Question

Water molecules in the atmosphere can form hydrogenbonded 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 VSF.PR 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?

Short answer

A water dimer consists of two water molecules connected by hydrogen bonding, exhibiting a bent structure due to VSEPR theory. The main intermolecular force involved is hydrogen bonding, which is an electrostatic attraction between hydrogen and oxygen. The given equilibrium constants indicate that the dimer formation is an exothermic process, as the equilibrium favors reactants at higher temperatures and products at lower temperatures.

Step-by-step solution

Draw the water dimer structure using VSEPR theory

: VSEPR (Valence Shell Electron Pair Repulsion) theory is used to predict the geometric structure of molecules. Water has the molecular formula H2O, and according to VSEPR theory, it exhibits a bent or angular structure because of the 2 lone pairs present on the oxygen atom. In the case of a water dimer, two water molecules are interacting via intermolecular forces. To show these interactions, draw two separate water molecules with their respective bent structures. Then, connect the hydrogen of one water molecule to the oxygen of the other water molecule with a dashed line to represent the hydrogen bond. Similarly, do this for the other hydrogen in the same water molecule as well.

Identify the intermolecular forces involved

: The main intermolecular force in water dimer formation is hydrogen bonding. This interaction arises because of the large difference in electronegativity between hydrogen and oxygen, which leads to an electrostatic attraction between the two. Hydrogen bonding is a strong intermolecular force and plays a major role in determining the properties of water, such as its high boiling point and surface tension.

Determine if the process is endothermic or exothermic

: We are given the equilibrium constant (\(K_p\)) values for water dimer formation at two different temperatures. At \(300 \ \mathrm{K}\), \(K_p = 0.050\), and at \(350 \ \mathrm{K}\), \(K_p = 0.020\). Notice that the equilibrium constant decreases as the temperature increases, which implies that the reaction favors the reactants (individual water molecules) at higher temperatures and the products (dimers) at lower temperatures. According to Le Châtelier's principle, this is indicative of an exothermic process, as increasing the temperature leads to a shift of the equilibrium towards the reactants, offsetting the temperature increase and releasing heat. Therefore, water dimer formation is an exothermic process.

Key concepts

Hydrogen Bonding

Hydrogen bonding is a type of strong intermolecular force that plays a crucial role in the chemistry of water dimer formation. It occurs when a hydrogen atom, which is covalently bonded to a highly electronegative atom like oxygen, forms an electrostatic attraction with another electronegative atom from a different molecule.

This kind of bonding is particularly significant in water due to the high electronegativity of oxygen compared to hydrogen. The partial positive charge on the hydrogen atoms of one water molecule is attracted to the partial negative charge on the oxygen of another molecule.

This interaction is represented by dashed lines in diagrams, and it's responsible for many of water's unique properties. For example:

• High boiling point
• High specific heat capacity
• Cohesive and adhesive properties

Without hydrogen bonding, the water molecule would not form dimers as readily in the gaseous phase, crucially affecting phenomena such as ice crystal nucleation and acid rain.

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is a model that is vital for understanding the shape of molecules, including the bent shape of a water molecule. According to VSEPR theory, electron pairs around a central atom repel each other and arrange themselves as far apart as possible.

In a water molecule, the oxygen atom has two bonded pairs of electrons and two lone pairs. These lone pairs create greater repulsion compared to bonded pairs, pushing the hydrogen atoms closer together and resulting in a bent structure with an angle of approximately 104.5 degrees.

When two water molecules form a dimer, VSEPR helps us visualize how one molecule's oxygen can bond with another molecule's hydrogen.

• Lone pairs influence molecular shape significantly
• Helps predict molecular geometry based on electron repulsion
• Aids in identifying intermolecular interactions

Understanding VSEPR theory is essential for drawing accurate structural diagrams of molecular interactions, such as those seen in water dimers.

Intermolecular Forces

Intermolecular forces are interactions that occur between molecules, influencing their physical properties and behavior. These forces are typically weaker than covalent or ionic bonds but crucial in processes involving phase changes and molecular stability.

In the context of water dimer formation, the primary intermolecular force is hydrogen bonding. However, it is not the only force that can be considered.

Other types of intermolecular forces include:

• London dispersion forces: Temporary fluctuations in electron density in atoms can induce weak attractions. These are present in all molecules, although very minor in comparison to hydrogen bonds in water dimers.
• Dipole-dipole interactions: These occur between polar molecules, although they are typically weaker than hydrogen bonds.

By understanding these forces, we gain insight into why water behaves the way it does in different states of matter and environments. Intermolecular forces are key to explaining phenomena like cohesion and adhesion, surface tension, and the liquid nature of water under standard atmospheric conditions.