Question

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:

Answer 1

533.92 m/s

Step-by-step 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