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phase diagram
The temperature-composition diagram for hexane and nitrobenzene at 1atm. The region below the curve corresponds to the compositions and temperatures at which the liquids form two phases. The upper critical temperature, $T_\mathrm{uc}$, is the temperature above which the two liquids are miscible in all proportions.

Am I right in assuming that the right side (green line) is the nitrobenzene rich phase? Is that always the case? Whichever one has the side with a mol fraction of 1 that side is more abundant? If you don't understand my question just tell me, and I'll clarify

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first of all, the picture should have two arrows on top of the bars that are perpendicular (ie parallel to each other), because those represent the two components. Lets just call one A and the other B. If you choose a point on the right hand side of the curve, it means that you have little of component B that is "rich in" component A.

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Here is the same diagram with more annotation from the physical chemistry textbook by Atkins:

phase diagram

It shows that above the temperature $T_{uc}$, there is only one phase (the substances mix in any ratio). Below that temperature, there are two phases, with compositions shown by the solid lines. The horizontal line shows that if you try to make a mixture with a mole fraction of $a$ at the given temperature, you will get two solutions with mole fraction $a'$ and $a''$ instead. You can calculate the approximate ratio of the volumes using this technique.

Am I right in assuming that the right side (green line) is the nitrobenzene rich phase?

Yes, because the x-axis is the mole fraction of nitrobenzene, the phase with higher fraction of nitrobenzene will be that on the right, as you say. It does not necessarily mean that the fraction is higher higher than 50% on the right and lower than 50% on the left, though.

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