Thursday, January 10, 2008

Ideal Solutions, Raoult's Law and Azeotropes

We begin pchem II by examining the behavior of solutions. In Chapter 9 we briefly study nonelelectrolyte solutions and then, in Chapter 10, focus on the more common ionic solutions and activity.

Ideal solutions are those solutions in which components A and B attract each other to the same degree that they attract themselves and would thus posses zero values for ∆mixV and ∆mixH. Examples of solutions that approximate ideality are hexane:heptane and CCl4:SiCl4 (approximately the same structure and intermolecular forces).

Though originally obtained experimentally, Raoult's Law can be derived from chemical potentials and describes how the vapor pressure of a solution compares to that of the pure solvent: Pi=XiP*i. Since this relationship only works for ideal solutions, some have argued that it could just as easily be used as a second definition of what constitutes ideality in a solution.

In a binary ideal solution, if both components are volatile they will both contribute to the overall vapor pressure: P=X1P*1+X2P*2. Using the fact that mole fractions add up to 1, it is easy to obtain the equation P=P*2+(P*1-P*2)X1. Clearly, if we were to plot the vapor pressure versus composition, we obtain a line connecting the pure vapor pressures (which represents the liquid-vapor coexistence curve for this P-X phase diagram).

With a little bit of work, we also obtain an expression for the total vapor pressure in terms of Yi, the vapor-phase mole fraction, whose plot is squashed-hyperbolic and also shown above. Both are typically superimposed together to form a P-Z (pressure-composition) diagram.

A generally more useful diagram however is one that plots the boiling temperature rather than the vapor pressure on the vertical axis. Such plots are useful to explain the physical chemistry of simple and fractional distillation. For example, this T-Z diagram shows the analysis of an ideal benzene:toluene solution in which Xbenzene=0.20 initially. As the solution is slowly heated, the temperature eventually reaches the coexistence curve at about 375°C. The corresponding vapor-phase mole fraction is found by drawing a straight line across to the other coexistence curve (which represents Y values): Here we find a value of 0.36 which is clearly richer in benzene than the original solution. If we were to simply remove this vapor and condense it, we'd get a solution in which Xbenzene=0.36 and we could start the process again. By using a Vigreaux condensor, however, we can do it all in one process.

When solutions possess considerable nonideality, kinks in
the T-Z diagram can occur, leading to azeotropes (solutions that boil at constant temperature). Positive deviations from Raoult's Law lead to minimum boiling point azeotropes while negative deviations lead to maximum boiling point azeotropes. Azeotropic pairs, like the famous ethanol:water solution, can not be completely separated by distillation methods.


5 comments:

tori said...

thanks!

Jay said...

Yay! The blog continues.....

Anonymous said...

dear the writer of the page and the commentators,

I am looking for a equation with which I can compute the boiling temperature of a mixture as a function of molar fraction and the pressure of the environment. Do you have any idea? Or at least, in the boiling temperature vs. mole fraction graph, is there any way to express the curve as an analytical function, or is it just a curve-fit?

Thanks.

rod said...

The only such equations would be empirical at best, unless the solutions were very nearly ideal. So, yes, it is curve-fitting.

Anonymous said...

Thank you Rod! I am studying on this emprical fitting!