Question

calculate the root mean square velocity and kinetic energyof CO,CO2 and SO3 at 300k?

Answer 1

1)

root mean square velocities

V(rms) = sqrt(3*RT/MW)

R = gas constant 8.314 J/molK

T = abs T = 300 K

MW = molar mass

MW CO = 28 = 0.028 (in kg)

MW CO2 = 44 = 0.044

MW SO3 = 80.066 = 0.08006

then

a) for CO

V(rms) = sqrt(3*RT/MW

V(rms) = sqrt(3*8.314*300/0.028) = 516.948 m/s

b) for CO2

V(rms) = sqrt(3*RT/MW

V(rms) = sqrt(3*8.314*300/0.044) = 412.3m/s

c)

for SO3

V(rms) = sqrt(3*RT/MW

V(rms) = sqrt(3*8.314*300/0.080066) = 305.70 m/s

2)

for kinetic energy

E = 1/2 (m) (vrms)2

for 1 mol of gas then:

E = 3/2 R*T J

E= 3/2*8.314*300 = 3741.3 J for any gas

note that this makes sense, since high mass molecules will have lower speed (if we keep Energy constant)

= 13.78 joules per mole