The number of Helium atoms in the balloon

[jinx007]

A balloon contains 0.40 mol of helium at 300K. calculate

1/ The number of Helium atoms in the balloon

2/ The average kinetic energy of the helium atom in the balloon

3/ The total kinetic energy of the helium atoms in the balloon

I am having a lot of difficulties to manage the ideal gas chapter..Please help me to answer these questions. However the question seems easy and this make me worried as i cannot answer these questions.

My attempt (i don't really know if it is correct as i don't have the asnwer)

1/ 1 mol = 6.02 x 10^23 ataoms

0.4 mol = 6.02 x 10 ^23 x 0.4

2/



3/

 

[Onamor]

1 is correct

for 2, remember kinetic theory: each degree of freedom makes 1/2 kT available to the energy of each atom.
Kinetic theory is VERY important in thermodynamics, if you don't know where this result comes from, and understand why, you will have trouble later.

3 is combining your answers from 1 and 2.

Can you do it now?

 

[ehild]

Have you learned about the Equipartition Theorem? In an ideal gas, the molecules move in random, and their average kinetic energy for each degrees of freedom is kT/2, where k is the Boltzmann constant. Helium is a mono-atomic gas, it has only translational kinetic energy, 1/2 mv², but has the "freedom to choose" all the three components of the velocity, v_x, v_y, v_z. It is said that the He atom has 3 degrees of freedom. One He atom has 3(kT/2) kinetic energy in average.

If the molecule consists of three or more atoms, like H₂O or CH₄, rotational kinetic energy (Er_ot=1/2 Iw^2) can be associated to each degrees of rotational freedom, which are also three. Such molecules have three translational and three rotational degrees of freedom, so their average kinetic energy is 6 (kT/2).

Diatomic or linear molecules like H₂ and CO₂ also have three independent directions of rotation, but no energy is associated to the rotation around the axis of the molecule as the moment of inertia with respect to this axis is negligible. Therefore the diatomic or linear molecules have 5 (kT/2) kinetic energy in average.

ehild