The radius of Xe is 1.3*10^-8 cm. A 100-mL flask is filled with Xe at a pressure of 1.4 atm and the temperature is 290 K. Calculate the fraction of the volume that is occupied by Xe atoms.

To calculate the fraction of the volume occupied by Xe atoms, we need to first determine the volume occupied by a single Xe atom, and then divide it by the total volume of the flask.

To find the volume occupied by a single Xe atom, we first need to calculate the volume of the Xe atom itself. The given radius of Xe is 1.3 * 10^-8 cm, which corresponds to the diameter of the atom. The volume of a sphere is given by the formula V = (4/3) * π * r^3, where V is the volume and r is the radius.

Let's plug in the values:

V = (4/3) * π * (1.3 * 10^-8 cm)^3

Now we can calculate the volume in cubic centimeters.

V = (4/3) * 3.14 * (1.3 * 10^-8 cm)^3

Next, we need to convert the volume from cubic centimeters to liters, as the volume of the flask is given in liters. Since 1 liter is equal to 1000 cubic centimeters, we divide the volume by 1000.

V = [(4/3) * 3.14 * (1.3 * 10^-8 cm)^3] / 1000

Now we have the volume occupied by a single Xe atom in liters.

To calculate the fraction of the volume occupied by Xe atoms, we divide this volume (V) by the total volume of the flask (100 mL = 100 cm^3).

Fraction of volume occupied by Xe atoms = V / flask volume

Fraction of volume occupied by Xe atoms = [(4/3) * 3.14 * (1.3 * 10^-8 cm)^3] / 1000 / 100 cm^3

Fraction of volume occupied by Xe atoms = [(4/3) * 3.14 * (1.3 * 10^-8 cm)^3] / 100000 cm^3

Now, we can evaluate this expression to find the fraction of the volume occupied by Xe atoms.