Why is chlorine a gas at rtp even though the bonding between atoms is strong?

Answer 1

The bulk state of matter (i.e. gas, liquid, solid) is not dependent on the forces operating within that molecule. Although the bonding between two atoms of chlorine in chlorine gas (or dichloride, Cl2) is strong, the interactions between different molecules, known as the intermolecular interactions, are quite weak. It is the intermolecular interactions that determine the boiling point of a substance, and hence it's state at a given temperature.

In the case of chlorine gas, the reason it is a gas is simply because it's a relatively light molecule, and so at room temperature the energy provided by the surroundings is enough to break the weak intermolecular interactions that hold it as a liquid.

Answer 2

Chlorine is a gas at room temperature and pressure because the weak van der Waals forces between chlorine molecules are not strong enough to keep them together in a solid form. Despite the strong covalent bonding within each chlorine molecule, the intermolecular forces are not sufficient to overcome the kinetic energy of the molecules, resulting in a gas state at room temperature.