Understanding Critical Temperature

The critical temperature (\(T_c\)) of a substance is the highest temperature at which a gas can be liquefied by pressure alone. Above the critical temperature, the substance exists only as a gas, regardless of how much pressure is applied. At the critical temperature and critical pressure, the substance is at its critical point, where the liquid and gas phases coexist in equilibrium, and their densities become equal.

The value of the critical temperature is closely related to the strength of the intermolecular forces present in the substance. Substances with stronger intermolecular forces require more energy to overcome these attractions, and therefore have higher critical temperatures. Conversely, substances with weaker intermolecular forces have lower critical temperatures.

Intermolecular Forces in Given Gases

Let's examine the intermolecular forces present in each of the given gases:

• Helium (He): Helium is a noble gas. It is nonpolar and monatomic. The only intermolecular forces present are very weak London dispersion forces. These forces arise from temporary fluctuations in electron distribution.
• Hydrogen (H\(_2\)): Hydrogen is a diatomic molecule. It is nonpolar. The intermolecular forces are primarily London dispersion forces. These are weak due to the small size and low number of electrons in the molecule.
• Oxygen (O\(_2\)): Oxygen is a diatomic molecule. It is nonpolar. The intermolecular forces are London dispersion forces. Compared to He and H\(_2\), O\(_2\) has more electrons and a larger size, leading to stronger London dispersion forces.
• Carbon Dioxide (CO\(_2\)): Carbon dioxide is a linear triatomic molecule (\(O=C=O\)). While the individual C=O bonds are polar, the molecule as a whole is nonpolar due to its linear symmetry. The primary intermolecular forces are London dispersion forces. CO\(_2\) has significantly more electrons and is larger than He, H\(_2\), and O\(_2\). This results in stronger London dispersion forces. Additionally, CO\(_2\) has a quadrupole moment, which contributes to slightly stronger intermolecular attractions compared to simple nonpolar molecules of similar size.

Comparing Intermolecular Forces and Critical Temperature

Based on the discussion of intermolecular forces, we can compare their relative strengths among the given gases:

He \(\approx\) H\(_2\) < O\(_2\) < CO\(_2\)

The strength of intermolecular forces increases in this order. Since a higher critical temperature is associated with stronger intermolecular forces, the gas with the strongest forces among the options will have the highest critical temperature.

Carbon dioxide (CO\(_2\)) has the strongest intermolecular forces among He, H\(_2\), O\(_2\). Therefore, CO\(_2\) is expected to have the highest critical temperature.

Conclusion on Highest Critical Temperature

Considering the strength of intermolecular forces, carbon dioxide (CO\(_2\)) exhibits the strongest forces among the options provided (He, O\(_2\), H\(_2\)). Consequently, CO\(_2\) requires the highest temperature to remain in the gaseous state irrespective of pressure, meaning it has the highest critical temperature.