The vessel contains gas; what pressure does it produce on the walls of the vessel, if the mass of the gas is 5 g

The vessel contains gas; what pressure does it produce on the walls of the vessel, if the mass of the gas is 5 g, its volume is 1 liter, the root mean square velocity of molecules is 500 m / s.

Given: m = 5 g; V = 1 L; v = 500 m / s;
Find: p
Decision:
1) First, let’s translate the known values into a more convenient system. m = 5g = 5 * 10 ^ -3 kg; V = 1 l = 1 * 10 ^ -3 m ^ 3.
2) We use the Mendeleev-Clapeyron law. It looks like this: p * V = m * R * T / M.
3) Find the root mean square velocity: v = √ (3 * RT / M). Let’s square to get rid of the root. V ^ 2 = 3RT / M. -> RT / M = V ^ 2/3.
4) We return to our formula and get: p * V = m * v ^ 2/3. Let us express p and substitute the known values. p = m * v ^ 2/3 * V) = 5 * 10 ^ -3 * 500 ^ 2 / (3 * 1 * 10 ^ -3) ≈ 420,000 Pa
Answer: 420000