# 3 component (ternary) system in equilibrium

If the components of a system were Cl2, Br2, and I2, how could I describe this system under equilibrium conditions when the number of phases is at a maximum?

If there are 3 components, using the formula, F=M+2-P and solving for P under equilibrium conditions there would be a total of 5 phases.

Since these above components are all gases, and we know there are 5 phases, can I assume that 3 of the 5 phases will be Cl2 (gas), Br2 (gas), and I2 (gas).

For the other two phases, can I assume they consist of liquid iodine as it's commonly in the liquid phase, and cl2 (solid) as it's commonly in the liquid phase.

I'm not sure if this is correct.

• No, you cannot assume much of anything. The Gibbs Phase Rule only tells you how many phases can coexist, not what they are. For example, here you have left out things like ClBr as a species, or dissociated Cl (which would be stable at high temperatures). What species will be present will depend on the temperature and pressure of the system, and the Gibbs free energies of the various possible components. – Jon Custer Jul 13 '16 at 20:18
• I know that it is not part of your question, but you also need to consider that $$\ce{Cl2 + I2 <=> 2ICl}$$ – Ben Norris Jul 13 '16 at 21:19
• This makes perfect sense. Thank you for clarification. – JHOP515 Jul 13 '16 at 21:24

I understand from that you set $F=0$. Equilibrium does not necessarily mean that you have no degrees of freedom. In this case, you actually have two degrees of freedom: the molar fractions of two components, for example $X(\rm{Cl}_2)$ and $X(\rm{I}_2)$.
$X(\rm{F}_2) = 1 - X(\rm{Cl}_2) -X(\rm{I}_2)$ and cannot vary independently, so it is not a degree of freedom. Once you consider $F=2$, you only need three phases.
What about liquids and solid? Let's say that you vary temperature, and you reach the melting/condensation/etc curve in $T$ space. On the curve itself you will have four phases, three gases and (for instance) liquid chlorine. This causes you to lose a degree of freedom, which in this case is temperature. These four phases can exist only in that specific temperature.