[iyc]

Is there any differences in m.p./b.p. between ³⁵Cl₂ and ³⁷Cl₂?

In general, van der Waals' forces between the molecules increase with increasing molecular mass.
But, in the case of isotopes, I don't know whether it is true or not.

As both ³⁵Cl₂ and ³⁷Cl₂ have the same number of electron, the fluctuation in symmetry of charge cloud will be almost the same, resulting similar strength of instantaneous dipole- induced dipole atrraction. Therefore, I think they will have the same m.p./ b.p.

But this contradicts with that van der Waals' forces between the molecules increase with increasing molecular mass.

Can anybody help?

[Mitch]

There will be a slight difference, the lighter isotope will boil at a lower temperature.

[iyc]

is it due to the slight difference in surface area between the isoptopes?

[Yggdrasil]

As both ³⁵Cl₂ and ³⁷Cl₂ have the same number of electron, the fluctuation in symmetry of charge cloud will be almost the same, resulting similar strength of instantaneous dipole- induced dipole atrraction.

I think this explanation is right on and the two isotopes will have the same van der Waals forces between them.  However, I think there will be a slight difference in the thermal energy needed to free the heavier ³⁷Cl₂ from the solid and/or liquid phase during the phase change, which accounts for the slight increase in bp/mp.