Final answer:
The new volume of oxygen gas after reducing the mass from 5.4 grams to 1.7 grams, while keeping temperature and pressure constant, is 1.33 liters.
Step-by-step explanation:
The question relates to the behavior of gases and involves the use of gas laws to determine the new volume of a gas when a certain amount of it is removed. We can start by recognizing that, if the beaker is closed (except when the valve was briefly opened), and temperature and pressure are constant, the volume of the gas and its mass are directly proportional. This relationship is part of the Ideal Gas Law, but as we are keeping temperature and pressure constant, it simplifies to Avogadro's Law.
When the amount of oxygen decreases from 5.4 grams to 1.7 grams, it becomes one-third of the initial amount. So, if the volume was held constant before the valve was opened, once we lose two-thirds of the gas, the volume directly available for the gas would also be reduced to one-third, because the pressure and temperature are constant in this scenario (it assumes that the remaining space in the beaker isn't filled with any other gas or affected in any other way).
Therefore, to find the new volume of gas, we take the initial volume and divide it by the ratio of the initial to final mass:
4.0 L (initial volume) / (5.4 g / 1.7 g) = 1.33 L (new volume)