Question

Iodine, like most substances, exhibits only three phases: solid, liquid, and vapor. The triple point of iodine is at 90 torr and \(115^{\circ} \mathrm{C} .\) Which of the following statements concerning liquid \(\mathrm{I}_{2}\) must be true? Explain your answer. a. \(\mathrm{I}_{2}(l)\) is more dense than \(\mathrm{I}_{2}(g).\) b. \(\mathrm{I}_{2}(l)\) cannot exist above \(115^{\circ} \mathrm{C}.\) c. \(\mathrm{I}_{2}(l)\) cannot exist at 1 atmosphere pressure. d. \(\mathrm{I}_{2}(l)\) cannot have a vapor pressure greater than 90 torr. e. \(\mathrm{I}_{2}(l)\) cannot exist at a pressure of 10 torr.

Short answer

The correct statements are: a. I₂(l) is more dense than I₂(g), because the density of a substance in the liquid phase is usually higher than in the gas phase. c. I₂(l) cannot exist at 1 atmosphere pressure, as the pressure needed for liquid iodine to exist is 90 torr (approximately 0.118 atmosphere), which is lower than 1 atmosphere. d. I₂(l) cannot have a vapor pressure greater than 90 torr, since 90 torr is the maximum vapor pressure at the triple point. e. I₂(l) cannot exist at a pressure of 10 torr, as the pressure needed for liquid iodine to exist is 90 torr (about 0.118 atmosphere), which is higher than 10 torr.

Step-by-step solution

Answer: a. I2(l) is more dense than I2(g).

Usually, the density of a substance in the liquid phase is higher than in the gas phase, as the molecules/atoms are closer together. So, I₂ in the liquid state will most certainly be more dense than in the gaseous state.

Answer: b. I2(l) cannot exist above \(115^{\circ} \mathrm{C}.\)

This statement is not necessarily true. At the triple point (\(115^{\circ} \mathrm{C}\) and 90 torr), all three phases of iodine coexist. However, at temperatures above \(115^{\circ} \mathrm{C}\) and different pressures, liquid iodine could still exist, depending on the specific temperature and pressure conditions.

Answer: c. I2(l) cannot exist at 1 atmosphere pressure.

This statement is true. At the triple point, the pressure needed for liquid iodine to exist is 90 torr (approximately 0.118 atmosphere). Therefore, if the pressure is 1 atmosphere, it is beyond the conditions needed for liquid iodine. As a result, I₂ in liquid form cannot exist at 1 atmosphere pressure.

Answer: d. I2(l) cannot have a vapor pressure greater than 90 torr.

This statement is true. The triple point corresponds to 90 torr, which is the maximum vapor pressure that iodine can have while still being in the liquid phase. If the vapor pressure is greater than 90 torr, iodine cannot be in the liquid phase, as it has already turned into a gas.

Answer: e. I2(l) cannot exist at a pressure of 10 torr.

This statement is also true. At the triple point, the pressure needed for liquid iodine to exist is 90 torr (about 0.118 atmosphere). If the pressure is only 10 torr (about 0.0132 atmosphere), it is below the conditions needed for liquid iodine. As a result, I₂ in liquid form cannot exist at a pressure of 10 torr.

Key concepts

Triple Point

The triple point of a substance, like iodine, is an essential concept in understanding phase diagrams. It is the unique set of conditions at which all three phases – solid, liquid, and vapor – exist in equilibrium.
The triple point of iodine occurs at a temperature of 115°C and a pressure of 90 torr. This means that at these specific conditions, iodine can be found in its solid, liquid, and gaseous states simultaneously.
The triple point is significant because it indicates the only conditions under which all three phases can coexist. Outside of these conditions, one phase will typically dominate, preventing the others from existing.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its solid or liquid phases at a specific temperature. It rises with temperature as more molecules have the energy to escape from the liquid or solid phase into the gas phase.
In the context of iodine, the vapor pressure at the triple point is 90 torr. This pressure signifies the maximum vapor pressure at which iodine can exist as a liquid. If the vapor pressure exceeds 90 torr, iodine cannot remain in liquid form and will instead transition to gas.
This is because, beyond the triple point, the increased kinetic energy allows more molecules to transition to the vapor phase, surpassing the point where liquid can stably exist.

Density in Different Phases

Density is a measure of how much mass is packed into a given volume. Typically, a substance's density is higher in the solid or liquid phases compared to the gaseous phase. This is because, in solids and liquids, molecules are closer together, whereas in gases, molecules are more spread out.
This concept helps explain why liquid iodine \(I_2(l)\) is denser than its gaseous form (I_2(g)). In liquid form, iodine molecules are more closely packed compared to when they are in the gaseous state.
Understanding the density differences across the phases assists in predicting how the substance will behave under various temperature and pressure conditions, and how it transitions between phases.

Pressure and Temperature Conditions

Pressure and temperature are key factors influencing phase changes. They determine the state in which a substance exists at any given moment.
According to the phase diagram of iodine, liquid iodine requires a specific range of pressure and temperature to exist. Beyond the triple point temperature of 115°C and pressure of 90 torr, different rules apply:

• At pressures above 90 torr, iodine will evaporate to gas.
• At pressures below 90 torr, liquid iodine cannot exist, as solid or gas forms will predominate.
• At temperatures above 115°C, other pressures may allow liquid iodine, but this specific condition is sensitive to changes.

These conditions demonstrate how delicate the balance is in maintaining a phase.