why are volumes not additive?

Although we can't see them, liquid molecules have tiny holes (spaces) in them here and there (which most of us like to call interstices) and each of the liquids, solute and solvent, can fit into those spaces. Solvents and solutes whose interstices don't allow the other one to fit into, because of size considerations, are additive but many liquids are not additive. A common example is ethanol and water. I THINK I remember, but I'm not positive, that 500 mL ethanol + 500 mL water, mixed thoroughly together, has a total volume of 950 mL and not 1000 mL.

Volumes are not always additive because the concept of volume depends on the shape and arrangement of an object. When two objects with certain shapes are combined, their volumes do not simply add up.

To understand why volumes may not be additive, let's consider two objects: Object A and Object B.

Object A has a certain volume, which can be found by measuring the length, width, and height of the object and multiplying these dimensions together. Let's denote the volume of Object A as "V(A)".

Similarly, Object B has its own volume, denoted as "V(B)".

Now, if we combine Object A and Object B, we might expect the total volume, let's call it "V(total)", to be the sum of the individual volumes: V(A) + V(B). However, this assumption is not necessarily correct.

Volumes are not additive because the shape and arrangement of the objects may cause them to intersect or overlap in a way that affects the total volume. When two objects are combined, there might be gaps or overlapping regions that change the overall shape and, consequently, the volume.

Consider pouring two liquids, such as water and oil, into the same container. The volume of the mixture will not be the sum of the volumes of each liquid individually because they do not fully occupy the same space due to their different densities.

In summary, volumes are not always additive because the shape, arrangement, and combination of objects can lead to variations in the resulting volume. To determine the total volume, one must consider the specific characteristics of the objects involved and how they are combined.

Volumes are not always additive because of the concept known as "packing efficiency" or "void space." When objects are packed together, there may be empty spaces between them that cannot be filled by additional objects. These empty spaces reduce the overall volume of the packed system and make the sum of individual volumes less than the total volume.

For example, imagine placing two identical rectangular boxes side by side. The total volume of the two boxes combined should be equal to the sum of their individual volumes. However, when placed together, there will be a small empty space between them that cannot be filled with another box. This empty space decreases the overall volume of the system.

This principle applies to any objects that are packed together. In real-world scenarios, irregularly shaped objects or objects with gaps between them can further decrease the overall volume when combined.

There are situations when volumes can be additive. For example, if the objects being combined can pack tightly without any empty spaces, the total volume would be equal to the sum of individual volumes. This can occur in special cases such as perfectly shaped spheres or cubes that fit together perfectly.