At a temperature of 300 K, the density of the gas is 1.2 kg / m3, and the mean square velocity

At a temperature of 300 K, the density of the gas is 1.2 kg / m3, and the mean square velocity of the molecules is 500 m / s. Determine the gas concentration.

Data: T (temperature) = 300 K; ρ (density of the taken gas) = 1.2 kg / m3; V (root mean square velocity of molecules) = 500 m / s.

Constants: k – Boltzmann’s constant (k = 1.38 * 10 ^ -23 J / K).

To determine the concentration of molecules of the taken gas, we apply the equality: n * k * T = P (gas pressure) = 1/3 * ρ * V ^ 2, whence n = ρ * V ^ 2 / (3 * k * T).

Let’s perform the calculation: n = 1.2 * 500 ^ 2 / (3 * 1.38 * 10 ^ -23 * 300) = 241.5 * 10 ^ 23 m-3.

Answer: The concentration of the taken gas molecules is 241.5 * 10 ^ 23 m-3.