34. The smell of fresh-cut pine is due in part to a cyclic alkene called pinene. A graph of the natural logarithm of the vapor pressure of pinene vs. 1/temperature produces a straight line with a slope of -4936.37 K. What is the enthalpy of vaporization of pinene?
34. The smell of fresh-cut pine is due in part to a cyclic alkene called pinene. A graph of the natural logarithm of the vapor pressure of pinene vs. 1/temperature produces a straight line with a slope of -4936.37 K. What is the enthalpy of vaporization of pinene?
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
Related questions
Question
![### Understanding the Enthalpy of Vaporization of Pinene
**Problem Statement:**
The distinct smell of fresh-cut pine is attributed to a cyclic alkene known as pinene. By graphing the natural logarithm of the vapor pressure of pinene against the inverse of temperature (1/temperature), a straight line is produced with a slope of -4936.37 K. Determine the enthalpy of vaporization of pinene.
**Explanation:**
This problem involves analyzing the relationship between vapor pressure and temperature for pinene. The graph described represents a common approach in thermodynamics where the Clausius-Clapeyron equation is used to determine the enthalpy of vaporization (\( \Delta H_{vap} \)).
**Key Concepts:**
- **Pinene:** A naturally occurring compound in pine trees, known for its characteristic pine scent.
- **Vapor Pressure:** The pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature.
- **Clausius-Clapeyron Equation:** This equation relates the natural logarithm of the vapor pressure (P) to the reciprocal of the temperature (1/T):
\[ \ln P = -\frac{\Delta H_{vap}}{R} \left(\frac{1}{T}\right) + C \]
Where:
- \( \ln P \) is the natural logarithm of the vapor pressure.
- \( \Delta H_{vap} \) is the enthalpy of vaporization.
- \( R \) is the universal gas constant (8.314 J/mol·K).
- \( T \) is the temperature in Kelvin.
- \( C \) is a constant.
**Finding the Enthalpy of Vaporization:**
The slope (\(-4936.37\) K) from the graph corresponds to \(-\frac{\Delta H_{vap}}{R}\). Thus, the enthalpy of vaporization can be calculated as:
\[ \Delta H_{vap} = -(\text{slope}) \cdot R \]
Substitute:
\[ \Delta H_{vap} = -(-4936.37 \, \text{K}) \times 8.314 \, \text{J/mol·K} \]
**Conclusion:**
The calculated value will give the enthalpy of vaporization of pinene, which indicates the amount of energy required to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F277ae00b-d056-42ed-a729-386f4fca5973%2F03f21e97-dce1-4085-a6a1-5d0b463ddc2b%2Fdnluspq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Enthalpy of Vaporization of Pinene
**Problem Statement:**
The distinct smell of fresh-cut pine is attributed to a cyclic alkene known as pinene. By graphing the natural logarithm of the vapor pressure of pinene against the inverse of temperature (1/temperature), a straight line is produced with a slope of -4936.37 K. Determine the enthalpy of vaporization of pinene.
**Explanation:**
This problem involves analyzing the relationship between vapor pressure and temperature for pinene. The graph described represents a common approach in thermodynamics where the Clausius-Clapeyron equation is used to determine the enthalpy of vaporization (\( \Delta H_{vap} \)).
**Key Concepts:**
- **Pinene:** A naturally occurring compound in pine trees, known for its characteristic pine scent.
- **Vapor Pressure:** The pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature.
- **Clausius-Clapeyron Equation:** This equation relates the natural logarithm of the vapor pressure (P) to the reciprocal of the temperature (1/T):
\[ \ln P = -\frac{\Delta H_{vap}}{R} \left(\frac{1}{T}\right) + C \]
Where:
- \( \ln P \) is the natural logarithm of the vapor pressure.
- \( \Delta H_{vap} \) is the enthalpy of vaporization.
- \( R \) is the universal gas constant (8.314 J/mol·K).
- \( T \) is the temperature in Kelvin.
- \( C \) is a constant.
**Finding the Enthalpy of Vaporization:**
The slope (\(-4936.37\) K) from the graph corresponds to \(-\frac{\Delta H_{vap}}{R}\). Thus, the enthalpy of vaporization can be calculated as:
\[ \Delta H_{vap} = -(\text{slope}) \cdot R \]
Substitute:
\[ \Delta H_{vap} = -(-4936.37 \, \text{K}) \times 8.314 \, \text{J/mol·K} \]
**Conclusion:**
The calculated value will give the enthalpy of vaporization of pinene, which indicates the amount of energy required to
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY