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?
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Ch.11 - Liquids, Solids & Intermolecular Forces
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831
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Table of contents
- Ch.1 - Matter, Measurement & Problem Solving107
- Ch.2 - Atoms & Elements100
- Ch.3 - Molecules, Compounds & Chemical Equations127
- Ch.4 - Chemical Quantities & Aqueous Reactions114
- Ch.5 - Gases103
- Ch.6 - Thermochemistry92
- Ch.7 - Quantum-Mechanical Model of the Atom50
- Ch.8 - Periodic Properties of the Elements89
- Ch.9 - Chemical Bonding I: The Lewis Model84
- Ch.10 - Chemical Bonding II: Molecular Shapes & Valence Bond Theory74
- Ch.11 - Liquids, Solids & Intermolecular Forces60
- Ch.12 - Solids and Modern Material50
- Ch.13 - Solutions90
- Ch.14 - Chemical Kinetics111
- Ch.15 - Chemical Equilibrium65
- Ch.16 - Acids and Bases135
- Ch.17 - Aqueous Ionic Equilibrium145
- Ch.18 - Free Energy and Thermodynamics92
- Ch.19 - Electrochemistry100
- Ch.20 - Radioactivity and Nuclear Chemistry68
- Ch.21 - Organic Chemistry121
Chapter 11, Problem 65
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.
Verified step by step guidance1
Identify the Clausius-Clapeyron equation: \( \ln \left( \frac{P_2}{P_1} \right) = -\frac{\Delta H_{\text{vap}}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) \), where \( P_1 \) and \( P_2 \) are the vapor pressures at temperatures \( T_1 \) and \( T_2 \), respectively, and \( R \) is the ideal gas constant.
Recognize that the normal boiling point is the temperature at which the vapor pressure equals 1 atm (760 torr). Thus, \( P_2 = 760 \text{ torr} \) and \( T_2 = 46.3 \degree C \) (convert to Kelvin by adding 273.15).
Use the given vapor pressure at 25 °C: \( P_1 = 363 \text{ torr} \) and \( T_1 = 25 \degree C \) (convert to Kelvin by adding 273.15).
Substitute the known values into the Clausius-Clapeyron equation to solve for \( \Delta H_{\text{vap}} \).
Rearrange the equation to isolate \( \Delta H_{\text{vap}} \): \( \Delta H_{\text{vap}} = -R \cdot \frac{\ln \left( \frac{P_2}{P_1} \right)}{\left( \frac{1}{T_2} - \frac{1}{T_1} \right)} \).
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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. A higher vapor pressure indicates a greater volatility of the substance, which is crucial for understanding phase changes and calculating thermodynamic properties like enthalpy of vaporization.
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Raoult's Law and Vapor Pressure
Enthalpy of Vaporization (ΔH<sub>vap</sub>)
The enthalpy of vaporization (ΔH<sub>vap</sub>) is the amount of energy required to convert a unit quantity of a liquid into vapor at constant temperature and pressure. It is a critical parameter in thermodynamics that helps quantify the energy changes associated with phase transitions. This value can be determined using the Clausius-Clapeyron equation, which relates vapor pressure and temperature to ΔH<sub>vap</sub>.
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Clausius-Clapeyron Equation
The Clausius-Clapeyron equation describes the relationship between the vapor pressure of a substance and its temperature, allowing for the calculation of the enthalpy of vaporization. It is expressed as d(ln P)/dT = ΔH<sub>vap</sub>/(RT²), where P is the vapor pressure, T is the temperature, R is the ideal gas constant, and ΔH<sub>vap</sub> is the enthalpy of vaporization. This equation is essential for solving problems involving phase changes and thermodynamic properties.
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Related Practice
Textbook Question
An 8.5-g ice cube is placed into 255 g of water. Calculate the temperature change in the water upon the complete melting of the ice. Assume that all of the energy required to melt the ice comes from the water.
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Textbook Question
How much energy is released when 65.8 g of water freezes?
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Textbook Question
How much ice (in grams) would have to melt to lower the temperature of 352 mL of water from 25 °C to 5 °C? (Assume the density of water is 1.0 g/mL.)
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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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