Find the concentration of oxygen molecules, if at a pressure of 2 * 10 ^ 5 pascal, the root mean square velocity is 700 m / s.

univerkov | March 8, 2021 | education

To calculate the concentration of oxygen molecules, use the formula: P = 1/3 * m0 * n * V ^ 2 = 1/3 * m0 * n * V ^ 2 = 1/3 * (M / Na) * n * V ^ 2 , whence n = 3 * P * Na / (M * V ^ 2).

Variables and constants: P – oxygen pressure (P = 2 * 10 ^ 5 Pa); V is the mean square velocity (V = 700 m / s); Na – Avogadro’s number (Na = 6.02 * 10 ^ 23 mol-1); M is the molar mass of oxygen (M = 0.032 kg / mol).

Let’s calculate: n = 3 * P * Na / (M * V ^ 2) = 3 * 2 * 10 ^ 5 * 6.02 * 10 ^ 23 / (0.032 * 700 ^ 2) = 23 * 10 ^ 24 m- 3.

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