Question

According to kinetic-molecular theory, in which of the following gases will the root-mean-square speed of the molecules be the highest at 200C?

A) Cl₂

B) H₂O

C) SF₆

D) HCl

E) None. The molecules of all gases have the same root-mean-square speed at any given temperature

Answer 1

vrms = sqrt (3*R*T/M)

here : T is temperature in Kelvin

M is molar mass

vrms = sqrt (3*R*T/M)

here : T is temperature in Kelvin

M is molar mass

Since T is same for all, the one with lower molar mass will have higher speed

Lets list out molar mass of all given compounds

Molar mass of Cl2 = 70.9

Molar mass of H2O = 18.016

Molar mass of SF6 = 146.07

Molar mass of HCl = 36.46

Increasing order of molar mass is:

H2O

HCl

Cl2

SF6

Same is the order of decreasing vrms

From fastest to slowest

H2O

HCl

Cl2

SF6

Answer: H2O