PHYSICAL CHEMISTRY

I. KINETIC MOLECULAR THEORY: Ideal Gas

Assumptions for the establishment of Kinetic Molecular Theory

On Motion: The gas consists of molecules moving at random motion.
On Size: The volume of the particle is negligible compared to the volume of its container.
On Interaction: The spherical particles undergo brief, perfectly elastic collision.

A. Molecular Speed

$v = \sqrt{\frac{3RT}{M}}$ M is Molar Mass

Example 1:
What is the average speed of the oxygen gas at T = 45 ^oC?
Solution:

$v = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3(8.314)(45+273.15)}{\frac{32 }{1000 }}}$ (Note: Division by 1000 of Molar Mass is to convert g to kg)
$v = 497.988 \;\frac{ m}{s}$

B. Kinetic Energy of a Particle

The assumption in KMT is that gas particles are spheres and therefore only exhibiting translational motion. Hence, the gas only possesses translational kinetic energy.

$KE = \frac{3}{2}kT$
k is Boltzmann Constant (Casio Calculator 991 #25); k = 1.3805 x 10^-23 Joules/particle.K

Example 2:
What is the Kinetic Energy of an Argon molecule at T = 45 ^oC?
Solution:
$KE = \frac{3}{2}kT$
$KE = \frac{3}{2}(1.3805 \times 10^{-23})(45 + 273.15)$
$KE = 6.59 \times 10^{-21} \;\frac{J }{particle}$