Combine sugar, preserves, and 1 cup of the soda in a medium saucepan and stir over low heat until sugar and preserves are melted. Add citrus juice and zest. Stir in the remaining soda, move to a clean, lidded container and chill thoroughly, 2 to 3 hours.
Churn mixture in ice cream maker per maker's instructions or until mixture reaches the consistency of a firm slush. Return mixture to lidded container and harden in freezer 1 hour before serving.
If sorbet is to be held frozen for longer than 2 hours, move from freezer to refrigerator for about 30 minutes before serving. If you'd like a more assertive sorbet, double the amount of citrus zest.