Question

determine the most probable velocity of the gas molecules, whose density is ρ = 0,35 kg / m³ at a pressure of ρ = 40 kPa.

Answer 1

You probably want the most probable SPEED, because the most probable velocity is always zero. I hope you see why. There are always equal numbers going in each direction (assuming no mean flow).


Use the kinetic theory relationship

P = (1/3)(density)*V^2

You should not be using the same symbol for both pressure and density.

V^2 = 3*P/ñ = 3*40*10^3 N/m^2/0.35 kg/m^3
= 3.43*10^5 N*m/kg
= 3.43*10^5 m^2/s^2
V = 586 m/s

This V is the r.m.s. velocity.

The most probable speed is lower by a factor sqrt(2/3) = 0.8165, for a Maxwellian velocity distribution. For the relationship, see
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html