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Ch.12 - Liquids, Solids & Intermolecular Forces
All textbooksTro 6th EditionCh.12 - Liquids, Solids & Intermolecular ForcesProblem 66
Chapter 12, Problem 66

This table displays the vapor pressure of nitrogen at several different temperatures. Use the data to determine the heat of vaporization and the normal boiling point of nitrogen. Temperature (K) Pressure (torr) 65 130.5 70 289.5 75 570.8 80 1028 85 1718

Verified step by step guidance
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The Clausius-Clapeyron equation relates the vapor pressure of a substance to its temperature and is given by: \( \ln P = -\frac{\Delta H_{vap}}{R} \left( \frac{1}{T} \right) + C \), where \( P \) is the vapor pressure, \( \Delta H_{vap} \) is the heat of vaporization, \( R \) is the ideal gas constant (8.314 J/mol·K), \( T \) is the temperature in Kelvin, and \( C \) is a constant.
To use the Clausius-Clapeyron equation, convert the given temperature and pressure data into a linear form by plotting \( \ln P \) versus \( \frac{1}{T} \). Calculate \( \ln P \) for each pressure value and \( \frac{1}{T} \) for each temperature.
Plot the calculated \( \ln P \) values against \( \frac{1}{T} \) values. The slope of the resulting line is equal to \( -\frac{\Delta H_{vap}}{R} \). Use linear regression to find the slope of the line.
Use the slope from the linear regression to calculate the heat of vaporization \( \Delta H_{vap} \) by rearranging the slope formula: \( \Delta H_{vap} = -\text{slope} \times R \).
The normal boiling point is the temperature at which the vapor pressure equals 760 torr. Use the linear equation from the plot to solve for \( T \) when \( P = 760 \) torr.

Key Concepts

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

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It reflects the tendency of particles to escape from the liquid phase into the vapor phase. As temperature increases, vapor pressure typically increases, indicating that more molecules have enough energy to enter the vapor phase.
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Raoult's Law and Vapor Pressure

Heat of Vaporization

The heat of vaporization is the amount of energy required to convert a unit mass of a liquid into vapor without a change in temperature. This value is crucial for understanding phase changes and is typically expressed in joules per gram or calories per gram. It can be determined using the Clausius-Clapeyron equation, which relates vapor pressure and temperature.
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Normal Boiling Point

The normal boiling point of a substance is the temperature at which its vapor pressure equals the standard atmospheric pressure (1 atm or 760 torr). At this point, the liquid turns into vapor throughout the liquid, not just at the surface. For nitrogen, determining the normal boiling point involves analyzing the vapor pressure data to find the temperature at which the pressure reaches 760 torr.
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Related Practice
Textbook Question

Suppose that 0.95 g of water condenses on a 75.0-g block of iron that is initially at 22 °C. If the heat released during condensation goes only to warming the iron block, what is the final temperature (in °C) of the iron block? (Assume a constant enthalpy of vaporization for water of 44.0 kJ/mol.)

Textbook Question

This table displays the vapor pressure of ammonia at several different temperatures. Use the data to determine the heat of vaporization and normal boiling point of ammonia.

Temperature (K) Pressure (torr)

200 65.3

210 134.3

220 255.7

230 456.0

235 597.0

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Textbook Question

Ethanol has a heat of vaporization of 38.56 kJ/mol and a normal boiling point of 78.4 °C. What is the vapor pressure of ethanol at 15 °C?

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Textbook Question

Benzene has a heat of vaporization of 30.72 kJ/mol and a normal boiling point of 80.1 °C. At what temperature does benzene boil when the external pressure is 445 torr?

Textbook Question

Carbon disulfide has a vapor pressure of 363 torr at 25 °C and a normal boiling point of 46.3 °C. Find ΔHvap for carbon disulfide.

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