At what temperature is the root-mean-square velocity of nitrogen molecules 850 m / s?

Data: V (required root mean square velocity of the taken nitrogen molecules) = 850 m / s.

Constants: M (molar mass of nitrogen) = 0.028 kg / mol; R (universal gas constant) = 8.31 J / (mol * K).

To determine the desired temperature of taken nitrogen, we apply the formula: V = √ (3 * R * T / M), whence V2 = (3 * R * T / M) and T = V2 * M / (3 * R).

Let’s make a calculation: T = 8502 * 0.028 / (3 * 8.31) ≈ 811.5 K (538.5 ºС).

Answer: Nitrogen molecules will reach a speed of 850 m / s at a temperature of 538.5 ºС.