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= $\frac{3}{2}$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= $\frac{4790 X 2}{3 X 8.314}$

T=384.09 K

Root mean square velocity= $\sqrt{\frac{3RT}{M} }$

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

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

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