Volume mean molar

In subsequent works, Marcus developed his theory further in a series of papers providing expressions for the work terms, the reorganization energy and the macroscopic ET rate constants [3 6]. Assuming a sharp liquid-liquid boundary, the solution of the mean molar volume of reactants yields an expression for of the form... 

Liquids with equal solubility parameters are miscible, there is no heat of mixing. With increasing difference of <5, two phases coexist, which become miscible at elevated temperature, at the critical consolute temperature Tc. Tc increases with the difference of the <5 s and with the mean molar volume of the two liquids. Another polarity scale was recently introduced by Middleton and co-workers13 based on the bathochromic shift of UV-visible 2max. The obtained spectral polarity index ranks the solvents at one end of the scale is the nonpolar perfluorohexane and at the opposite the highly polar and acidic l,l,2,3,3.3-hexafluoropropan-2-ol. The latter is much more polar than its hydrocarbon analog. 

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.]...

This excess volume vE is the difference between the mean molar volume of the non-ideal binary solution, v"° dcal = V+ n2), and the mean molar volume of the perfect binary solution vper/ = XjV + x2v2 (the sum of the volume of the two pure substances before mixing... 

Figure 2.16 shows the plot of the mean molar volume of thesolution multiplied by the compressibility of the solution as a function of the molar fraction of the NaCl solute Xj. At Xj = 0.07 ( 4 mol dm ), the values for the three temperatures become identical. Onori arbitrarily decided to take this to mean that jSV has no further temperature dependence, thus indicating that all the water in the solution is now in the hydrated sphere of the ions and these, Onori thought, would have a fi with no temperature dependence (for they would be held tight by the ion and be little dependent on the solvent temperature). 

The magnitude of the fluctuations in volume (dilatation) and density (condensation) associated with US wave is controlled by the properties of the medium and the applied forces. The velocity of sound in mixtures and suspensions will therefore be controlled by the mean density and mean compressibility as expressed by the Urick equation (see Eq.9.7-9.10). The equation can be formulated in terms of partial molar volumes by forming an identity between the volume fraction of the solute, its partial volume Vm2), the mean molar volume of the solution Vm) and the mole fraction Cm) as follows ... 

The pre-exponential factor Z in Eq. (63) is proportional to the volume of molecular dimensions (e.g., the mean molar volume of reactants) and to the thickness of the inner layer, d ... 

Furthermore by considering the Gibbs free energy per mole, and, by applying the same argument as we did to the mean molar volume (cf. 1.35), we obtain ... 

The effect of pressure on the consolute temperature is thus determined by the curvature of the mean molar volume v x. ) at the critical point. We may represent the two simple cases by the curves (1) and (2) in fig. 18.6, and ignore for the moment any more complicated behaviour. 

Fig. 18.6. Mean molar volume as function of composition at constant T and p.

In an analogous manner, a mean molar volume wj may be defined which at constant T and p fulfils the relationships... 

V is the mean molar volume and sfj are interaction parameters for the molecule species i and /,... 

In (7 38) the term occurring on the right-hand side is usually quite trivial compared to the various terms which occur on the left-hand side. Thus, if we put RT= pVg, where Vg is the mean molar volume of the vapour phase, the equation may be rewritten... 

The partial molar volumes Va and Fb in a binary mixture can be evaluated by the method of intercepts. To use this method, we plot experimental values of the quantity V/n (where is A + b) versus the mole fraction xb. V/n is called the mean molar volume. 

This equation is the same as Eq. 2.2.2 for a pure gas, except that the molar volume Vm is replaced by the mean molar volume V/n, and the virial coefficients B,C,... depend on composition as well as temperature. 

Ha q) scattering contribution of CTOSS-term-correlations between atoms of type a and P (alpha and beta are O, H, or CHx) adiabatic compressibility V mean molar volume... 

Here is the molar volume of the pure solvent and is its mean molar volume change on the solvent being electrostricted, so that is the mean molar... 

This method is a graphical method for the determination of partial molar quantities in a two-component solution. From Euler s theorem, the mean molar volume is given by... 

Figure 4.2 shows V, the mean molar volume of a solution of ethanol (component 1) and water (component 2), as a function of xi. Let x be a particular value of xi for which we desire the values of the partial molar quantities Vi and V2. To apply the method, we draw a tangent line to the curve at xi = Xj, as shown in the figure. The intercepts of this line at the edges of the figure give the values of the two partial molar quantities for the composition xi = Xj. A proof of the validity of this method is contained in Appendix D. 

Figure 4.2 The Mean Molar Volume of an Ethanol-Water Solution as a Function of Mole Fraction of Ethanol.

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