Question

13.9 mol of helium is confined to a 19 L vessel at a pressure of 7 atm. Boltzmann’s constant is 1.38 × 10−23 J/K, and the universal gas constant is 8.31 J/K. Find the average kinetic energy of a helium molecule of mass 5.34 × 10−26 kg. Answer in units of J.

Answer 1

Solution:

Given;

no. of moles

n = 13.9

volume of the vessesl $V=19L$

Pressure $P=7atm$

Boltzmann's constant $k=1.38\times 10^{-23}J/K$

Gas constant

R = 8.31J/mol.K

Using the ideal gas equation, we can find the temperature of the vessel.

PV nRT

We have to use, the value of $R=0.0821atm.L/mol.K$ .So,

  $T=\frac{PV}{nR}=\frac{7\times 19}{13.9\times0.0821}=116.55K$

The Average Kinetic energy of the helium molecule is given by,

$K=\frac{3}{2}kT=\frac{3}{2}\times1.38\times10^{-23}\times116.55=2.41\times10^{-21}J$

Thus, the Average kinetic energy of the helium molecule is $2.41\times10^{-21}J$ .