For the jalapeno simple syrup: Add the sugar, jalapeno and 1 cup water to a saucepan. Bring to a boil, stirring to dissolve the sugar. When the sugar is dissolved, remove from the heat and let cool for 1 hour. Remove the jalapeno before using.
For the mojitos: Divide the mint leaves between two pitchers, and muddle. Squeeze the juice of 1 lime into each pitcher, then add the simple syrup, evenly divided. Fill the pitchers with ice and top off with club soda. Add the rum to one of the pitchers. Stir and serve.