Question

If He(g) has an average kinetic energy of 4790 J/mol under certain conditions, what is the root mean square speed of Cl2(g) molecules under the same conditions?

Answer 1

We need to know the root mean square speed of Cl₂ molecule.

The root mean square speed of Cl₂ molecule is:3.67 X 10⁴ cm/sec.

Average kinetic energy=
`(3)/(2)`RT, where R=Molar gas constant and T=absolute temperature in Kelvin.

Given, average kinetic energy= 4790 J/mol, R= 8.314 J/mol/K

So, T=
`(4790 X 2)/(3 X 8.314)`

T=384.09 K

Root mean square velocity=
`\sqrt{(3RT)/(M) }`

For, Cl₂ molecule, M= 71 g/mol, T=384.09 K (as condition is same as previous)

So, Root mean square velocity=
`\sqrt{(3 X 8.314 X 10^(7) X 384.09)/(71) }`=3.67 X 10⁴ cm/sec

Hence, Root mean square velocity= 3.67 X 10⁴ cm/sec.