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: (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 11.81. (d) Calculate the vapor pressure of octane at - 30 °C.
A watch with a liquid crystal display (LCD) does not function properly when it is exposed to low temperatures during a trip to Antarctica. Explain why the LCD might not function well at low temperature.

Key Concepts
Liquid Crystal Properties
Temperature Effects on LCDs
Electro-optic Effect
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.
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.
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?