Question

calculate the root mean square velocity and kinetic energy of CO,CO2, and SO3 at 284K.

Answer 1

The molar gas constant "R", has the value 8.3143 J/mol K,
and the Temperature "T", is in Kelvin.
Since the joule is the kg-m²/s², the molar mass must be in kg/mol

v_rms = (3RT/M)^1/2,

v_rms CO = [(3)(284K)(8.3143 J/mol K) / (0.02801 kg/mol)]^1/2 = 502.89 m/sec

v_rms CO₂ = [(3)(284K)(8.3143 J/mol K) / (0.04401 kg/mol)]^1/2 = 401.2 m/sec

v_rms SO₃ = [(3)(284K)(8.3143 J/mol K) / (0.08006 kg/mol)]^1/2 = 297.46 m/sec

K.E. = 1/2 (mass) (velocity)² or
= 3/2 RT Joules/mole
= 1.5 (8.314 J/mol-K)(284K)
= 3542 joules per mole
3542 J/mole is the average K.E. for any of the three gases