Problem 10 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

Explain the trend in hydrogen bond strengths: \(\mathrm{F}-\mathrm{H} \cdot \cdot \cdot \mathrm{F}\) in \(\mathrm{HF}_{2}^{-} \quad+220 \mathrm{kJmol}^{-1}\) \(\mathrm{O}-\mathrm{H} \cdot \cdot \cdot \mathrm{O} \operatorname{in} \mathrm{H}_{2} \mathrm{O} \quad+22 \mathrm{kJmol}^{-1}\) \(\mathrm{S}-\mathrm{H} \cdot \cdots \sin \mathrm{H}_{2} \mathrm{S} \quad+7 \mathrm{kJmol}^{-1}(\text {Section } 25.3)\)

Step-by-Step Solution

Answer

Hydrogen bond strength decreases from fluorine to oxygen to sulfur due to decreasing electronegativity and increasing atomic size.

Step 1: Define Hydrogen Bond Strength

Hydrogen bond strength refers to the energy required to break one mole of hydrogen bonds. The values are measured in kilojoules per mole (kJ/mol). A higher numerical value indicates a stronger hydrogen bond.

Step 2: Identify Patterns in Electronegativity

Consider the electronegativity of the atoms involved in the hydrogen bonds: fluorine (F), oxygen (O), and sulfur (S). - Fluorine is the most electronegative (3.98 on the Pauling scale), - Oxygen follows (3.44), - Sulfur is the least electronegative (2.58).

Step 3: Correlate Electronegativity and Hydrogen Bond Strength

A greater difference in electronegativity between the hydrogen (H) and the other atom in the bond generally enhances hydrogen bonding. This is because stronger polarization allows the hydrogen to act more effectively as a bridge between the two electronegative atoms.

Step 4: Analyze Given Data for Trends

Examine the bond strengths: - \(\mathrm{F}-\mathrm{H} \cdot \cdot \cdot \mathrm{F}\) in \(\mathrm{HF}_2^-\) is +220 kJmol^{-1}, - \(\mathrm{O}-\mathrm{H} \cdot \cdot \cdot \mathrm{O}\) in \(\mathrm{H_{2}O}\) is +22 kJmol^{-1}, and - \(\mathrm{S}-\mathrm{H} \cdot \cdot \cdot \mathrm{S}\) in \(\mathrm{H_{2}S}\) is +7 kJmol^{-1}.Observe that the bond strengths decrease as we move from fluorine to oxygen to sulfur.

Step 5: Conclusion on the Trend

The strength of the hydrogen bond increases with the decreasing atomic size and increasing electronegativity of the atoms involved. Thus, the hydrogen bond between fluorine atoms is the strongest due to fluorine's highest electronegativity, followed by oxygen and then sulfur.

Key Concepts

Electronegativity

Electronegativity is a fundamental concept in chemistry, essential for understanding the strength of hydrogen bonds. It refers to the tendency of an atom to attract shared electrons when forming a chemical bond. The more electronegative an atom, the stronger its pull on electrons.
For hydrogen bonds, the difference in electronegativity between hydrogen and the atom to which it is bonded plays a crucial role. Consider fluorine, oxygen, and sulfur, the atoms involved in our hydrogen bonds:

• Fluorine, with an electronegativity of 3.98, is the most electronegative.
• Oxygen has an electronegativity of 3.44.
• Sulfur, with an electronegativity of 2.58, is the least electronegative among the three.

A higher electronegativity difference between hydrogen and the bonded atom results in stronger polarization, allowing hydrogen to act more effectively as a bridge between electronegative atoms. This is why the hydrogen bond strength is greatest in HF, followed by H2O, and weakest in H2S.

Atomic Size Trend

Atomic size, or atomic radius, is the average distance from the nucleus of an atom to its outermost electron shell. This size affects the ability of atoms within a molecule to form strong hydrogen bonds.
In general, smaller atoms can approach closer to one another, allowing stronger interactions:

• Fluorine is the smallest, which helps form the strongest hydrogen bonds.
• Oxygen is slightly larger than fluorine, resulting in moderately strong hydrogen bonds.
• Sulfur is the largest of the trio, leading to the weakest hydrogen bonds in our examples.

As you can see, atomic size is inversely related to hydrogen bond strength. Smaller atoms can form tighter and stronger interactions, making fluorine-hydrogen bonds the strongest. When hydrogen bonds form between larger atoms like sulfur, the bond is inherently weaker due to the increased distance between bonded nuclei.

Bond Energy

Bond energy is the amount of energy required to break one mole of bonds in a chemical compound. In the context of hydrogen bonding, it reflects the strength of the bond:

• Strong hydrogen bonds, like those in HF, have high bond energies of +220 kJ/mol.
• Moderate hydrogen bonds, such as in H2O, have lower bond energies of +22 kJ/mol.
• Weak hydrogen bonds, as seen in H2S, have the lowest bond energies of just +7 kJ/mol.

The greater the bond energy, the stronger and more stable the bond. This concept is crucial in understanding molecular interactions and the role of hydrogen bonds in chemical and biological processes.
In daily chemistry, bond energies guide us in predicting reaction behavior and stability under various conditions. For students, the takeaway is simple: high electronegativity and small atomic size lead to high bond energies, illustrating why hydrogen bonds vary in strength.

Pauling Scale

The Pauling scale is a numeric scale concerned with the electronegativity of an atom. Coined by Linus Pauling, it is one of the most used methods to compare electronegativities across different elements.
On this scale:

• Fluorine tops the rankings at 3.98, the highest among all elements, highlighting its exceptional ability to attract electrons.
• Oxygen ranks at 3.44 and is known for its involvement in moderate hydrogen bond formation.
• Sulfur, at 2.58, illustrates a significant drop in tendency to attract electrons, corresponding with weaker hydrogen bonds.

Understanding the Pauling scale helps students make sense of why certain atoms form stronger or weaker bonds, based largely on where these atoms fall on the scale. This understanding has broader impacts across chemistry, aiding predictions about molecular behavior and serving as a tool for studying reactivity patterns among elements.