Volume graphical determination

We now turn our attention to the graphical determination of the various parameters of our two-compartmental model, i.e. the plasma volume of distribution Vp,... 

Graphical determination of the partial molar volumes of binary systems... 

Figure 6.2. Graphical determination of partial molar volumes in a binary system.

Fig. 1.3. Partial molar volume (a) the molar volume v,° of a pure substance i and the partial molar volume v, of substance i in a homogeneous mixture (b) graphical determination of the partial molar volumes of constituent substances in a homogeneous binary system by the Bakhuis-Rooseboom Method v = V/(n, + nt) = the mean molar volume of a binary mixture x2= the molar fraction of substance 2 Vj = v - x2(dv/dx2) = the partial molar volume of substance 1 v2 = v-(l-x2 avldx2) = the partial molar volume of substance 2. [Ref. 1.]...

Figure 4.10 Graphical determination of free volume fraction /. The thick curved line is the total reduced volume v/Vg as a function of temperature during cooling. Extrapolating the linear high-temperature portion of this line to Tq (the VFTH temperature at which the relaxation time be-comes infinite) and drawing a thin line of slope o = ag through this point, one obtains / at any tem-perature as the difference between the ordinates of the thick and thin lines.

Fig. 9-47. Graphic determination of the break-through volume in silicate pre-concentration.

A 1.5.7 Plot the effluent azobenzene concentration versus the effluent volume, and graphically determine the effluent volume at 0.5 mass % azobenzene concentration (50 % of the starting solution concentration). This is the azobenzene equivalence of the clay. 

Measurements of the effective viscosity as a function of composition may be fitted to equation 80 or presented in graphic form as in Figure 16. The correction factor, R, also may be determined by accounting for the volume fraction, ti , of particles through the Andress formula ... 

If he selects the still pressure (which for a binary system will determine the vapour-liquid-equilibrium relationship) and one outlet stream flow-rate, then the outlet compositions can be calculated by simultaneous solution of the mass balance and equilibrium relationships (equations). A graphical method for the simultaneous solution is given in Volume 2, Chapter 11. 

This will be possible for only a few practical design problems. The technique is illustrated in Example 1.1, and in the derivation of the formula for optimum pipe diameter in Chapter 5. The determination of the economic reflux ratio for a distillation column, which is discussed in Volume 2, Chapter 11, is an example of the use of a graphical procedure to find the optimum value. 

The distillation of binary mixtures is covered thoroughly in Volume 2, Chapter 11, and the discussion in this section is limited to a brief review of the most useful design methods. Though binary systems are usually considered separately, the design methods developed for multicomponent systems (Section 11.6) can obviously also be used for binary systems. With binary mixtures fixing the composition of one component fixes the composition of the other, and iterative procedures are not usually needed to determine the stage and reflux requirements simple graphical methods are normally used. 

In experimental kinetics studies one measures (directly, or indirectly) the concentration of one or more of the reactant and/or product species as a function of time. If these concentrations are plotted against time, smooth curves should be obtained. For constant volume systems the reaction rate may be obtained by graphical or numerical differentiation of the data. For variable volume systems, additional numerical manipulations are necessary, but the process of determining the reaction rate still involves differentiation of some form of the data. For example,... 

If the reaction occurs in the liquid phase at 25 °C, determine the reactor volume requirements for cascades of one and three identical CSTR s. The rate at which liquid feed is supplied is 0.278 m3/ksec. Use the graphical approach outlined previously. The following constraints are applicable. 

The electrical conductance of a solution is a measure of its current-carrying capacity and is therefore determined by the total ionic strength. It is a nonspecific property and for this reason direct conductance measurements are of little use unless the solution contains only the electrolyte to be determined or the concentrations of other ionic species in the solution are known. Conductometric titrations, in which the species of interest are converted to non-ionic forms by neutralization, precipitation, etc. are of more value. The equivalence point may be located graphically by plotting the change in conductance as a function of the volume of titrant added. 

How are partial molar quantities determined experimentally Sidebar 6.3 illustrates the general procedure for the special case of the partial molar volumes VA, Vr of a binary solution (analogous to the graphical procedure previously employed in Section 3.6.7 for finding differential heats of solution). As indicated in Sidebar 6.3, each partial molar... 

Matano developed a graphical method which, for certain classes of boundary value problems, relates the form of the diffusion profile with the concentration dependence of the interdiffusivity, D(c), introduced in Section 3.1.3 [5]. This method can determine D(c) from the diffusion profile in chemical concentration-gradient diffusion experiments where atomic volumes are sufficiently constant so that changes in overall specimen volume are insignificant and diffusion can be formulated in a F-frame. The method uses scaling, as discussed in Section 4.2.2. 

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