Volume changes on mixing

This simple mo l contiimes to ignore the possibility of volume changes on mixing, so for simplicity the molar volumes and are taken as those of the pure components. It should come as no surprise that in... 

When both phases form ideal thermodynamic solutions, ie, no heat of mixing, no volume change on mixing, etc, Raoult s law apphes ... 

When the flux expressions are consistent, as in Eq. (5-182), the dif-fusivities in Eq. (5-181) are identical. As a result, experimental diffu-sivities are often measured under constant volume conditions but may be used for applications involving open systems. It turns out that the two versions are veiy nearly equivalent for gas-phase systems because there is negligible volume change on mixing. That is not usually true for hquids, however. 

Employing an iterative computer program, in conjunction with the above equations, Katz et al. examined a wide range of values for (k) and (Vmw) nd calculated the volume change on mixing of a series of methanol/water mixtures having assumed volume fractions of methanol. The results for each selected values of (k) and (Vmw) and each volume fraction of methanol were compared with experimentally determined values of (vj) and the specific values of (k) and (Vmw) that gave the minimum error... 

Figure 25. Graph of Volume Change on Mixing against Solvent Composition for Methanol/Water Mixtures...

Since Ag is a function of pressure, it follows that, under certain conditions, a change in pressure may produce immiscibility in a completely miscible system, or, conversely, such a change may produce complete miscibility in a partially immiscible system. The effect of pressure on miscibility in binary liquid mixtures is closely connected with the volume change on mixing, as indicated by the exact relation... 

The association of methanol and water was examined by Katz, Lochmiiller and Scott (11) using volume change on mixing and refractive index data and established that the methanol/water solvent system was indeed a complex ternary system. 

In high pressure mixing devices each solvent is piunped separately in the proportions required by the gradient into a mixing chamber before being delivered to the column. Solvent compressibility and thermodynamic volume changes on mixing may Influence the accuracy of the composition delivered to the column. 

For many gaseous solutions, even if the gases are not ideal, the partial molar volumes of the components are equal to the molar volumes of the pure components at the same total pressure. The gases are said to obey Amagat s mle, and the volume change on mixing is zero. Under these conditions, the gaseous solution behaves ideally in the sense that it obeys the equation... 

Measures of the composition of solutions of a solute B (2-bromoethanol, d = 1.7629 g cm"3 at 20°C) in a solvent A (water, d = 0.9982 g cm 3 at 20°C) against the mass fraction WB XB is the mole fraction and cpB is the volume fraction (assuming negligible volume change on mixing) (left hand ordinate) and mB is the molality and CB is the molarity (right hand ordinate). 

Conversion of solubilities from thex-scale to the mol dm-3 scale, c, and vice versa requires knowledge of the volume change on mixing the components (the excess volume of mixing, VE). If this is ignored, then the approximate relationships ... 

A liter flask contains a mixture of two liquids (A and B) of specific gravity 1.4. The specific gravity is the density of the sample relative to that of water. The specific gravity of liquid A is 0.8 and that of liquid B is 1.8. What volume of each must have been put into the flask Assume the volumes are additive with no volume changes on mixing. 

The Equation-of-state terms as calculated by Flory and co-workers , which take account of volume changes on mixing become more unfavourable at higher temperatures. The effect of the polymer properties and the resultant phase diagrams using this theory have been explored by McMaster... 

Huggins theory but differs in one important respect in that it allows the lattice to have some vacant sites and to be compressible. Thus the compressible lattice theory is capable of describing volume changes on mixing as well as LCST and UCST behaviours. As with the theory of Flory and his co-workers, (which is proportional to the change in energy that accompanies the formation of a 1-2 contact from a 1-1 and a 2-2 contact) is obtainable from experimental values of heats of mixing. 

Many variations on these and similar theories have been developed and their relative merits have been discussed We beUeve that most theories suffer because they do not address themselves to the important problem of the specific interaction directly. In our own work we have used the Equation-of-state theory of Flory and coworkers. Although it cannot fully describe systems with specific interactions it does have the merits of being moderately easy to use. of allowing volume changes on mixing, and of using parameters which are mostly obtainable either by experimental measurement or calculation. 

The parameter is best obtained by fitting the equation for to the experimental heats of mixing of analogous materials as reported elsewhere It can also be obtained from any other binary quantity such as the second virial coefficient, the thermal expansion coefficient of mixture, or the volume change on mixing. is assumed to be independent of temperature but as we described in the previous section this may not be valid. At present there is no way of predicting the temperature variation and one can only use empirical expressions or assume a constant value most appropriate for the temperature range of interest. 

The partial molal volume of the constituent i in a mixture of ideal gaseSf which do not react, is equal to its molar volume Vi in the system, since there is no volume change on mixing if p, is the partial pressure of the constituent, then Vi is equal to RTfpi, where R is the gas constant per mole and T is the absolute temperature. It can be shown by means of thermodynamics that the partial molal volume (Vi) is related to the chemical potential by the equation... 

The volume changes on mixing non-aqueous liquids, the densities of mixed liquids, of solutions of non-polar solutes in non-polar solvents, and the changes of total volume on the solution of solid salts in water, noticed at an early period and much investigated, can only be mentioned here some aspects of these will be dealt with later. Hyde found the densities of solutions of jp-nitrotoluene in carbon disulphide smaller than the density of either component, but the anomaly disappears if the p-nitrotoluene is supposed to be in the liquid state. Biron found that the volume change on mixing two liquids was Av=kx( —x where x , (1— ) are the mol fractions, and he investigated the effect of pressure on the value of Av. The apparent specific volume of alcohol in aqueous mixtures was determined by Brown, lo... 

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