At what temperature will the root mean square velocity of oxygen molecules become equal to 600 m / s?

We calculate the required temperature using the formula:

V = √ (3kT / m0); V is the value of the root mean square velocity (V = 600 m / s), k is the Boltzmann constant (k = 1.38 * 10 ^ -23 J / K), T is the absolute temperature of oxygen (K), m0 is the mass of the molecule (m0 = M * Na, where M is the molar mass (diatomic gas, M = 32 g / mol = 0.032 kg / mol), Na is Avogadro’s number (const, Na = 6 * 10 ^ 23 mol-1)).

V2 = 3kT * Na / M.

V2 * M = 3kT * Na.

T = V ^ 2 * M / (3k * Na) = 600 ^ 2 * 0.032 / (3 * 1.38 * 10 ^ -23 * 6 * 10 ^ 23) ≈ 464 K.