Determine the nitrogen pressure in the ampoule if there are 3.5 * 10 ^ 14 molecules in 1m ^ 3

Determine the nitrogen pressure in the ampoule if there are 3.5 * 10 ^ 14 molecules in 1m ^ 3, the average speed of which is 490 m / s.

Data: V (ampoule volume) = 1 m3; N (number of nitrogen molecules in 1 m3) = 3.5 * 10 ^ 14 molecules; Vav (average velocity of nitrogen molecules) = 490 m / s.

Constants: Na (Avogadro’s number) = 6.02 * 10 ^ 23 mol-1; M (molar mass of nitrogen) = 28 g / mol (0.028 kg / mol).

The nitrogen pressure in the ampoule is determined by the formula: P = 1/3 * m0 * n * Vcr ^ 2 = 1/3 * (M / Na) * (N / V) * Vcr ^ 2.

Calculation: P = 1/3 * (0.028 / (6.02 * 10 ^ 23)) * (3.5 * 10 ^ 14/1) * 4902 = 1.3 * 10 ^ -6 Pa (1.3 μPa ).

Answer: The nitrogen pressure in the ampoule is 1.3 μPa.