A 0.50 m3 gas tank holds 3.0 moles of ideal diatomic nitrogen gas at a temperature of 350 K. The atomic mass of nitrogen is 14 g/mol. What is the rms speed of the molecules? (The Boltzmann constant is 1.38 × 10-23 J/K, NA = 6.022 × 1023 molecules/mol.)

558.37 m/s is the root means square speed of the molecules.

Explanation:

Molar mass of the nitrogen gas , M= 2 × 14 g/mol = 28 g/mol

1 g = 0.001 kg

M = 28 g/mol = 28 × 0.001 kg/mol = 0.028 kg/mol

Temperature of the gas = T = 350 K

The root mean square speed is given by :

Where :

R = Universal gas constant = 8.314 J/mol k

k = Boltzmann constant =

= Avogadro number

So, root means square speed of nitrogen molecule is :