Put sugar, mint, and lime quarters into glass and muddle lightly. Add Calcium lactate.
Pour in rum and sprite. Mix together until sugar is dissolved.
Strain liquid into cup. Place 1 mint leaf in each mold. Pour mix into each semi circle mold to the rim. Make sure the leaves are fully submerged. Put tray into a freezer.
In a new bowl add sodium alginate to water. Blend with hand blender. Let mixture rest for 20 minutes. Pour into a bowl. Place another bowl of water next to sodium alginate bath.
Remove ice tray and place each sphere into sodium bath. Rinse off in water bath and remove immediately. Sphere is complete.