Question

At what temperature should helium have the same effusion rate as CO2 at 25°C?

a) 27°C b) –246°C c) –189°C d) 2.27°C e) 25°C

Answer: b: -246

How do you get this?

Answer 1

we know that

effusion rate is proportional to sqrt ( 3RT / M)

so for C02 and He

we get

rHe / rC02 = sqrt ( THe x Mco2 / Tco2 / MHe)

given

rates are same

so

rHe = rC02

so

1 = sqrt ( THe x Mco2 / Tco2 / MHe)

THe x MCo2 = TCo2 x MHe

now

Tco2 = 25 + 273 = 298 K

Molar mass of C02 (Mco2) = 44

molar mass of He ( MHe) = 4

so

we get

THe x 44 = 298 x 4

THe = 27 K

THe = 27 - 273 C

THe = -246 C

so

the temperature of helium should be -246 C

so

the answer is option b) -246 C