Yes, the volume will increase but not necessarily in a linear way. The solute – the thing you’re dissolving – may occupy space in between the molecules of your solvent. This is why, for example, adding salt to water lowers its freezing point. The salt gets split up into its ions, sodium and chloride, and those ions get between the water molecules so that they can’t stick to each other quite as well, so they can’t freeze.
The ions do take up *some* space and push the water molecules apart slightly. However, they don’t push the water molecules apart as much as another water molecule; and the ions stick closer to the water molecules than two whole salt molecules would to each other.
In this way, the volume does increase but not as much as if you mixed two substances that don’t dissolve.
Another way to say this is that the density of saltwater is higher than water or salt.
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