how long would it take for say a gallon pitcher of water to sit before the chlorine to dissipate?

Answer 1

Would depend on several factors including height and depth of the pitcher, temp of water, etc.

A normally shaped 1 gallon pitcher at or near room temp should take about 20 minutes for MOST of the chlorine to dissipate. If you wanted all of it out you could boil the water. If you do this make sure the pitcher is made of pyrex.