Problem 101 - Chemistry The Central Science

Question

Water molecules in the atmosphere can form hydrogen-bonded dimers, \(\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\) . The presence of these dimers is thought to be important in the nucleation of ice crystals in the atmosphere and in the formation of acid rain. (a) Using VSEPR theory, draw the structure of a water dimer, using dashed lines to indicate intermolecular interactions. (b) What kind of intermolecular forces are involved in water dimer formation? (c) The \(K_{p}\) for water dimer formation in the gas phase is 0.050 at 300 \(\mathrm{K}\) and 0.020 at 350 \(\mathrm{K}\) . Is water dimer formation endothermic or exothermic?

Step-by-Step Solution

Answer

In summary, a water dimer \(\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\) has hydrogen bonds between the hydrogen atoms of one water molecule and the oxygen atoms of the other water molecule. The intermolecular forces involved in the formation of the water dimer are hydrogen bonds. Based on the given \(K_p\) values, the formation of water dimers is an exothermic process.

Step 1: Draw the structure of a water dimer

Using VSEPR theory, we can draw the structure of a water molecule, \(\mathrm{H}_2\mathrm{O}\). Oxygen has 6 valence electrons, and each hydrogen has 1 valence electron. Two of the valence electrons on oxygen are shared with the two hydrogen atoms, while the other four valence electrons form two lone pairs. Now, let's focus on forming the dimer, \(\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\). In this structure, the hydrogen atoms of one water molecule will form a hydrogen bond with the lone pairs of electrons on the oxygen of the other water molecule. These hydrogen bonds will be represented by dashed lines in our drawing.

Step 2: Identify intermolecular forces

The intermolecular forces involved in the water dimer formation are hydrogen bonds. Hydrogen bonds are formed between a hydrogen atom attached to an electronegative atom (in this case, oxygen) and another electronegative atom with a lone pair of electrons (also oxygen, in this case).

Step 3: Determine endothermic or exothermic process

To determine whether the water dimer formation is endothermic or exothermic, we will observe the trend of \(K_p\) with temperature changes. We know that \(K_{p}\) for water dimer formation in the gas phase is 0.050 at 300 \(\mathrm{K}\) and 0.020 at 350 \(\mathrm{K}\). Since the value of \(K_p\) decreases with an increase in temperature, we can infer that water dimer formation is an exothermic process. This is because, as temperature increases, the reaction shifts towards the reactants (water molecules) to counteract the increase in heat, which results in a lower \(K_p\) value.

Key Concepts

VSEPR Theory

Valence Shell Electron Pair Repulsion (VSEPR) theory is a model used in chemistry to predict the geometry of individual molecules based on the number of electron pairs surrounding their central atoms. In our example of water molecules, the central oxygen atom is surrounded by two bonded pairs (with hydrogen) and two lone pairs of electrons.

This leads to a 'bent' molecular geometry with a bond angle of approximately 104.5 degrees. VSEPR theory helps us visualize how water molecules orient themselves when they form dimers. The lone pairs on one oxygen atom repel the bonded pairs on the other, creating an optimal arrangement that minimizes repulsions, leading to the characteristic 'bent' shape critical for hydrogen bonding.

Hydrogen Bonding

Hydrogen bonding is an essential intermolecular force responsible for many of the unique properties of water, including its high boiling point and surface tension. A hydrogen bond is a weak bond formed when a hydrogen atom covalently bonded to a highly electronegative atom like oxygen or nitrogen experiences attraction to another electronegative atom with a lone pair of electrons.

In the case of the water dimer, \(\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\), each water molecule forms a hydrogen bond with the neighboring molecule; the positively charged hydrogen of one molecule is attracted to the negatively charged lone pair of the other molecule's oxygen atom. This attraction is visualized with dashed lines in molecular drawings.

Intermolecular Forces

Intermolecular forces are the forces of attraction or repulsion between neighboring particles (atoms, molecules, or ions). They are weaker than the intramolecular forces that hold compounds together. There are several types of intermolecular forces, including dipole-dipole interactions, where polar molecules are aligned so that the positive end of one molecule is near the negative end of another; dispersion or London forces, which occur due to momentary changes in the distribution of electrons around an atom or molecule; and, as mentioned, hydrogen bonds, which are especially strong types of dipole-dipole interactions.

These forces are critical in explaining the behavior of substances in various states of matter and applying to the water dimer formation, where hydrogen bonds are the primary interaction.

Endothermic and Exothermic Processes

An exothermic reaction is a chemical reaction that releases energy by light or heat. It is the characteristic of bond-forming exothermic processes, where the chemical potential energy of the bonds being formed is less than that of the bonds being broken. Conversely, an endothermic reaction is one that requires energy input.

In the context of water dimer formation, the process is exothermic, as indicated by the decrease in the equilibrium constant \(K_p\) with an increase in temperature. The system releases heat as it forms the more stable dimeric structure, and as the temperature rises, the reaction shifts to favor the disassociation of the dimers, thereby absorbing the excess heat to maintain equilibrium.