Problem 88 - General Chemistry: Principles and Modern Applications

Question

Despite the fact that it has the higher molecular mass, XeO \(_{4}\) exists as a gas at \(298 \mathrm{K},\) whereas \(\mathrm{XeO}_{3}\) is a solid. Give a plausible explanation for this observation.

Step-by-Step Solution

Answer

The observed difference in physical states of \(\mathrm{XeO}_{3}\) and \(\mathrm{XeO}_{4}\) at 298 K can be explained by their differences in molecule polarity. Though \(\mathrm{XeO}_{4}\) has a higher molecular mass, it is a non-polar molecule while \(\mathrm{XeO}_{3}\) is polar. Non-polar molecules have weaker intermolecular forces and thus require less energy to break, hence \(\mathrm{XeO}_{4}\) exists as a gas.

Step 1: Identify the molecular geometry of each compound

For \(\mathrm{XeO}_{4}\), the central atom (Xe) has 8 valence electrons, and each O atom contributes 1 electron for bonding. Hence, the molecule obeys the octet rule with all Oxygen atoms forming double bonds with the Xe atom. This leads to a square planar geometry. Similarly, in \(\mathrm{XeO}_{3}\), Xe has 4 outer shell electrons and each Oxygen shares 1 each. The fourth pair is unbonded (lone pair). This gives a pyramidal shape to the molecule.

Step 2: Determine the Polarity of each compound

The polarity of a molecule is determined by its geometry and electronegativity difference between the atoms. In \(\mathrm{XeO}_{4}\) with either 4 bonding pairs and no lone pairs the molecule is symmetrical and hence it is non-polar. In contrast, \(\mathrm{XeO}_{3}\) is polar because of its pyramidal structure that results in an unequal distribution of electrons.

Step 3: Relate the phase of each compound to their polarity

Polar molecules are generally associated with higher melting and boiling points due to strong intermolecular dipole-dipole interactions, which require a greater amount of energy to break. This is the case with \(\mathrm{XeO}_{3}\), hence, it is a solid at room temperature. On the other hand, non-polar molecules like \(\mathrm{XeO}_{4}\) have weak Van der Waals forces which require less energy to break. Therefore, it exists as a gas at room temperature despite having a larger molecular mass.

Key Concepts

Molecular Polarity

When discussing molecules, whether they are polar or non-polar is crucial in understanding their physical properties. **Molecular polarity** depends on the shape of the molecule and the electronegativity of its atoms.
A molecule is considered **polar** if it has an uneven distribution of electron density, often resulting in a net dipole moment. This can occur if the central atom has lone pairs or if bonded atoms differ significantly in electronegativity. For instance,

• **\(\mathrm{XeO}_{3}\)** has a pyramidal shape due to a lone pair on the central xenon atom. This results in an uneven electron distribution, making \(\mathrm{XeO}_{3}\)polar.

In contrast, **non-polar** molecules have a symmetrical shape that ensures an equal distribution of charge. They do not exhibit a net dipole moment.

• **\(\mathrm{XeO}_{4}\)** is square planar and symmetrical, which results in non-polar characteristics.

Understanding the concept of molecular polarity is foundational for grasping why different compounds exhibit varying physical properties, such as their state at room temperature.

Intermolecular Forces

**Intermolecular forces** are forces of attraction or repulsion between molecules. The type and strength of these forces significantly impact a molecule's physical properties, including phase changes. Molecular polarity directly affects these forces.
For **polar molecules** like \(\mathrm{XeO}_{3}\), **dipole-dipole interactions** are a primary intermolecular force. These interactions are strong because they involve permanent dipoles attracting one another. Thus, they require more energy to overcome, resulting in **higher melting and boiling points**. Hence, \(\mathrm{XeO}_{3}\) stays solid at room temperature. In **non-polar molecules** such as \(\mathrm{XeO}_{4}\), **Van der Waals forces** (or London dispersion forces) are the primary intermolecular forces. These forces are much weaker because they arise from temporary dipoles created by electron movement. Consequently, non-polar molecules like\(\mathrm{XeO}_{4}\) are more likely to be gases at room temperature due to their lower melting and boiling points. Understanding these forces helps explain why substances with similar chemical compositions can have different physical states.

Phase Transitions

The interrelationship between molecular polarity, intermolecular forces, and **phase transitions** is fascinating. Knowing this can help us predict and explain why substances exist in different phases under various conditions. Phase transitions occur when the amounts of energy absorbed or released are enough to alter the physical state of a substance.
For example, when heat is applied:

• **Solids** can become **liquids** through the process of melting.
• **Liquids** can change to **gases** via vaporization.

The high energy requirement to break strong intermolecular forces in polar molecules, such as in \(\mathrm{XeO}_{3}\), results in a substance remaining solid under the same conditions that cause a less energy-intensive phase change in non-polar molecules like \(\mathrm{XeO}_{4}\). Therefore, non-polar molecules require less energy to transition to the gaseous state and exhibit these phase transitions more readily at room temperature.In summary, understanding the factors that influence phase transitions allows us to predict the states of substances accurately and comprehend their changes under varying temperature conditions.