# Deviation from Raoult's Law--Smith Van Ness Abbott

1. Jul 17, 2015

### swmmr1928

The book I am reading, Smith Van Ness Abbott has several figures of Pressure vs Composition for Vapor Liquid Equilibrium of a Binary system. It often includes a dashed straight line to represent Raoult's Law.

What confuses me is that only the liquid phase ( P-x1 ) is said to exhibit deviations from the Raoult's Law-the dashed line. I have uploaded two pictures. In Figure 10.11, P-x1 is a straight line, characteristic of Raoult's Law. However, P-y1 is not a straight line.

Figure 12.5 is a graph of real VLE behavior. The P-x1 curve deviates from the dashed line, as does the P-y1 curve, which also was nonlinear in Raoult's Law system. From the book's description, only the liquid phase deviates from Raoult's law. And in a system obeying Raoult's Law, only the liquid phase has a linear P-x1 behavior. Am I understanding this correctly?

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2. Jul 17, 2015

### Bystander

A conditional "yes." You might try applying Raoult's law without a condensed phase.

3. Jul 17, 2015

### Staff: Mentor

Your interpretation is not correct. In chapter 10, Smith and Van Ness make it clear that the system being considered obeys Raoult's law. Nowhere do they indicate that P-x "exhibits deviations from Raoult's Law" (whatever that means). For a system that obeys Raoult's law, a line of P (total pressure) vs x is a straight line at constant temperature. In the book, they give the simple algebra that leads to this result. Raoult's law is a combination thing, and there is no such thing as Raoult's law for a liquid alone.
This is because of non-idealities in the liquid phase.
There can also be non-idealities in the vapor phase causing deviations from Raoult's law, but maybe, for the case being considered (e.g., low pressure), the dominant factor is the liquid phase.

For constant temperature only.

Chet

4. Jul 18, 2015

### swmmr1928

I agree that Chapter 10 does not describe any examples with deviations from Raoult's Law. I was not clear in my first post.

Raoult's Law for Binary system at Constant Temperature
$P_{t}(x)=P_{2}^{sat}+(P_{1}^{sat}-P_{2}^{sat})x_{1} \\ P_{t}(y)=\frac{1}{y_{1}/P_{1}^{sat}+y_{2}/P_{2}^{sat}}$

I get it. Quite simply, Raoult's Law (at constant Temperature) is linear P-x1 but nonlinear for P-y1. That means that P-x1 deviations from Raoult's Law are immediately evident, but P-y1 are not. When viewing real VLE data, could the P-y1 curve from Raoult's Law also be plotted to see those deviations?

5. Jul 18, 2015

Sure.