When you mix two liquids 50/50, and one has a freezing point of 20 Celcius and the other has a freezing point of 0 Celcius, does the new liquid have a freezing point of 10 Celcius?
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Only in an ideal world. “Ideal” means “if everything worked perfectly without special rules for the specific thing”, in a way. In an ideal world, a mixture will have a property which varies directly in proportion to the relative contents of each item.
A two-end-member ideal mixture such as this would show a straight line in the value of the property (melting point in this example) and the fractional proportion of the two components. The fraction is in terms of atoms, not weight or mass or volume. How many little balls are present and what fraction are type A and what fraction are type B. In an ideal system, the balls (the particles) do not behave differently depending upon size or shape.
An ideal system is usually only true in reality when one of the two components is at a tiny concentration (variations of Henry and Raoult laws). Few solutions or mixtures behave ideally in actual fact. the two different compounds react to each other differently from how they react to themselves, either interacting more than expected or repelling more than expected.
So, even for an ideal mixture or solution, how you define that idea of 50/50 matters: 50 ml of one thing and 50 ml of another will not be 50% of each in fractional percent except when the molar volume (the number of atoms per unit volume) are the same. If you measure 50/50 by mass, then density comes into play and 50% mass will not be 50% atomic fraction.
The ideal system assumes perfect behavior, that all particles behave identically without regard to size or composition. Real systems differ from that.
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