Final answer:
5.0 moles of a gas occupy 15.0 L, so 2.0 moles would occupy 6.0 L, as the volume a gas occupies is directly proportional to the amount of gas in moles at constant pressure and temperature.
Step-by-step explanation:
If 5.0 moles of gas take up 15.0 L of space under constant pressure and temperature conditions, we can find out how much volume 2.0 moles of gas would take using a direct proportion, since at constant pressure and temperature, volume and amount of gas (in moles) are directly proportional according to Avogadro's law. To solve the problem, set up the proportion as follows:
V1/n1 = V2/n2,
where V1 is the volume of the first amount of gas, n1 is the number of moles of the first amount of gas, V2 is the volume of the second amount of gas, and n2 is the number of moles of the second amount of gas.
Substituting into the equation:
15.0 L / 5.0 moles = V2 / 2.0 moles,
V2 = (2.0 moles × 15.0 L) / 5.0 moles,
V2 = 6.0 L.
Therefore, 2.0 moles of the gas would occupy a volume of 6.0 L under the same conditions.