To determine whether [tex]\(\Delta H\)[/tex] (the enthalpy change) is positive or negative for the sublimation and melting processes, we need to consider the nature of each phase transition.
1. Sublimation of [tex]\(I_2 (s)\)[/tex] to [tex]\(I_2 (g)\)[/tex]:
[tex]\[
I_2 (s) \rightarrow I_2 (g)
\][/tex]
Sublimation is the process where a substance transitions directly from a solid to a gas without passing through the liquid phase. This process requires the input of energy to overcome the intermolecular forces holding the molecules in the solid state. Hence, the enthalpy change [tex]\(\Delta H\)[/tex] for sublimation is positive because energy is absorbed from the surroundings.
2. Melting of [tex]\(I_2 (s)\)[/tex] to [tex]\(I_2 (l)\)[/tex]:
[tex]\[
I_2 (s) \rightarrow I_2 (l)
\][/tex]
Melting, or fusion, is the process where a solid transitions to the liquid state. Similar to sublimation, melting requires energy to break some of the intermolecular forces in the solid to allow the molecules to move more freely in the liquid state. Thus, the enthalpy change [tex]\(\Delta H\)[/tex] for melting is also positive because energy is absorbed.
In both cases, [tex]\(\Delta H\)[/tex] is positive.
Next, we need to determine in which process the magnitude of [tex]\(\Delta H\)[/tex] is greater.
Sublimation involves a direct transition from the solid state to the gaseous state, bypassing the liquid phase. This requires overcoming both the intermolecular forces present in the solid and providing the additional energy needed to transition from the liquid to the gas phase. Therefore, the enthalpy change for sublimation includes both the enthalpy change for fusion (melting) and the enthalpy change for vaporization.
Mathematically:
[tex]\[
\Delta H_{\text{sub}} = \Delta H_{\text{fus}} + \Delta H_{\text{vap}}
\][/tex]
Since [tex]\(\Delta H_{\text{sub}}\)[/tex] includes the enthalpy change for both melting and vaporization, it will have a greater magnitude than [tex]\(\Delta H_{\text{fus}}\)[/tex] alone.
In summary:
- [tex]\(\Delta H\)[/tex] is positive for both sublimation and melting processes.
- The magnitude of [tex]\(\Delta H\)[/tex] is greater for the sublimation process than for the melting process.
