Problem 99 - Chemistry The Central Science

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 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

(a) The structure of a water dimer consists of two individual water (\(H_2O\)) molecules with a central oxygen atom bonded to two hydrogen atoms and two lone electron pairs. These water molecules interact with each other through hydrogen bonds between the oxygen of one molecule and hydrogen of the other, represented by dashed lines. (b) Hydrogen bond interactions are the intermolecular forces involved in water dimer formation. (c) Water dimer formation is exothermic since the equilibrium constant, \(K_{p}\), decreases as the temperature increases from \(300~K\) to \(350~K\).

Step 1: (a) Drawing the water dimer structure using VSEPR theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory explains the idea that the electron pairs surrounding an atom repel each other and try to get as far away as possible while maintaining a stable structure. To draw the structure, we first draw the two individual water (\(H_2O\)) molecules. These consist of a central oxygen atom bonded to two hydrogen atoms, with two lone electron pairs on the oxygen atom. To form a water dimer (\(\left(H_{2}O\right)_{2}\)), we need the Oxygen atom of one water molecule to interact with a hydrogen atom of the other water molecule through a hydrogen bond. Dashed lines will represent these intermolecular hydrogen bond interactions between the water molecules.

Step 2: (b) Determining intermolecular forces involved in water dimer formation

The intermolecular forces involved in water dimer formation are hydrogen bond interactions. A hydrogen bond is an interaction between a hydrogen atom covalently bound to an electronegative atom (such as Oxygen, Nitrogen, or Fluorine) and a lone pair of electrons on another electronegative atom. In this case, Oxygen is the electronegative atom, and it forms a hydrogen bond with the hydrogen atom of another water molecule.

Step 3: (c) Determine whether water dimer formation is endothermic or exothermic

We are given the \(K_{p}\) values for water dimer formation at two different temperatures: \(0.050\) at \(300~K\) and \(0.020\) at \(350~K\). From the Van't Hoff equation, the equilibrium constant, \(K_{p}\), is inversely proportional to the temperature if the reaction is exothermic and directly proportional to the temperature if the reaction is endothermic. In this case, the equilibrium constant, \(K_{p}\), decreases as the temperature increases from \(300~K\) to \(350~K\). This indicates that water dimer formation is exothermic because the equilibrium shifts towards the reactants (individual water molecules) as the temperature increases.

Key Concepts

VSEPR Theory

The 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. The theory posits that electron pairs will arrange themselves as far apart as possible around the central atom to minimize repulsion. For water (
H₂O
), VSEPR theory predicts a bent structure due to the two lone pairs of electrons on the oxygen atom, which push the two hydrogen atoms down, creating a ‘V’ shape.

Hydrogen Bonding

Hydrogen bonding is a special type of intermolecular force that is critical in many biological structures and processes. It occurs when a hydrogen atom, which is covalently bonded to a highly electronegative atom like oxygen or nitrogen, experiences an attractive force to another electronegative atom bearing a lone pair of electrons. In the case of the water dimer, a hydrogen bond forms between the hydrogen atom of one water molecule and the lone pair of an oxygen atom of another molecule, creating a delicate yet significant interaction that plays a huge role in the properties of water.

Intermolecular Forces

Intermolecular forces are interactions that occur between molecules, playing a key role in determining the physical properties of substances. Besides hydrogen bonds, other types of intermolecular forces include London dispersion forces, which arise from temporary dipoles, and dipole-dipole interactions, which occur between polar molecules. The strength and type of these forces together influence boiling points, melting points, and solubility.

Endothermic and Exothermic Reactions

Chemical reactions can be classified as endothermic or exothermic. Endothermic reactions absorb heat from the surroundings, resulting in a temperature drop in the environment. In contrast, exothermic reactions release heat, warming up the surroundings. The formation of water dimers is exothermic as it releases energy to the atmosphere, an insight discerned by observing how the equilibrium constant for the process decreases with increasing temperature.

Equilibrium Constant

The equilibrium constant (
K_p
) in a chemical reaction is a number that provides the ratio of products to reactants at equilibrium. It reflects the extent of a reaction at a given temperature and has a unique value for each reaction. The concept is central to understanding reaction dynamics as the value of
K_p
changes with temperature; it is high for a favorable formation of products at lower temperatures and lower when the formation of products is less favorable at higher temperatures.