The type of solution that would cause a bacterium with a weak or damaged cell wall to burst as water moves into the cell is a hypotonic solution.
When a bacteria with a weak cell wall is kept in a hypotonic solution, the concentration of the water outside the cell is large, and within the cell it is low. This concentration gradient of water forces the water from the outside to exert force onto the cell wall. If the cell wall is weak, then the water rushes in bursting the cell.
