] = 0 intersects r = k at a point corresponding to [S] = k - This method of tangent can be used to determine the kinetic parameters k and k - Alternatively, we can write the rate equation in linear form as (l/fp) = kM/k) l/[S]) + (1/k) by inverting Equation 2.169. Thus, by making a linear plot of... [Pg.63]

The partial enthalpies of Eq. (8.76) can be obtained in a number of ways, e.g., from activity-coefficient data [12] or from integral heats of solution by the method of tangent intercepts [22, 40]. Since, however, the equilibrium partial pressures of components A and C from these solutions are required over a range of temperatures in any event, the simplest procedure is that described earlier in connection with Fig. 8.2 and Eq. (8.3). For ideal solutions,, is the enthalpy of pure liquid J at /, for all Xj... [Pg.317]

If we have experimental data, or an equation that is believed to represent such experimental data for some extensive property as a function of concentration, we can compute the partial molar values by the method of tangent slopes or the method of tangent intercepts. In either case we could plot the data and make the geometric constructions. However, the mathematical procedure, which our computers can do for us is much more useful. [Pg.78]

The corresponding equation for the method of tangent slopes (Eq. 4.19) requires that we have the property equation in the form of an extensive property, stated as a function of the number of mols present of each species. If we have, for example, an equation for v as a function of Xj we can multiply both sides of that equation by the total number of mols present, j-. This makes the following changes... [Pg.78]

Example 6.5 Repeat Example 6.4, for ethanol only, using the method of tangent slopes. Multiplying both sides of Eq. 6.G by n and inserting those in Eq. 4.19 we find... [Pg.78]

If we do that (Problem 6.9) we find analogs to most of the equations and procedures shown in this chapter, with partial molar properties replaced by those same properties divided by the molecular weight. Such properties have no common name perhaps they are best called partial mass properties. The most commonly seen application is with plots of enthalpy per unit mass vs. mass fraction, as shown for water and sulfuric acid in Figure 6.8. As shown in Problem 6.9, if we apply the method of tangent intercepts to this figure, the intercept values are the partial mass enthalpies. [Pg.80]

Example 6.7 Using Figure 6.8 and the method of tangent intercepts, estimate the partial molar enthalpies of both water... [Pg.80]

The method of tangent intercepts is shown in the main text, based on the partial molar equation, Eq. 6.5. It may also be shown purely geometrically as follows. Figure 6.13 is the same as Figure 6.6, but the point of tangency has been moved to move points b and d further apart, points c, d, and e have been added, and unnecessary text has been deleted. [Pg.84]

FIGURE 7.9 Finding the partial molar volume residual amethane by the method of tangent intercepts. The line is tangent to the curve at Jmethane = 0.784. Its intercept on the right hand axis is 0.6 ft / Ibmol. [Pg.101]

In principle, we should be able to begin with Eq. F.6, take the partial derivatives with respect to yi, and use the method of tangent intercepts to find fi/ytP. In practice, this is very difficult, because it is very difficult to write out the derivatives of z from a pressure-explicit EOS. Instead, we begin with Eq. 7.15, rewritten as... [Pg.342]


See other pages where Method of Tangents is mentioned: [Pg.493]    [Pg.616]    [Pg.356]    [Pg.229]    [Pg.231]    [Pg.75]    [Pg.78]    [Pg.84]    [Pg.86]    [Pg.164]    [Pg.165]    [Pg.165]    [Pg.342]    [Pg.77]    [Pg.155]   


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