Question

The root mean square speed of O₂ molecules at 29°C is about 0.485 km/s. What is the root mean square speed (in km/s) of a H₂ molecule at 29°C?

____km/s

Answer 1

root mean square speed = (3RT/M)^1/2

where, R = ideal gas constant = 8.3145 (Kg.m²/sec²) / (K.mol)

T = absolute tempreture = 29⁰C = 273.15 + 29 = 302.15 K

M = mass of mole of gas in kilogram = 2.01 gm/mol = 2.01 10^-3 kg/mol

Substitute value in above equation

root mean square speed of H₂ = [[3 (8.3145 (Kg.m²/sec²) / (K.mol)) (302.15 K)] / [(2.01 10^-3 kg/mol)]]^1/2

= [749591.306 m²/s²]^1/2

= 865.789 m/s

= 0.866 km/s

root mean square speed (in km/s) of a H2 molecule at 29°C = 0.866 km/s