Question

Why does iodine, \(\mathrm{I}_{2}(\mathrm{~s})\), spontaneously sublime at room temperature?

Short answer

Iodine sublimates spontaneously because the entropy increase outweighs the energy required at room temperature, making the Gibbs free energy negative.

Step-by-step solution

Understanding Sublimation

Sublimation is the process by which a solid changes into a gas without passing through the liquid phase. For iodine, this process occurs when iodine atoms gain enough energy to overcome intermolecular forces and enter the gas phase.

Evaluating Energy Changes

Consider the thermodynamics of the sublimation process. The key factors are the enthalpy change ( abla H ext{), which is the heat required to break iodine's solid structure, and the entropy change ( abla S ext{), which is the change in disorder as iodine transitions from solid to gas.

Using Gibbs Free Energy

The spontaneity of the sublimation process at room temperature is determined by the Gibbs free energy change ( abla G = abla H - T abla S ext{), where T is the temperature in Kelvin. For a process to be spontaneous, abla G must be negative.

Calculating abla G

In the case of iodine sublimation, while abla H is positive (energy is absorbed), abla S is also positive since going from solid to gas increases disorder. At room temperature, the term T abla S is large enough to make abla G negative, hence making the sublimation spontaneous.

Key concepts

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat, work, temperature, and energy. It explains how these quantities interact and transfer across natural processes. In the context of sublimation, thermodynamics helps us understand why and how the phase transition from solid to gas takes place.

• Energy is required to break the intermolecular forces holding the solid structure intact. This energy uptake is known as endothermic reaction and is crucial for substances like iodine to sublime.
• The change in enthalpy ( abla H) reflects the amount of heat absorbed during the sublimation. As solids transition directly into gases, the energy input surmounts the lattice energy that binds solid molecules.

Considering these energy exchanges, thermodynamics enables us to predict not only the direction of change but the conditions required for such changes, such as temperature and pressure parameters.

Gibbs Free Energy

Gibbs free energy is a vital thermodynamic property used to predict the spontaneity of a process. It combines enthalpy, entropy, and temperature into a single value, the change in Gibbs free energy ( abla G), governed by the equation abla G = abla H - T abla S.

• For any process to be spontaneous, abla G should be negative. abla G's negativity implies that the entropy-driven term (T abla S) overcomes the enthalpic cost ( abla H).
• In simple terms, if you reach a situation where the disorder (entropy) created by the process provides enough energy, it could offset the energy required to trigger the process.

For iodine sublimation, although the initial energy requirement is high ( abla H is positive), the increase in disorder ( abla S positive) at room temperature achieves a negative abla G, ensuring spontaneity of the sublimation.

Iodine Sublimation

Iodine sublimation occurs when iodine changes its state from solid directly to gas without becoming liquid. This phenomenon happens readily at room temperature.

• Iodine crystals have weak intermolecular forces, making it easier for iodine atoms to escape into the gas phase with just a moderate energy input.
• When iodine sublimes, the considerable increase in entropy, due to the loosening of rigid solid structures into a free gaseous state, contributes positively to making the overall transition spontaneous.

Because of the relatively simple energy balance established by temperature and Gibbs free energy components, iodine sublimates with little difficulty. The balance creates conditions favoring the sublimation even at lower temperatures, providing an excellent example of solid-gas transitions in everyday environments.