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

[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?

 

[Bystander]

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

 

[Chestermiller]

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.

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.

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.

This is because of non-idealities in the liquid phase.

From the book's description, only the liquid phase deviates from Raoult's law.

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.

And in a system obeying Raoult's Law, only the liquid phase has a linear P-x1 behavior.

For constant temperature only.

Chet

 

[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?

 

[Chestermiller]

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?

Sure.