What is the concentration of nitrogen molecules if at a pressure of 100 kPa their thermal velocity is 600 m / s?

To find the value of the concentration of nitrogen molecules under these conditions, we apply the formula: P = 1/3 * m0 * n * V ^ 2 = 1/3 * (M / Na) * n * V ^ 2, whence we express: n = 3 * P * Na / (M * V ^ 2).

Variables and constants: P – effective pressure (P = 100 kPa = 10 ^ 5 Pa); Na – Avogadro’s number (Na = 6.02 * 10 ^ 23 mol-1); M – molar mass (M = 0.028 kg / mol); V – thermal speed (V = 600 m / s).

Calculation: n = 3 * P * Na / (M * V ^ 2) = 3 * 105 * 6.0 ^ 2 * 10 ^ 23 / (0.028 * 600 ^ 2) = 1.79 * 10 ^ 25 m-3 …

Answer: The concentration of nitrogen molecules is 1.79 * 10 ^ 25 m-3.