Question

(a) Why is the heat of fusion \(\left(\Delta H_{\text {lus }}\right)\) of a substance smaller than its heat of vaporization \(\left(\Delta H_{\text {vap }}\right) ?\) (b) Why is the heat of sublimation \(\left(\Delta H_{\text {subl }}\right)\) of a substance greater than its \(\Delta H_{\text {vap }} ?\) (c) At a given temperature and pressure, how does the magnitude of the heat of vaporization of a substance compare with that of its heat of condensation?

Short answer

(a) Breaking fewer intermolecular forces (b) Includes both fusion and vaporization energies (c) Magnitudes are equal but opposite in sign

Step-by-step solution

Understanding Heat of Fusion and Heat of Vaporization

The heat of fusion, \(\text{Δ}H_{\text{fus}}\), is the energy required to change a substance from solid to liquid at its melting point. The heat of vaporization, \(\text{Δ}H_{\text{vap}}\), is the energy required to change a substance from liquid to gas at its boiling point.

Compare Heat of Fusion and Heat of Vaporization

The heat of fusion is smaller than the heat of vaporization because melting requires breaking fewer intermolecular forces compared to vaporization. During melting, only the forces keeping the solid structure intact are broken, while vaporization requires breaking nearly all intermolecular forces to go into the gas phase.

Understanding Heat of Sublimation

The heat of sublimation, \(\text{Δ}H_{\text{subl}}\), is the energy required to change a substance from solid to gas without passing through the liquid state.

Compare Heat of Sublimation and Heat of Vaporization

The heat of sublimation is greater than the heat of vaporization because sublimation includes both the energy required to melt the solid (heat of fusion) and the energy required to vaporize the resulting liquid (heat of vaporization). Hence, \(\text{Δ}H_{\text{subl}} = \text{Δ}H_{\text{fus}} + \text{Δ}H_{\text{vap}}\).

Understanding Heat of Condensation

The heat of condensation is the energy released when a gas changes to a liquid at its boiling point. It is numerically equal but opposite in sign to the heat of vaporization.

Compare Heat of Vaporization and Heat of Condensation

At a given temperature and pressure, the magnitude of the heat of vaporization of a substance is equal to that of its heat of condensation. This is because the energy needed to vaporize a liquid is the same as the energy released when the vapor condenses back into the liquid.

Key concepts

Thermodynamics

Thermodynamics is the branch of physics that deals with heat, work, and energy transfers. It is foundational for understanding how substances change phases (e.g., from solid to liquid, or liquid to gas). In phase changes, energy in the form of heat is either absorbed or released.
The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed, only transferred or converted. Understanding this principle helps in calculating the energy required for phase changes.
The second law of thermodynamics introduces the concept of entropy, a measure of disorder. During phase changes, entropy usually increases when moving from a solid to a liquid to a gas, meaning the system becomes more disordered.

Phase changes

Phase changes are transitions between different states of matter (solid, liquid, gas). Common phase changes include melting, freezing, vaporization, condensation, sublimation, and deposition.
During melting or fusion, a solid turns into a liquid. This process absorbs heat, called the heat of fusion, \(\text{Δ}H_{\text{fus}}\). In vaporization, a liquid changes into a gas, absorbing the heat of vaporization, \(\text{Δ}H_{\text{vap}}\).
Sublimation is a direct change from solid to gas, bypassing the liquid phase. The heat required for this change is the heat of sublimation, \(\text{Δ}H_{\text{subl}}\). Each of these transitions requires different amounts of energy due to varying intermolecular forces being disrupted or formed.

Heat of sublimation

The heat of sublimation, \(\text{Δ}H_{\text{subl}}\), is the total energy required for a substance to transition directly from a solid to a gas phase. This includes both the energy needed to melt the solid (heat of fusion) and the energy required to vaporize the resulting liquid (heat of vaporization):
\[ \text{Δ}H_{\text{subl}} = \text{Δ}H_{\text{fus}} + \text{Δ}H_{\text{vap}} \]
Sublimation involves overcoming all intermolecular forces holding the particles together in the solid state and then further energy to convert the liquid molecules into gas. Therefore, \(\text{Δ}H_{\text{subl}}\) is typically much greater than just \(\text{Δ}H_{\text{vap}}\).

Intermolecular forces

Intermolecular forces are the forces of attraction or repulsion between molecules. These forces determine the physical properties of substances and the energy required for phase changes. There are several types of intermolecular forces:

• London dispersion forces: Weak forces resulting from temporary dipoles in molecules. Present in all molecules but more apparent in nonpolar molecules.
• Dipole-dipole interactions: Occur between molecules with permanent dipoles, generally stronger than dispersion forces.
• Hydrogen bonds: A strong type of dipole-dipole interaction that occurs when hydrogen is bonded to electronegative atoms like oxygen, nitrogen, or fluorine.

Stronger intermolecular forces require more energy to break, which is why the heat of vaporization, where nearly all forces between molecules must be overcome, is greater than the heat of fusion, where only a portion of these forces are disrupted.