Final answer:
The measure in question is osmolarity, which determines how a solution can change cell volume by affecting osmosis. It is associated with tonicity and is crucial in maintaining fluid balance through osmotic pressure.
Step-by-step explanation:
The measure of a solution's ability to change the volume of cells by altering their water content is known as osmolarity. This property is directly linked to tonicity and affects osmosis, leading to water moving across a semi-permeable membrane from a solution with lower osmolarity to one with higher osmolarity. Notably, the terms hypotonic, isotonic, and hypertonic describe the relative osmolarity of a solution in comparison to another. Osmolarity is a key concept in understanding how solutions influence the behavior of cells through osmotic pressure, which is a colligative property that describes the flow of solvent molecules (like water) through a semi-permeable membrane. Osmotic pressure is proportional to the number of solute particles in a solution and is responsible for maintaining the balance of fluids in cells and tissues.