# What is the average kinetic energy of the molecules in a gas at 273K?

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Jul 31, 2014

The average kinetic energy of the molecules is 5.66 × 10⁻²¹ J.

According to Kinetic Molecular Theory, the average kinetic energy of gas molecules is a function only of temperature.

The formula is

$K E = \frac{3}{2} k T$

where $T$ is the Kelvin temperature and $k$ is Boltzmann's constant.

KE = 3/2 × 1.381 × 10⁻²³ "J·K⁻¹" × 273"K" = 5.66 × 10⁻²¹ J

For a mole of molecules, the average kinetic energy is

(5.66 × 10⁻²¹"J")/(1"molecule") × (6.022 × 10²³"molecules")/(1"mol") = 3.41 ×10³ J/mol = 3.41 kJ/mol

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