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Chapter 10: Problem 32

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

Expert verified
The true statements concerning liquid iodine are: a. \(I_{2}(l)\) is more dense than \(I_{2}(g)\), and e. \(I_{2}(l)\) cannot exist at a pressure of 10 torr.

Step by step solution

01

Understanding the Triple Point

The triple point of a substance is the temperature and pressure at which the three phases—solid, liquid, and gas—of that substance coexist in equilibrium. For iodine, the triple point is at 115°C and 90 torr. We can use this information to analyze each statement.
02

Statement a: Density comparison of iodine liquid and gas

In general, liquid phases of substances are denser than their gas phases. This is true for iodine, as the molecules in the liquid phase are closer together than the molecules in the gas phase. Therefore, statement a is true: \(I_{2}(l)\) is more dense than \(I_{2}(g)\).
03

Statement b: Existence of liquid iodine above 115°C

At the triple point, the three phases of iodine coexist simultaneously. Above the triple point temperature and at a pressure higher than the triple point pressure, liquid iodine can still exist. However, if we have a lower pressure at temperatures above the triple point, the iodine will sublimate directly from solid to gas. Therefore, statement b is false: \(I_{2}(l)\) can exist above \(115^{\circ}C\) under certain conditions (higher pressure).
04

Statement c: Existence of liquid iodine at 1 atmosphere pressure

One atmosphere pressure is approximately equal to 760 torr. The triple point pressure of iodine is 90 torr. When the pressure is higher than the triple point pressure and at a temperature above 115°C, liquid iodine can exist. Therefore, statement c is false: \(I_{2}(l)\) can exist at 1 atmosphere pressure considering the appropriate temperature.
05

Statement d: Vapor pressure of liquid iodine

Vapor pressure is the pressure of a vapor in equilibrium with its non-vapor phases. At the triple point, the three phases of iodine coexist in equilibrium, meaning that the vapor pressure of liquid iodine is equal to the triple point pressure (90 torr). At higher temperatures, the vapor pressure of \(I_{2}(l)\) will increase. Therefore, statement d is false: \(I_{2}(l)\) can have a vapor pressure greater than 90 torr.
06

Statement e: Existence of liquid iodine at 10 torr pressure

As discussed earlier, at higher pressures than the triple point pressure (90 torr), the liquid phase of iodine can exist. When the pressure is lower than the triple point pressure (like 10 torr), liquid iodine cannot exist, because iodine will either be in the solid phase or directly sublimate into the gas phase without going through the liquid phase. Therefore, statement e is true: \(I_{2}(l)\) cannot exist at a pressure of 10 torr.
07

Conclusion

Based on the analysis of each statement, the true statements concerning liquid iodine are: a. \(I_{2}(l)\) is more dense than \(I_{2}(g)\), and e. \(I_{2}(l)\) cannot exist at a pressure of 10 torr.

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