It turns out that the van dar waals constant b is equal to four times the total volume actually occupied by the molecules of a mole of gas. using this figure, calculate the fraction of the volume in a container actually occupied by ar atoms:
a) at stp
b) at 100 atm pressure and 0 degrees celsius

The fraction of the volume in a container actually occupied by Ar atoms is a) 6.1L/mol and b) 0.2L/mol

Explanation:

The constant b is equal to four times the total volume actually occupied by the molecules of a mole of gas thus,

(1)

where Vm is the molar volume, V is the volume and n is the number of moles.

Also, for an ideal gas the equation of gases is P.V = n.R.T (2)

where P is the pressure, V is the volume, n is the number of moles, R is the gases constant and T is the temperature.

In a) the STP conditions establishes pressure (P) of 1 atm and a temperature (T) of 298K.  Using the equation (2) the volume of 1 mol of argon is 24.4L, thus

In b) at 100 atm pressure and 0 degrees Celsius (or 273K) using the equation (2) the volume of 1 mol of argon is 0.2L, thus

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