You and a friend each synthesize a compound with the formula \(\mathrm{XeCl}_{2} \mathrm{F}_{2} .\) Your compound is a liquid and your friend's compound is a gas (at the same conditions of temperature and pressure). Explain how the two compounds with the same formulas can exist in different phases at the same conditions of pressure and temperature.

First, we need to know that XeCl2F2 is a compound formed by the central atom xenon (Xe) bonded to two chlorine (Cl) atoms and two fluorine (F) atoms. The electron configuration and repulsion between electron pairs determine the shape of the molecule.

There are two possible molecular structures for XeCl2F2. In one structure, the XeCl2F2 molecule has a square planar shape, with the Cl and F atoms arranged in an alternating pattern in the same plane around the Xe atom. In the other structure, the XeCl2F2 molecule has a T-shaped arrangement with two F atoms in the same plane as the Xe atom and one Cl atom above and one below the plane. These different arrangements lead to variations in intermolecular forces between the molecules, affecting their phase under the same temperature and pressure.

Intermolecular forces play a crucial role in determining the phase of a substance under a given temperature and pressure. There are three main types of intermolecular forces: London dispersion forces, dipole-dipole interactions, and hydrogen bonding. The stronger the intermolecular forces, the higher the boiling point of the substance, making it more likely to be in the liquid phase.

For the square planar structure, the molecule is nonpolar as the dipole moments of the Xe-Cl and Xe-F bonds cancel each other out due to symmetry. Hence, only London dispersion forces are present in this variation of the compound, which are relatively weak, resulting in a lower boiling point and allowing the compound to exist as a gas. In the T-shaped arrangement, the molecule is polar because the two Xe-F bonds have a greater dipole moment directed toward the fluorine atoms, which doesn't cancel out with that of the Xe-Cl bonds. This leads to stronger dipole-dipole interactions between the XeCl2F2 molecules, in addition to the London dispersion forces. This increases the boiling point of the compound, causing it to exist as a liquid at the same temperature and pressure.

In conclusion, the two compounds with the same chemical formula, XeCl2F2, can exist in different phases (liquid and gas) under the same temperature and pressure, because of their different molecular structures. The square planar structure has weaker intermolecular forces (only London dispersion forces), allowing it to exist as a gas, while the T-shaped structure has stronger intermolecular forces (dipole-dipole interactions and London dispersion forces), causing it to exist as a liquid.