Question

The value of \(\ldots \ldots \ldots\) is less for \(\mathrm{D}_{2} \mathrm{O}\) compared to that of \(\mathrm{H}_{2} \mathrm{O}_{2}\) (a) boiling point (b) latent heat of vaporization (J \(\mathrm{g}^{-1}\) ) (c) density \(\left(\mathrm{g} / \mathrm{mL}^{-1}\right)\) at \(20^{\circ} \mathrm{C}\) (d) dielectric constant at \(20^{\circ} \mathrm{C}\)

Short answer

The dielectric constant of \(\mathrm{D}_{2}\mathrm{O}\) is less than that of \(\mathrm{H}_{2}\mathrm{O}_{2}\).

Step-by-step solution

Understanding the Property

We need to compare different properties of two substances: \(\mathrm{D}_{2}\mathrm{O}\) (heavy water) and \(\mathrm{H}_{2}\mathrm{O}_{2}\) (hydrogen peroxide). The properties considered are boiling point, latent heat of vaporization, density, and dielectric constant. We must identify which property of \(\mathrm{D}_{2}\mathrm{O}\) is less than that of \(\mathrm{H}_{2}\mathrm{O}_{2}\).

Boiling Point Comparison

Boiling point is a measure of the temperature at which a substance changes from liquid to gas. Typically, hydrogen peroxide has a higher boiling point than water and, consequently, higher than heavy water. This is due to stronger hydrogen bonding in \(\mathrm{H}_{2}\mathrm{O}_{2}\).

Latent Heat of Vaporization Analysis

The latent heat of vaporization is the heat required to turn a substance from a liquid into a vapor at constant temperature. \(\mathrm{D}_{2}\mathrm{O}\) has a significant latent heat since it is an isotope of water, and heavier molecules require more energy to vaporize. \(\mathrm{H}_{2}\mathrm{O}_{2}\) typically has lower latent heat compared to \(\mathrm{D}_{2}\mathrm{O}\).

Density Comparison

Density indicates how much mass a substance has in a given volume. \(\mathrm{D}_{2}\mathrm{O}\) is known as heavy water because it is denser than ordinary water, and \(\mathrm{H}_{2}\mathrm{O}_{2}\) generally has less density than \(\mathrm{D}_{2}\mathrm{O}\).

Dielectric Constant Investigation

The dielectric constant is a measure of a substance's ability to store electrical energy in an electric field. \(\mathrm{H}_{2}\mathrm{O}_{2}\) has a higher dielectric constant than \(\mathrm{D}_{2}\mathrm{O}\) because it can store more energy, owing to the presence of an extra oxygen atom which increases molecular polarity and shape.

Conclusion on Property with Lesser Value

Among the evaluated properties, the property that has less value for \(\mathrm{D}_{2}\mathrm{O}\) compared to \(\mathrm{H}_{2}\mathrm{O}_{2}\) is the dielectric constant, as \(\mathrm{H}_{2}\mathrm{O}_{2}\)'s molecular structure allows it to store more electrical energy.

Key concepts

Boiling Point

The boiling point of a substance is the temperature at which its liquid form transitions to a gas. This temperature remains constant during the phase change. Super easy fact: you know when water boils, right? It's at 100°C at sea level.

• Hydrogen peroxide (H_2O_2) boasts a higher boiling point than regular water (H_2O) and heavy water (D_2O), thanks to its stronger hydrogen bonds.

So, what are hydrogen bonds? They are strong types of attractions between molecules caused by the positive hydrogen in one molecule being attracted to the electronegative oxygen in another.

• These bonds require more energy (i.e., higher temperature) to break, which is why H_2O_2 has a higher boiling point.
• As a result, heavy water boils at a lower temperature compared to hydrogen peroxide.

Latent Heat of Vaporization

The latent heat of vaporization is the energy needed to transform a liquid at its boiling point into a gas without changing the temperature. It's like the invisible magic that turns a pot of boiling water into steam!
For D_2O, or heavy water, the larger, heavier molecules require even more energy to make this change. Imagine trying to blow up a heavier balloon. It takes a little more air, right? That’s because:

• Heavy water molecules, due to their mass, demand more energy input.
• Thus, D_2O has a larger latent heat of vaporization than H_2O_2.

In essence, heavy water holds its liquid state longer before turning into vapor when compared to hydrogen peroxide.

Density

Density tells us how tightly packed the mass of a substance is within a unit volume. Think about it as how "heavy" something feels for its size.
Heavy water, noted as D_2O, is literally heavier per given volume because:

• It contains deuterium, a heavier isotope of hydrogen.
• This makes D_2O denser than regular water (H_2O) and hydrogen peroxide.

With H_2O_2, while its structure is slightly more complex due to the additional oxygen, it doesn’t quite pack the same weight per volume like heavy water does.
This means that if you were to measure out equal volumes of D_2O and H_2O_2 at the same temperature, D_2O would weigh more.

Dielectric Constant

The dielectric constant is a measure of a material's ability to store electrical energy. It’s like a trick tool for holding electric power.
Hydrogen peroxide (H_2O_2) features a higher dielectric constant compared to heavy water (D_2O). Here’s why:

• The presence of an extra oxygen atom in H_2O_2 increases its molecular polarity.
• This molecular structure allows H_2O_2 to store more electrical energy.

Why does this matter? In practical terms, this means H_2O_2 is a better medium for electrical insulation and capacitor applications when compared to heavy water.
So, if you're looking for a compound with a stronger ability to handle electric fields, H_2O_2 would be the go-to choice.