Question

At 4.00 L, an expandable vessel contains 0.864 mol of oxygen gas. How many liters of oxygen gas must be added at constant temperature and pressure if you need a total of 1.48mol of oxygen gas in the vessel? Express the volume to three significant figures, and include the appropriate units.

Answer 1

To achieve a total of 1.48 mol of oxygen gas in the vessel at constant temperature and pressure, approximately 2.86 L of oxygen gas must be added to the initial 4.00 L volume. This calculation is based on the proportionality of volume to the number of moles in the ideal gas law.

Step-by-step explanation:

The question refers to the calculation of the volume of oxygen gas needed at constant temperature and pressure to increase the number of moles in the vessel from 0.864 mol to 1.48 mol. Using the ideal gas law, we can assume that the volume of a gas is directly proportional to the number of moles if the temperature and pressure remain constant (Avogadro's Law). The initial volume is 4.00 L for 0.864 mol of oxygen. To find the new volume for 1.48 mol, we set up a proportion: (4.00 L / 0.864 mol) = (V2 / 1.48 mol).

Solving for V2, we get V2 = (4.00 L / 0.864 mol) × 1.48 mol. Calculating this gives us V2 ≈ 6.86 L. Therefore, to have a total of 1.48 mol of oxygen at the same temperature and pressure, the volume should be increased to about 6.86 L.

To find out how many liters of oxygen gas must be added, we subtract the initial volume from the final volume: 6.86 L - 4.00 L = 2.86 L. Hence, approximately 2.86 L of oxygen gas must be added to the vessel to achieve a total of 1.48 mol of oxygen.

Answer 2

I think the question means at this certain temperature and pressure, 0.864 mol gas has a volume of 4.00 L. Under same temperature and pressure, the mole number is related directed with volume. So 1.48-0.864=0.616 mol gas has a volume of 2.85 L.