At what temperature does the oxygen molecule have a root mean square velocity of 700 m / s?

Given: V (mean square velocity of taken oxygen molecules) = 700 m / s.

Constants: M (molar mass) = 0.032 kg / mol; R (universal gas constant) = 8.31 J / (mol * K).

We express the sought temperature of the molecules of the taken oxygen from the formula: V = √ (3 * R * T / M), whence V ^ 2 = 3 * R * T / M, whence T = V ^ 2 * M / (3 * R).

Let’s perform the calculation: T = 700 ^ 2 * 0.032 / (3 * 8.31) ≈ 629 K (356 ºС).

Answer: Oxygen molecules should have a temperature of 356 ºС.