A 0.6-m3 gas tank holds 5 moles of nitrogen gas (N2), at a temperature of 320 K. The atomic mass of nitrogen is 14 g/mol, the molecular radius is 3.0 * 10-10 m, and the Boltzmann constant is 1.38 * 10-23 J/K. The root-mean-square speed (thermal speed) of the molecules is closest to:

Question

Physics

Mullen

19 August, 11:36

A 0.6-m3 gas tank holds 5 moles of nitrogen gas (N2), at a temperature of 320 K. The atomic mass of nitrogen is 14 g/mol, the molecular radius is 3.0 * 10-10 m, and the Boltzmann constant is 1.38 * 10-23 J/K. The root-mean-square speed (thermal speed) of the molecules is closest to:

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Ashlyn Huynh · Answer 1

533.92 m/s

Explanation:

The root-mean-square speed of a gas is given by v = √ (3RT/M)

R = molar gas constant = 8.3145 J/mol-K

T = Temperature = 320 K

M = Molar mass of Nitrogen in kg/mol = 2 * 14 * 10⁻³ kg/mol = 28 * 10⁻³ kg/mol

v = √ (3RT/M) = √ (3 * 8.3145 J/mol-K * 320 K/28 * 10⁻³ kg/mol) = √7981920/28 = √285.068.57 = 533.92 m/s