Question

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

Short answer

The trend in the heats of fusion for hydrogen halides (HI, HBr, and HCl) can be explained by the difference in the strength of the dipole-dipole interactions between the molecules. As the size of the halogen atom increases (from I to Br to Cl) and its electronegativity decreases, the dipole-dipole interactions become weaker, requiring less energy for the phase transition from solid to liquid. This results in the observed decreasing trend in heats of fusion from HI (2.87 kJ/mol) to HBr (2.41 kJ/mol) and finally to HCl (1.99 kJ/mol).

Step-by-step solution

Arrange the given data in a comprehensible manner

First, let's organize the given heats of fusion for each substance in a table: | Substance | Heat of Fusion (kJ/mol) | |-----------|--------------------------| | HI | 2.87 | | HBr | 2.41 | | HCl | 1.99 |

Identify the nature of the substances involved

The substances in question are all hydrogen halides. They consist of a hydrogen atom bonded to a halogen atom (halogens are the elements in Group 17 of the periodic table). Specifically, the substances are hydrogen iodide (HI), hydrogen bromide (HBr), and hydrogen chloride (HCl).

Recognize the trend in heats of fusion

Looking at the table, we can see that the heats of fusion decrease as we move from HI (2.87 kJ/mol) to HBr (2.41 kJ/mol) and then to HCl (1.99 kJ/mol).

Analyze the relationship between molecular structure and the trend

Now, let's try to understand the reason behind this trend by considering the nature of the intermolecular forces present in each substance. In hydrogen halides, the dominant force is dipole-dipole interaction due to the electronegativity difference between the hydrogen and halogen atoms. As we move down Group 17 of the periodic table, the size of the halogen atom increases, and the electronegativity decreases. The larger atom size leads to weaker dipole-dipole interactions between molecules, as the positive and negative poles are farther apart. This means that less energy is required to change the substance from a solid to a liquid state.

Conclude the explanation for the trend

In conclusion, the trend observed in the heats of fusion of hydrogen halides (HI, HBr, and HCl) is due to the difference in the strength of the dipole-dipole interactions between the molecules. As the size of the halogen atom increases and its electronegativity decreases, the dipole-dipole interactions become weaker, requiring less energy for the phase transition from solid to liquid. This explains the decreasing trend in heats of fusion from HI to HBr and finally to HCl.

Key concepts

Hydrogen Halides

Hydrogen halides are compounds formed between hydrogen and halogen elements. These compounds are known for their unique properties and play significant roles in chemistry. Hydrogen halides include hydrogen iodide (HI), hydrogen bromide (HBr), and hydrogen chloride (HCl). Each of these compounds is characterized by a hydrogen atom bonded to a halogen atom, which belongs to Group 17 of the periodic table. The halogens include iodine, bromine, and chlorine.

In terms of molecular structure, hydrogen halides are quite simple. They are diatomic molecules, meaning each molecule consists of just two atoms. The formation of hydrogen halides involves a covalent bond resulting from the sharing of electrons between hydrogen and a halogen atom. Because of their structure, they showcase specific physical and chemical behaviors. These behaviors are influenced by the nature of the bond and the properties of the constituent atoms.

Hydrogen halides are gases at room temperature (except hydrogen fluoride, which is a liquid due to strong hydrogen bonding). Their boiling points are usually low but increase with the size of the halogen atom involved, reflecting trends in molecular interactions.

Dipole-Dipole Interaction

Dipole-dipole interactions are a type of intermolecular force that occurs between polar molecules. These forces arise due to the electrical polarity of molecules, where there is an uneven distribution of electron density across the molecule.

• A dipole is created when there is a significant difference in electronegativity between two atoms.
• This polarity causes one end of the molecule to have a slight positive charge, while the other end has a slight negative charge.

In hydrogen halides, the difference in electronegativity between the hydrogen and halogen atoms generates a dipole. The more electronegative halogen attracts electrons more strongly, creating these partial charges.

These interactions determine many physical properties of substances, such as boiling and melting points. In the case of hydrogen halides, dipole-dipole interactions are a key reason why they exhibit a certain order in heats of fusion. Larger halogen atoms lead to weaker interactions because increased distance weakens the pull between opposite charges.

The importance of these interactions is evident in the changing heats of fusion across HI, HBr, and HCl. As atom size increases down Group 17 (from HCl to HI), dipole-dipole interactions decrease, directly affecting how easily these substances can transition between phases.

Periodic Table Trends

The periodic table organizes elements in a manner that reflects recurring trends in their chemical and physical properties. Understanding these trends is crucial in predicting the behavior of elements in different contexts.

• As you move down Group 17 in the periodic table, the size of the halogen atoms increases (from chlorine to iodine).
• However, their electronegativity tends to decrease. Electronegativity is a measure of how strongly an atom attracts electrons in a chemical bond.

These trends profoundly influence the interactions and properties of hydrogen halides. Larger atoms have more electron shells, helping accommodate more electrons, which increases their atomic radius. This results in weaker dipole-dipole interactions, as the poles (positive and negative) are further apart in larger atoms.

The decrease in electronegativity moving down the group also weakens these intermolecular forces. Therefore, the periodic trends explain why HI, HBr, and HCl have successively lower heats of fusion. Less energy is needed to overcome these weaker forces, thus explaining the observed trend.