In this scenario, we are examining a gas contained in a cylinder with a movable piston. Initially, the cylinder holds 10 grams of xenon gas, which corresponds to a specific volume of 10 liters. When an additional 10 grams of xenon gas is introduced, the volume of the gas increases. This situation can be explained using Avogadro's Law, which states that equal volumes of gases, at the same temperature and pressure, contain an equal number of moles. Therefore, as the mass of the gas increases, the number of moles also increases, leading to a corresponding increase in volume.

To find the new volume after adding the additional gas, one can first convert the mass of xenon to moles using the molar mass of xenon (approximately 131.29 g/mol). The initial amount of xenon can be calculated as:

$$ n_1 = \frac{10 \text{ g}}{131.29 \text{ g/mol}} \approx 0.076 \text{ moles} $$

After adding another 10 grams, the total mass becomes 20 grams, and the new number of moles is:

$$ n_2 = \frac{20 \text{ g}}{131.29 \text{ g/mol}} \approx 0.152 \text{ moles} $$

Using Avogadro's Law, the relationship between the volume and the number of moles can be expressed as:

$$ \frac{V_1}{n_1} = \frac{V_2}{n_2} $$

Substituting the known values allows for the calculation of the new volume, \( V_2 \). This illustrates the direct relationship between the volume of a gas and the number of moles, reinforcing the principles of Avogadro's Law in gas behavior.