Final answer:
The condition for a cell to survive is that it must maintain an isotonic environment, preventing it from swelling and bursting due to osmotic pressure. This involves balancing the solute concentrations on both sides of the plasma membrane to ensure no net water movement into or out of the cell.
Step-by-step explanation:
The condition for a cell to survive is not that the ion concentrations inside and outside the cell need to be the same, or that extra ions need to be pumped out, or that water should not enter the cell. Rather, the crucial factor is that the cell should not swell and burst. This typically happens when cells are in a hypotonic environment where water enters the cell, causing it to swell. For a cell to maintain homeostasis, it must be in an isotonic solution, where the solute concentrations inside and outside the cell are approximately equal, leading to no net movement of water across the cell membrane, thus preventing the cell from lysing or shrinking.
Cells have evolved mechanisms to handle osmotic pressure, including various ways of pumping ions to maintain the correct concentration gradients. Organisms without a cell wall, such as animal cells, must either reside in an environment that mirrors their internal osmolarity, or employ structures like the contractile vacuole to pump out excess water. Cells with a cell wall, like plant cells, are supported by that wall against the pressure of incoming water in a hypotonic environment, preventing them from bursting.