Question

The heats of fusion of three substances are listed below. Explain the trend this list reflects. $$\begin{array}{ll} \mathrm{HI} & 2.87 \mathrm{kJ} / \mathrm{mol} \\ \mathrm{HBr} & 2.41 \mathrm{kJ} / \mathrm{mol} \\ \mathrm{HCl} & 1.99 \mathrm{kJ} / \mathrm{mol} \end{array}$$

Short answer

The trend of decreasing heats of fusion from HI to HCl can be attributed to the change in the size of the halogen atom, with larger atoms forming weaker covalent bonds and requiring less energy to break those bonds. As we move from HI to HCl, the atomic size of the halogen atom decreases, making covalent bonds stronger and the required energy for breaking these bonds higher.

Step-by-step solution

Understand Heats of Fusion

Heats of fusion are the amounts of energy required to change a substance from its solid phase to its liquid phase at constant temperature, without changing the temperature. In this case, we are looking at three substances: HI, HBr, and HCl. The list shows us the heats of fusion for these substances in kJ/mol. The goal is to explain the trend that this list reflects.

Identify the Given Information

We are provided with the heats of fusion for the following substances in kJ/mol: HI (2.87 kJ/mol), HBr (2.41 kJ/mol), and HCl (1.99 kJ/mol). We can see a clear trend in the given data: The heats of fusion decrease from HI to HCl.

Understand the Properties of HI, HBr, and HCl

In order to relate the change in heats of fusion to the properties of HI, HBr, and HCl, we need to consider the involved molecular interactions. All three substances are halogen hydrides, which consist of a hydrogen atom and a halogen atom. The fundamental force that holds these molecules together is the electrostatic attraction between the positively charged hydrogen atom and the negatively charged halogen atom, called covalent bonding. One of the factors that can help us explain the trend is the size of the halogen atom. As we move from HI to HCl, the atomic size of the halogen atom decreases (Iodine is the largest, while Chlorine is the smallest among these three).

Relate Heats of Fusion to Properties of HI, HBr, and HCl

The larger the halogen atom, the less efficient the overlapping of orbitals (which leads to covalent bonding) is, and the weaker the bond formed. Consequently, the larger the halogen atom, the weaker the covalent bond in the halogen hydride, and the less energy it takes to break this bond. That is why, as we move from HI to HCl, the heats of fusion decrease, reflecting the reduced energy needed to break the bonds within the substance. In conclusion, the trend of decreasing heats of fusion from HI to HCl can be attributed to the change in the size of the halogen atom, with larger atoms forming weaker covalent bonds and requiring less energy to break those bonds.

Key concepts

Halogen Hydrides

Halogen hydrides are simple molecules composed of a hydrogen atom bonded to a halogen atom. The halogens include fluorine, chlorine, bromine, and iodine. These compounds have the general formula HX, where X represents the halogen. The bonding between hydrogen and the halogen is primarily covalent, meaning that the atoms share electrons.

In the context of the heats of fusion, halogen hydrides such as HI, HBr, and HCl demonstrate how differing strengths of these covalent bonds can affect thermal properties. The heat of fusion refers to the energy required to convert a solid to a liquid at its melting point without a temperature change. Substances with higher heats of fusion have stronger intermolecular forces that require more energy to disrupt.

With HI, HBr, and HCl specifically, we note the incidental impact of molecular size on these energies.

Molecular Interactions

Molecular interactions refer to the various forces that act between molecules, affecting the physical properties of substances. For halogen hydrides, the main interaction is covalent bonding, though other interactions such as van der Waals forces can also play a role.

• Within each molecule, hydrogen and the halogen atom share electrons, forming a covalent bond. The specific nature and strength of these bonds depend on the electronegativity and size of the halogen.
• As we move from HI to HCl, these interactions are influenced by the decreasing size and increasing electronegativity of the halogen atoms.
• Larger atoms, like iodine, lead to weaker covalent bonds, which are more easily disrupted, while smaller atoms, such as chlorine, make for stronger bonds.

When considering the heat of fusion, remember that the energy reflects how strongly these interactions hold the solid structure together.

Covalent Bonding

In covalent bonding, atoms share pairs of electrons, leading to the formation of a stable molecule. This type of strong bond is pivotal in the structure and stability of halogen hydrides.

• The covalent bond's strength is influenced by the participating atoms' electronegativity and size.
• In the case of HI, HBr, and HCl, we see how covalent bond strength impacts the heat of fusion, with HI forming the weakest bond due to iodine's larger atomic size and lower electronegativity compared to bromine and chlorine.
• Chlorine, being smaller and more electronegative, creates stronger bonds, reflected in HCl's lower heat of fusion. This means more energy is needed to break these bonds, hence the higher melting temperature.

Thus, understanding covalent bonding sheds light on why some halogen hydrides require more energy to transition from solid to liquid.

Atomic Size

Atomic size plays a crucial role in determining the properties of molecules, especially in the context of bonding and molecular interactions. In halogen hydrides, the size of the halogen atom can drastically affect the heat of fusion.

• Iodine, being the largest atom among those in HI, HBr, and HCl, contributes to weaker bonding due to its larger atomic radius, which limits efficient orbital overlap with hydrogen.
• As we move to smaller atoms like bromine and chlorine, the ability to overlap and share electrons more effectively increases, leading to stronger bonds.
• This stronger bond results in a higher requirement of energy to disrupt the solid structure, hence a lower heat of fusion.

Understanding atomic size is key in explaining why large atoms like in HI have lower heats of fusion compared to smaller atoms like HCl. This concept also highlights how changes in atomic size can directly impact a compound's thermal stability.