Final answer:
The mechanism involved in equalizing the fluid concentration between ECF and the cells during administration of a hypertonic IV solution is osmosis, where water moves out of the cells, causing them to shrink.
Step-by-step explanation:
During the administration of a hypertonic IV solution, the mechanism involved in equalizing the fluid concentration between the extracellular fluid (ECF) and the cells is osmosis. Osmosis is the diffusion of water across a selectively permeable membrane from an area of higher water concentration to an area of lower water concentration. As the hypertonic solution has a higher solute concentration compared to the intracellular fluid, water will move out of the cell to equalize the solute concentration on both sides of the cell membrane, causing cells to shrink or shrivel.