The molarity of a solution is defined as the number of moles of solute per liter of solution. To calculate the molarity of a solution, we need to know the number of moles of solute and the volume of the solution in liters.

Step 1: Calculate the number of moles of MgCl2.

The molar mass of MgCl2 is 95.21 g/mol. Therefore, the number of moles of MgCl2 in 75.0 grams is:

$$n=\frac{m}{M}=\frac{75.0 \text{ g}}{95.21 \text{ g/mol}}=0.787 \text{ mol}$$

Step 2: Calculate the volume of the solution in liters.

500.0 milliliters is equal to 0.5000 liters.

Step 3: Calculate the molarity of the solution.

The molarity of the solution is:

$$M=\frac{n}{V}=\frac{0.787 \text{ mol}}{0.5000 \text{ L}}=1.57 \text{ M}$$

Therefore, the molarity of the solution is 1.57 M.