Transformed mole fraction

An equation identical to (13-129) defines the transformed mole fraction of component i in the vapor phase, Yj, where the terms in x are replaced by terms in y... 

X transformed mole fraction of i in the liquid phase Yi mole fraction of i in the vapor phase 7 transformed mole fraction of i in the vapor phase... 

Radioactivity The ability possessed by some natural and synthetic isotopes to undergo nuclear transformation to other isotopes, 513 applications, 516-518 biological effects, 528-529 bombardment reactions, 514-516 diagnostic uses, 516t discovery of, 517 modes of decay, 513-514 nuclear stability and, 29-30 rate of decay, 518-520,531q Radium, 521-522 Radon, 528 Ramsay, William, 190 Random polymer 613-614 Randomness factor, 452-453 Raoult s law A relation between the vapor pressure (P) of a component of a solution and that of the pure component (P°) at the same temperature P — XP°, where X is the mole fraction, 268... 

Because very small mole fraction solubilities correspond in practice to the molar ratio [45 a], the values can (considering the molar volume and density of the solvent) be easily transformed into hydrogen concentrations (see Table 10.1,... 

Infrared spectra suggested that a sulfate ion coordinates to two titanium atoms as a bidentate in particles. The maximum particle size was found at Aerosol OT mole fraction of 0.35 in the mixtures. The particle size increased linearly with increasing the concentration of sulfuric acid at any Wo, but with increasing Wo the effect was the opposite at any sulfuric acid concentration. These effects on the particle size can be explained qualitatively in relation with the extent of number of sulfate ions per micelle droplet. These precursor particles yield amorphous and nanosized TiO particles, reduced by 15% in volume by washing of ammonia water. The Ti02 particles transformed from amorphous to anatase form at 400°C and from anatase form to rutile form about at 800°C. In Triton X-100-n-hexanol-cyclohexane systems, however, spherical and amorphous titanium hydroxide precursor were precipitated by hydrolysis of TiCl4 (30). When the precursor particles were calcinated,... 

The concentration Zao is the mole fraction of A in the vapor phase in equilibrium with the pure liquid this equilibrium assumption is not necessarily correct, as has already been discussed in Sec. I,D,4. The problem may be transformed into simpler form by introduction of the following reduced quantities ... 

In order to conduct these analyses, the detection limit of the instrument must be known. The detection limit is defined (in ppm or ppb) as the concentration of analyte that allows a detectable signal to be measured with certainty - for example, three times the standard deviation of the background signal or the blank. If the volume of solution needed to obtain these results is known, the preceding values can be transformed to the absolute quantities or mole fractions (pico-mole, femtomole, etc.) that are needed to obtain the signal. In general, these values are excessively small because current instruments use excessively small volumes. 

Figure 19-9 (a) Spectrophotometric titration of 30.0 mL of EDTA in acetate buffer with CuS04 in the same buffer. Upper curve [EDTA] = [Cu2 ] = 5.00 mM. Lower curve [EDTA] = [Cu2 ] = 2.50 mM. The absorbance has not been corrected in any way. (b) Transformation of data into mole fraction format. The absorbance of free CuS04 at the same formal concentration has been subtracted from each point in panel a. EDTA is transparent at this wavelength. [From L D. Hill and P MacCarthy, Novel Approach to Job s Method Chem. Ed. 1986,63, 162.]... 

The method of continuous variation can be carried out with many separate solutions, as in Table 19-1. However, a titration is more sensible. Figure 19-9a shows a titration of EDTA with Cu2+. In Figure 19-9b, the abscissa has been transformed into mole fraction of Cu2+(= [moles of Cu2+]/[moles of Cu2+ + moles of EDTA]) instead of volume of Cu2+. The sharp maximum at a mole fraction of 0.5 indicates formation of a 1 1 complex. If the equilibrium constant is not large, the maximum is more curved than in Figure 19-9b. The curvature can be used to estimate the equilibrium constant.7... 

The vapor curve KLMNP gives the composition of the vapor as a function of the temperature T, and the liquid curve KKMSP gives the composition of die liquid as a function of die temperature. These two curves have a common point M. The state represented by M is that in which the two states, vapor and liquid, have the same composition xaB on die mole fraction scale. Because of die special properties associated with systems in this state, the Point M is called an azeotropic point and the system is said to form an azeotrope. In an azeotropic system, one phase may be transformed to the other at constant temperature, pressure and composition without affecting the equilibrium state. This property justifies the name azeotropy, which means a system diat boils unchanged. 

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