I have assume ,
The radius of a xenon atom is 1.3*10^-8cm
First find the amount of atoms.
PV = nRT
Where
P = Pressure in Kilopascals
V = Volume in Litres
R = The general gas constant, approx 8.31 J mol^-1 K^-1
T = Temeperature in Kelvin
We want to solve for n, or mol
n = PV/RT
Now to get our units straight.
Remember that 1 atm = 101.3 kPa
100 ml = 0.1 L
1.5 atm = 151.82 kPa
276K = 276K
n = PV/RT
n = (151.82 * 0.1) / (8.31 * 276)
n = 0.00662 mol
This is the amount of xenon atoms.
The number of particles in 1 mol is equivalent to Avogadros
constant, or 6.02 * 10^23 particles.
The equation is:
n = N/A
n = amount in mol
N = Number of particles in sample
A = Avogadros constant
n = N/A
N = nA
N = 0.00662 * 6.02 * 10^23
N = 3.98 * 10^21
Now to solve for the volume for one particle.
The volume of a sphere is given by:
V = 4/3 pi r^3
V(Xe atom) = 4/3 pi (1.3 * 10^-8)^3
V(Xe atom) = 9.2 * 10^-24 cm^3
Now to work out the volume of ALL the xenon atoms, simply multiply
this by the number of particles present:
V(Xe sample) = 9.2 * 10^-24 * 3.98 * 10^21
= 0.0366 cm^3
Now to calculate the fraction of the volume these atoms occupy
compared to the volume of the flask, simply divide the volume of
the atoms by the volume of the flask. Take care though.
The volume of the flask, or 0.1 litres, is equivalent to 0.1
decimetres cubed. The volume of atoms calculated was in
centrimetres cubed. To make the whole thing clearer, let us
evaluate both volumes in METRES cubed.
In one metre cubed, there are 1*10^6 cm^3
In one decimetre cubed, there are 1*10^3 dm^3
So the volume fraction is equal to
= (0.0366 * 10^3) / (0.1 * 10^6)
= 0.000366
As a percentage this is:
0.000357 * 100 = 0.0366 % of the flask's volume is occupied by
atoms.
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