The root mean square velocity (RMS velocity) is a method to find a single velocity value for the particles. The average velocity of gas particles in a mixture is found using the root mean square velocity formula:
μrms = sqrt (3RT/M)
Where,
R = universal gas constant = 8.3145 (kg·m^2/s^2)/K·mol
T = temperature = 35.9 ˚C = 309.05 K
M = molar mass = 28 * 10^-3 kg / mol
Substituting the given values into the equation:
μrms = sqrt [(3 * 8.3145 (kg·m^2/s^2) /K·mol) * (309.05 K) / (28 * 10^-3 kg / mol))]
μrms = sqrt (275,313.8813 m^2)
μrms = 524.7 m / s (ANSWER)