# The pressure of a gas in a 0.1 m^3 container is 150kPa.Find the number of gas molecules in the container if the average translational kinetic energy of each molecule is 5.0 x 10^-21 J?

Dec 21, 2015

$4.5 \times {10}^{24}$

#### Explanation:

The average translational kinetic energy is given by:

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

$k$ is the Boltzmann Constant which is effectively the gas constant per mole.

$T$ is the absolute temperature.

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

T=(5xx10^(-21)xx2)/(3xx1.38xx10^(-23)

$T = 241.5 \text{K}$

From the ideal gas equation we get:

$P V = N k T$

$N$ is the number of molecules.

$\therefore N = \frac{P V}{k T} = \frac{150 \times {10}^{3} \times 0.1}{1.38 \times {10}^{- 23} \times 241.5}$

$N = 4.5 \times {10}^{24}$