The purpose of a mordant in the Gram stain is to:
make gram-negative cells visible.
prevent the crystal violet from leaving the cells.
make the flagella visible.
make the bacterial cells larger.
remove the simple stain.

The purpose of a mordant in the Gram stain is to:

The answer is "prevent the crystal violet from leaving the cells."

Explanation:

Staining techniques are widely used to visualize those components that are  too difficult to see with the use of a light microscope. Staining involves 3 major steps/processes that include: Counter staining (using Safranin), De-colorization (using ethanol/acetone), and, Staining with crystal violet (a water soluble dye). During the staining procedure, the bacteria are bathed in alcohol, which causes the cell walls to shrink. The primary stain of the Gram's method is crystal violet.

A mordant is classically defined as an ion that binds a chemical dye and keeps it in place and it used for intensifying stains in cell or tissue preparations. Iodine mordant is used in Gram's Staining.

Gram staining is performed when the chemical dye crystal violet is mixed with the mordant iodine. Gram staining differentiates bacteria by the chemical and physical properties of their cell walls and it also distinguishes between Gram-positive and Gram-negative bacteria. Gram staining is based on the ability of bacteria cell wall to retaining the crystal violet dye during solvent treatment.

The purpose of a mordant in the Gram stain is to prevent the crystal violet from leaving the cells, in other words, increase the affinity of the primary stain.