How many grams of calcium carbonate ($\mathrm{CaCO}_3$) are required to completely neutralize 200 mL of 0.5 M HCl? Given the reaction:
$$
\mathrm{CaCO}_3 + 2 \mathrm{HCl} \rightarrow \mathrm{CaCl}_2 + \mathrm{H}_2 \mathrm{O} + \mathrm{CO}_2
$$
(Molar mass of $\mathrm{CaCO}_3 = 100 \, \text{g/mol}$)