Determine the number of oxygen molecules in 1 m3, if the pressure is 0.20 MPa, and the average velocity

Determine the number of oxygen molecules in 1 m3, if the pressure is 0.20 MPa, and the average velocity of its molecules is 700 m / s.

These tasks: V (volume of taken oxygen) = 1 m3; P (pressure) = 0.2 MPa (0.2 * 10 ^ 6 Pa); Vav. (average velocity of oxygen molecules) = 700 m / s.

Constants: Na (Avogadro’s number) = 6.02 * 10 ^ 23 mol-1; M (molar mass of oxygen) = 0.032 kg / mol.

The number of oxygen molecules can be expressed from the formula: P = 1/3 * ρ * Vav2 = 1/3 * (m / V) * Vav2 = 1/3 * (M * n / Na) * Vav2 / V, whence n = 3 * P * V * Na / (M * Vav2).

Let’s calculate: n = 3 * 0.2 * 10 ^ 6 * 1 * 6.02 * 10 ^ 23 / (0.032 * 7002) = 23 * 10 ^ 24 molecules.