Final answer:
The quantity of helium in moles remains the same at 0.65 mol when the volume of the syringe is doubled while keeping the temperature constant, according to Avogadro's law.
Step-by-step explanation:
The quantity of helium moles in the syringe will not change when the volume is doubled at constant temperature, according to Avogadro's law, which states that the volume of a gas at constant temperature and pressure is directly proportional to the number of moles of gas. Since the question specifies that only the volume changes and the temperature remains constant, the amount of helium (in moles) stays the same. Therefore, even when the syringe volume is doubled, the number of moles remains 0.65 mol.