Answer:
558.37 m/s is the root means square speed of the molecules.
Explanation:
Molar mass of the nitrogen gas [tex]N_2[/tex] , 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 :
[tex]u_{rms}=\sqrt{\frac{3RT}{M}}[/tex] [tex]( R = k \times N_A)[/tex]
Where :
R = Universal gas constant = 8.314 J/mol k
k = Boltzmann constant = [tex]1.38\times 10^{-23} J/K[/tex]
[tex]N_A[/tex] = Avogadro number
So, root means square speed of nitrogen molecule is :
[tex]u_{rms}=\sqrt{\frac{3\times 8.314 J/mol K\times 350 K}{0.028 kg/mol}[/tex]
[tex]=558.37 m/s[/tex]
