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

Statements a, b, c, and d concerning liquid iodine, \(\mathrm{I}_{2}(l)\), must be true: a. \(\mathrm{I}_{2}(l)\) is denser than \(\mathrm{I}_{2}(g)\) because molecules in the liquid phase are more closely packed together than in the gas phase. b. \(\mathrm{I}_{2}(l)\) cannot exist above \(115^{\circ}\mathrm{C}\) as solid iodine will directly vaporize into gas at higher temperatures. c. \(\mathrm{I}_{2}(l)\) cannot exist at 1 atmosphere pressure as iodine will vaporize directly from solid to gas in these conditions. d. \(\mathrm{I}_{2}(l)\) cannot have a vapor pressure greater than 90 torr since the vapor pressure generally increases with temperature, and this value is already at the triple point.

Step-by-step solution

Statement a

Comparing the density of liquid iodine (\(\mathrm{I}_2 (l)\)) with that of gaseous iodine (\(\mathrm{I}_{2}(g)\)): Liquid phase generally has a more dense structure than the gas phase for a substance because molecules are more closely packed together. This statement is true.

Statement b

Analyzing if liquid iodine (\(\mathrm{I}_{2}(l)\)) cannot exist above \(115^{\circ}\mathrm{C}\): At temperatures above the triple point temperature, any additional heat will cause solid iodine to vaporize directly into gas, without forming the liquid phase. Thus, the statement is true.

Statement c

Evaluating if liquid iodine (\(\mathrm{I}_{2}(l)\)) cannot exist at 1 atmosphere pressure: 1 atmosphere is approximately 760 torr. At the triple point, liquid iodine exists at a lower pressure (90 torr). Thus, to form liquid iodine at 1 atmosphere, the temperature must be higher than the triple point temperature. However, at higher temperatures, iodine directly vaporizes from solid to gas. So, liquid iodine cannot exist at 1 atmosphere pressure, which makes this statement true.

Statement d

Assessing if liquid iodine (\(\mathrm{I}_{2}(l)\)) cannot have a vapor pressure greater than 90 torr: The vapor pressure of liquid iodine at the triple point is 90 torr. Below the triple point temperature, vapor pressure of liquid iodine would be less than 90 torr because vapor pressure generally increases with temperature. Thus, liquid iodine cannot have a vapor pressure greater than 90 torr, which makes this statement true.

Statement e

Verifying if liquid iodine (\(\mathrm{I}_{2}(l)\)) cannot exist at a pressure of 10 torr: This statement is incorrect. If we were to cool iodine from its gaseous phase at 10 torr and achieve a temperature below \(115^{\circ} \mathrm{C}\), we could form the liquid phase, disproving this statement. In conclusion, statements a, b, c, and d must be true for liquid iodine, while statement e is false.

Key concepts

Triple Point of Iodine

Understanding the triple point of a substance, such as iodine, is critical for comprehending the conditions under which it can coexist in all three states: solid, liquid, and gas. The triple point is a unique combination of temperature and pressure where these phases achieve equilibrium. Specifically for iodine, this occurs at 90 torr and at a temperature of 115°C.

At this precise point, iodine can transition between the solid, liquid, and vapor states without the usual phase changes that might be expected under different temperature and pressure conditions. Importantly, the existence of liquid iodine above 115°C is not possible since any additional heat input will prompt a direct sublimation from solid to gas, bypassing the liquid phase entirely.

It's essential for students to grasp this concept to predict the behavior of substances under varying atmospheric conditions and to understand why liquid iodine cannot exist at 1 atmosphere pressure, as it's much higher than the triple point.

Phase Changes

Phase changes are fundamental processes in chemistry where a substance transforms from one state of matter to another. These changes—melting, freezing, vaporization, condensation, sublimation, and deposition—are governed by temperature and pressure. Melting and freezing occur between solid and liquid states, vaporization and condensation between liquid and gas, and sublimation and deposition between solid and gas.

For iodine, the discussion of phase changes is centered around its triple point. Below the triple point temperature, the vapor pressure of iodine is less, and the substance is likely to be in the solid or liquid state depending on the external pressure. Understanding that the conditions must be just right for liquid forms of iodine to exist provides a clear example of how the delicate balance of these two factors influences phase changes in a real-world context.

Vapor Pressure

Vapor pressure is another crucial concept in the study of states of matter. It's the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. As temperature increases, so does vapor pressure, because more molecules have sufficient kinetic energy to escape from the liquid or solid phase into the gas phase.

For liquid iodine at the triple point, the vapor pressure is exactly 90 torr, which defines its equilibrium condition. In general, liquids cannot have a vapor pressure above their equilibrium point without changing the temperature. Therefore, at any given temperature, there's a maximum vapor pressure for the liquid before it turns into gas. This concept is vital when considering statement d from the exercise, clarifying why liquid iodine can't have a vapor pressure greater than 90 torr at the triple point temperature.