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In my textbook it is written that $ΔV_{mix} = 0$ for ideal solutions i.e. $V_{solution} = V_{A} + V_{B}$. But why is this true? There is literally no explanation in my textbook as to why this is true. I am so confused. Please can someone explain it rigorously. Please help.

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    $\begingroup$ In simple words because the average intermolecular interaction is the same in X, in Y, and in X+Y. It is the analogue of the ideal gases case. $\endgroup$ – Alchimista May 6 at 13:45
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If you have two component mixture of A and B, most important reason for volume of mixing being zero is that when solution is ideal heterogeneous interactions (A - B) are the same as homogeneous (A - A and B - B). If interactions are the same than volume doesn't change when you mix components. Other reasons which contribute to non - ideality of mixing is size and shape of the molecules. If you mix water with some liquid polymer, you can expect that due to big difference in size and shape of water and polymer molecules, volumes will not be additive because water molecules being much smaller than polymer molecules can easily fit between them in free volume of polymer liquid. Such packing/fitting of water molecule is quite different than if you just look at water molecules in pure water or if you look at pure polymer since bulky polymer molecules can't just fit easily in free volume of other polymer molecules like water can.

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