Question

The average kinetic energy of the molecules in a gas sample depends only on the temperature, T. But given the same kinetic energies, a lighter molecule will move faster than a heavier molecule. What is the rms speed of Cl2 molecules at 347 K? What is the rms speed of He atoms at 347 K?

Answer 1

# Root mean square speed of Cl₂

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

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

T = absolute tempreture = 347 K

M = mass of mole of gas in kilogram = 70.906 gm/mol = 70.906 10^-3 kg/mol

Substitute value in above equation

root mean square speed of Cl₂ = [[3 (8.3145 (Kg.m²/sec²) / (K.mol)) (347 K)] / [(70.906 10^-3 kg/mol)]]^1/2

= [122068.57671 m²/s²]^1/2

= 349.383 m/s

root mean square speed of Cl₂ =  349.383 m/s

# Root mean square speed of He

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

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

T = absolute tempreture = 347 K

M = mass of mole of gas in kilogram = 4.0026 gm/mol = 4.0026 10^-3 kg/mol

Substitute value in above equation

root mean square speed of Cl₂ = [[3 (8.3145 (Kg.m²/sec²) / (K.mol)) (347 K)] / [(4.0026 10^-3 kg/mol)]]^1/2

= [2162443.037 m²/s²]^1/2

= 1470.524 m/s

root mean square speed of He =  1470.524 m/s