Hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\), is a syrupy liquid with a vapor pressure lower than that of water and a boiling point of \(152^{\circ} \mathrm{C}\). Account for the differences between these properties and those of water.

When examining the molecular structure of hydrogen peroxide ((H_2O_2)), it's essential to understand that this compound consists of two hydrogen atoms and two oxygen atoms arranged in a non-linear structure. The presence of an extra oxygen atom compared to water ((H_2O)) leads to different physical and chemical properties. The two oxygen atoms in hydrogen peroxide are linked by a single bond, and each oxygen is also bonded to a hydrogen atom. This structure creates a molecule with angular shape and results in specific intermolecular forces, such as hydrogen bonding and dipole-dipole interactions, which are stronger than those in water molecules because of the increased number of these bonds per molecule in hydrogen peroxide.

Understanding the molecular structure is fundamental to comprehending other properties such as boiling point and vapor pressure since these intermolecular forces dictate how the molecules interact with each other in different states of matter. For instance, the enhanced hydrogen bonding in hydrogen peroxide provides it with a more 'sticky' nature, making it denser and leading to a syrupy consistency.

The boiling point of hydrogen peroxide is notably higher than that of water, at (152^{circ}C) compared to water's (100^{circ}C). This difference is primarily because of the molecular weight and the structure of hydrogen peroxide. Since hydrogen peroxide has an additional oxygen atom, its molecular weight is greater, and with this comes stronger intermolecular interactions. These forces need to be overcome for the molecules to transition from the liquid state to the gas phase.

At the boiling point, the vapor pressure of a liquid equals the atmospheric pressure. Hence, to reach a point where the vapor pressure of hydrogen peroxide equals the environmental pressure, more energy is required because of the heftier intermolecular forces at play. This necessitates a higher temperature, raising the boiling point. Moreover, these intermolecular forces make it harder for molecules to leave the liquid phase, which relates directly back to the concept of vapor pressure.

Vapor pressure is a measure of a substance's propensity to evaporate, and it tells us how readily molecules of a liquid enter the gas phase at a particular temperature. For hydrogen peroxide, its vapor pressure is lower than that of water. This is a consequence of its molecular structure that encourages formidable intermolecular bonds, such as increased hydrogen bonding compared to water molecules.

Because of these strong bonds, less energy is available for the hydrogen peroxide molecules to break free and enter the vapor phase, resulting in fewer molecules being present in the gas state at a given temperature. Therefore, the equilibrium between the liquid phase and the vapor phase is reached with fewer vapor molecules, resulting in a reduced vapor pressure. The lower vapor pressure also means that hydrogen peroxide is less volatile and does not evaporate as readily as water, reflecting in its preservation and storage qualities.