Question

The radius of a xenon atom is 1.3×10−8cm. a 100-ml flask is filled with xe at a pressure of 1.2 atm and a temperature of 281 k . part a calculate the fraction of the volume that is occupied by xe atoms. (hint: the atoms are spheres.)

Answer 1

Radius of Xenon = 1.3Ă—10â’8 cm 
Volume = 100 ml = 0.1 L 
Pressure P = 1.2 atm = 121.59 Kpa 
Temperature = 281 K 
R = Gas Constant = 8.31 J mol^-1 K^-1 
Now find the number of atoms 
PV = nRT => n = PV / RT 
n = (121.59 x 0.1) / (8.31 x 281) = / 2335.11 = 0.0052 
Number of atoms in a mole is same as Avogadro constant A, which is 6.02 x
10^23 particles.  
n = number of atoms= 0.0052 
N = number of particles 
 Avogadro constant A = 6.02 x 10^23 
n = N/A => N = n x A = 0.0052 x 6.02 x 106^23 = 3.13 x 10^20 
Volume of Xe atom which would be a sphere = (4/3) x pi x r^3 
Volume = = (4/3) x 3.14 x (1.3Ă—10â’8)^3 = 9.2 x 10^-24 
Volume occupied by these particles = n x Volume = 3.13 x 10^20 x 9.2 x
10^-24 = 0.00288
 Fraction of volume will be = 0.00288 / 0.1 = 0.0288