Question

Iodine has a triple point at \(114^{\circ} \mathrm{C}, 90 \mathrm{~mm} \mathrm{Hg} .\) Its critical temperature is \(535^{\circ} \mathrm{C}\). The density of the solid is \(4.93 \mathrm{~g} / \mathrm{cm}^{3},\) and that of the liquid is \(4.00 \mathrm{~g} / \mathrm{cm}^{3} .\) Sketch the phase diagram for iodine and use it to fill in the blanks using either "liquid" or "solid." (a) Iodine vapor at \(80 \mathrm{~mm}\) Hg condenses to the __________ when cooled sufficiently. (b) Iodine vapor at \(125^{\circ} \mathrm{C}\) condenses to the _________ when enough pressure is applied. (c) Iodine vapor at \(700 \mathrm{~mm}\) Hg condenses to the ____________ when cooled above the triple point temperature.

Short answer

(a) Cooled sufficiently at a pressure lower than the triple point. (b) Pressure applied at a temperature higher than the triple point. (c) Cooled sufficiently at a pressure higher than the triple point. Answer: (a) Solid, (b) Liquid, (c) Liquid.

Step-by-step solution

Sketch the Phase Diagram

Using the given information, draw a graph with pressure (P) on the vertical axis and temperature (T) on the horizontal axis. Mark the triple point (114°C, 90 mm Hg) and critical temperature (535°C) on the graph. The solid and liquid densities will indicate the slope of the solid-liquid phase boundary. As the solid density is higher than the liquid density, the slope will be negative. Based on the densities and triple point information, the phase diagram will have three regions: 1. Solid below and left of the solid-liquid phase boundary and below the triple point. 2. Liquid above and right of the solid-liquid phase boundary and below the triple point. 3. Vapor above the triple point and right of the solid-liquid phase boundary.

Determine the phase of iodine vapor in each case

(a) The iodine vapor is at 80 mm Hg, which is below the triple point pressure, so when cooled sufficiently, it directly becomes a solid. The answer is Solid. (b) The iodine vapor is at a temperature of 125°C, which is above the triple point temperature, so when enough pressure is applied, it becomes liquid. The answer is Liquid. (c) The iodine vapor is at 700 mm Hg, which is above the triple point pressure, so it condenses to the liquid phase when cooled above the triple point temperature. The answer is Liquid.

Key concepts

Triple Point

The triple point of a substance is a unique combination of temperature and pressure at which three phases—solid, liquid, and vapor—coexist in thermodynamic equilibrium. In the case of iodine, this occurs at a temperature of 114°C and a pressure of 90 mm Hg. At this precise point, the distinctions between the solid, liquid, and gaseous phases of iodine vanish; they can all presence concurrently.

Understanding the triple point is crucial for several reasons. It not only marks a key reference for the phases of a substance but can also serve as a fixed point in the calibration of thermometers. For iodine, the triple point would be the exact state used to define the conditions wherein iodine can simultaneously be a solid, liquid, and vapor, serving as a benchmark in scientific measurements.

Critical Temperature

The critical temperature of a substance is the highest temperature at which it can exist as a liquid, regardless of pressure. Beyond this temperature, the substance enters a supercritical fluid state, where it exhibits properties of both a liquid and a gas. For iodine, the critical temperature is listed as 535°C. This means that if you heat iodine above this temperature, it cannot be condensed to a liquid by just increasing the pressure; it will stay in a gaseous or supercritical state.

The concept of critical temperature is integral to the understanding of phase transitions. At temperatures above the critical temperature, the meniscus that separates the liquid and vapor phases disappears, and the distinction between the phases is no longer visible. This is essential for the application of supercritical fluids in various industrial processes, such as in extraction, where the unique properties of supercritical fluids are utilized.

Phase Transition

A phase transition is the transformation from one state of matter to another, as a result of changing temperature, pressure, or other external conditions. For instance, when iodine vapor at 80 mm Hg is cooled sufficiently, it undergoes a phase transition from a gaseous state to a solid state. Similarly, iodine vapor at 125°C will change to a liquid upon the application of sufficient pressure.

The phase diagram for a substance like iodine illustrates the different phases and the transitions between them over various temperatures and pressures. The lines—or 'phase boundaries'—indicate the conditions under which two phases can coexist. Understanding these transitions helps in predicting the behavior of substances under various temperature and pressure environments, which is fundamental in designing processes in industries like manufacturing, food technology, and pharmaceuticals.