Question

Assume that the Van der Waals b constant for Xenon (see Table 1C.3- or 1.6 old version - van der Waals coefficients) divided by Avogadro's Number represents the volume of a single Xenon atom. Assume that Xenon atom is spherical, and estimate the radius (in meters) of a Xenon atom using the formula Vsphere = (4/3)rır3.

Answer 1

The estimated radius is 2.734*10^(-10) m.

Step-by-step explanation:

If we assume the van der Waals constant b for Xenon divided by Avogadro's number gives the volume of a single Xenon, we have

`V=(b)/(N)=(0.05156 l/mol)/(6.02214076*10x^(23))  =8.56*10^(-26)litres\\`

We can express this volume in other units, more suitable for the size of an atom:

`V=8.56*10^(-26)litres*(1m3)/(10^(3)litres )*((10^(9) nm)/(1m )  )^(3)\\\\V=8.56*10^(-26)litres*(1m3)/(10^(3)litres )*(10^(27) nm3)/(1m3 )  \\\\ V=0.0856 \, nm^(3)`

The volume of the sphere is

`V=(4\pi)/(3)*r^(3)`

Then we can rearrange to clear r

`r=\sqrt[3]{(3V)/(4\pi) }= \sqrt[3]{(3*0.0856nm^(3))/(4\pi) }=\sqrt[3]{0.0204 nm^(3) }=0.2734nm`

The estimated radius is 0.2734 nm. As the problem ask for the radius to be in meters (1 nm = 10^(-9) m), we can multiply it by 10^(-9) and determine that the radius is 2.734*10^(-10) m.