# Liquid-Liquid Systems

If we have a system with more than one phase, it is often important for us to determine the compositions for each phase, when we know the total compositions present in the combination of both phases (like we just did for vapor and liquid phases).

Having said that, when dealing with liquid-liquid systems, if they mixed completely (were completely miscible) then we wouldn't need to learn anything else, since there would only be one phase and we already know its composition.

Similarly, if they didn't mix at all (were completely immiscible), we would have two phases, but we would know that both of the phases were pure components.

# Solubility and Distribution Coefficients

There are two interesting cases then:

• partial miscibility
• three component systems
##### DEFINITION:

A liquid is partially miscible in another liquid if, when mixed, the two liquids make two (liquid) phases that contain some fraction of each liquid in each phase.

Systems of two partially miscible fluids are treated in the exact same fashion as a solid in a liquid. In other words, you look up a "solubility" (mass/mass) and then can determine what the compositions are. (see the solid-liquid example problem for how to use this type of data)

There are two ways to handle these problems: with a distribution coefficient (partition ratio); with a ternary phase diagram.

##### DEFINITION:

A distribution coefficient (partition ratio) is essentially the same as a K value (i.e., a number (with no units) that tells us the ratio of material in one phase relative to that in another) except that it is typically expressed as a ratio of mass fractions of a solute (in the two different (immiscible) phases).

##### NOTE:

It is necessary that two of the liquids are completely immiscible in order for this technique to work!

# Phase Diagrams

In reality, all liquid are partially miscible (to some small extent). If you are worried about the actual compositions (i.e., trace amounts are important; in drinking water, for example), one simple way to handle this is a ternary phase diagram (see page 274 for an example).

##### DEFINITION:

Tie lines are the lines that connect two phases which are in equilibrium on a ternary phase diagram.

##### NOTE:

This technique will always work!

##### Outcome:

Estimate the composition of immiscible liquids in equilibrium with each other (using either partition ratios or ternary phase diagrams)

##### Test Yourself

A liquid extractor is used to try to remove acetone from a water stream using MIBK (NOTE: Assume that MIBK and water are completely immiscible!). A flowchart of the process is shown below. If the partition ratio at the specified temperature is K = 1.72 ( this number is unitless, but you may think of it as g Ac in each g of MIBK mixture/g AC in each g of W mixture), determine the outlet streams.

Using the same liquid extractor as before to remove acetone from a water stream (using MIBK), let's now assume that the MIBK and water are not completely immiscible! A revised flowchart of the process is shown below. Determine the outlet streams.