Question

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

Answer 1

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

Step-by-step explanation:

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

`b = (V_(m))/(4) = (V)/(4.n)` (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

`b = (24.4L)/(4.1mol) = 6.1L/mol`

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

`b = (0.8L)/(4.1mol) = 0.2L/mol`