At about 15 degrees Celsius (about 60F), you can saturate a solution of NH3 in water of about 308 grams of gaseous NH3 per liter of water.

OK, so there's about 3.79 liters per gallon. 308 grams/liter of NH3 times 3.79 liters = 1,167 grams of NH3 (gas) in a gallon, or 1.167 kg in one gallon of water, or about 2.567 pounds of NH3 per gallon of water.

As the temperature goes up, the solubility of NH3 in water goes down, and that means that if you heat up the water, it will out-gas NH3.

Ammonia (as a gas) is probably one of the most soluble gases in water, if not the most soluble.