For adults and older children, the normal range is 137 to 145 millimoles per liter. For infants, the normal range is somewhat lower, up to one or two millimoles per liter from the adult range. As soon as a person has more than 145 millimoles per liter of blood serum, then he has hypernatremia, which is too great a concentration of sodium in his blood serum. If a person's serum sodium level falls below 137 millimoles per liter, then they have hyponatremia, which is too low a concentration of sodium in his blood serum.