Ch.11 - Liquids and Intermolecular Forces

Problem 90

Chapter 11, Problem 90

A particular liquid crystalline substance has the phase diagram shown in the figure. By analogy with the phase diagram for a nonliquid crystalline substance, identify the phase present in each area.

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Identify the axes of the phase diagram. Typically, the x-axis represents temperature and the y-axis represents pressure.

Locate the different regions or areas on the phase diagram. Each region corresponds to a different phase of the substance.

Identify the phase boundaries, which are the lines separating different regions. These lines indicate the conditions under which two phases coexist in equilibrium.

Determine the phases present in each region by comparing the phase diagram to a typical phase diagram for a nonliquid crystalline substance. Common phases include solid, liquid, and gas, but liquid crystalline substances may have additional phases such as nematic, smectic, or cholesteric.

Label each region with the appropriate phase name based on the characteristics of liquid crystalline substances and the analogy to nonliquid crystalline phase diagrams.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Phase Diagrams

Phase diagrams are graphical representations that show the phases of a substance as a function of temperature and pressure. They illustrate the conditions under which distinct phases, such as solid, liquid, and gas, exist and transition into one another. Understanding phase diagrams is crucial for predicting the state of a substance under varying environmental conditions.

Liquid Crystals

Liquid crystals are materials that exhibit properties between those of conventional liquids and solid crystals. They can flow like a liquid but have some degree of order, typically in their molecular arrangement. This unique behavior allows them to respond to electric fields and temperature changes, making them important in applications like displays and sensors.

Phase Transitions

Phase transitions refer to the changes in the state of matter that occur when a substance absorbs or releases energy, typically in the form of heat. Common transitions include melting, freezing, boiling, and condensation. In the context of liquid crystals, understanding these transitions is essential for identifying the different phases represented in a phase diagram.

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Related Practice

Textbook Question

The following table gives the vapor pressure of hexafluorobenzene (C₆F₆) as a function of temperature: (a) By plotting these data in a suitable fashion, determine whether the Clausius–Clapeyron equation (Equation 11.1) is obeyed. If it is obeyed, use your plot to determine ∆H_vap for C₆F₆.

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Textbook Question

Suppose the vapor pressure of a substance is measured at two different temperatures.

a. By using the Clausius–Clapeyron equation (Equation 11.1), derive the following relationship between the vapor pressures, 𝑃1 and 𝑃2, and the absolute temperatures at which they were measured, 𝑇1 and 𝑇2:

ln𝑃1𝑃2=−Δ𝐻vap𝑅(1𝑇1−1𝑇2)

b. Gasoline is a mixture of hydrocarbons, a component of which is octane (CH3CH2CH2CH2CH2CH2CH2CH3). Octane has a vapor pressure of 13.95 torr at 25°C and a vapor pressure of 144.78 torr at 75°C. Use these data and the equation in part (a) to calculate the heat of vaporization of octane.

c. By using the equation in part (a) and the data given in part (b), calculate the normal boiling point of octane. Compare your answer to the one you obtained from Exercise 11.83.

d. Calculate the vapor pressure of octane at −30°C.

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Textbook Question

Naphthalene (C₁₀H₈) is the main ingredient in traditional mothballs. Its normal melting point is 81 °C, its normal boiling point is 218 °C, and its triple point is 80 °C at 1000 Pa. Using the data, construct a phase diagram for naphthalene, labeling all the regions of your diagram.

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Textbook Question

In Table 11.3, we saw that the viscosity of a series of hydrocarbons increased with molecular weight, doubling from the six-carbon molecule to the ten-carbon molecule.

(a) The eight-carbon hydrocarbon, octane, has an isomer, isooctane. Would you predict that isooctane would have a larger or smaller viscosity than octane? Why?

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Textbook Question

The vapor pressure of ethanol (C₂H₅OH) at 19 °C is 40.0 torr. A 1.00-g sample of ethanol is placed in a 2.00 L container at 19 °C. If the container is closed and the ethanol is allowed to reach equilibrium with its vapor, how many grams of liquid ethanol remain?

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Textbook Question

Using information in Appendices B and C, calculate the minimum grams of propane, C3H8(g), that must be combusted to provide the energy necessary to convert 5.50 kg of ice at -20 °C to liquid water at 75 °C

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