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A 0.513 mol sample of N,(g) initially at 298 K and 1.00 atm Molar heat capacity at constant Туре of gas is held at constant volume while enough heat is applied to volume (Cym) R R raise the temperature of the gas by 11.1 K. atoms Assuming ideal gas behavior, calculate the amount of heat (q) linear molecules in joules required to affect this temperature change and the nonlinear molecules 3R total change in internal energy, AU. Note that some books use where R is the ideal gas constant AE as the symbol for internal energy instead of AU. J AU = J

A 0.513 mol sample of N,(g) initially at 298 K and 1.00 atm Molar heat capacity at constant Туре of gas is held at constant volume while enough heat is applied to volume (Cym) R R raise the temperature of the gas by 11.1 K. atoms Assuming ideal gas behavior, calculate the amount of heat (q) linear molecules in joules required to affect this temperature change and the nonlinear molecules 3R total change in internal energy, AU. Note that some books use where R is the ideal gas constant AE as the symbol for internal energy instead of AU. J AU = J

Chemistry
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...
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**Problem Statement:** A 0.513 mol sample of \( \text{N}_2(g) \) initially at 298 K and 1.00 atm is held at constant volume while enough heat is applied to raise the temperature of the gas by 11.1 K. Assuming ideal gas behavior, calculate the amount of heat (\( q \)) in joules required to affect this temperature change and the total change in internal energy, \( \Delta U \). Note that some books use \( \Delta E \) as the symbol for internal energy instead of \( \Delta U \). **Formula Details:** - The provided table shows the molar heat capacity at constant volume (\( C_{V,m} \)) for different types of gases: | Type of gas | Molar heat capacity at constant volume (\( C_{V,m} \)) | |----------------------|---------------------------------------------------------| | atoms | \( \frac{3}{2} R \) | | linear molecules | \( \frac{5}{2} R \) | | nonlinear molecules | \( 3 R \) | where \( R \) is the ideal gas constant. **Results:** - \( q =\ \underline{\hspace{100pt}} \) J - \( \Delta U =\ \underline{\hspace{100pt}} \) J **Note:** To solve, use \( q = n \cdot C_{V,m} \cdot \Delta T \) where: - \( n \) is the number of moles, - \( C_{V,m} \) is the specific heat at constant volume for nitrogen (\( \text{N}_2 \)), - \( \Delta T \) is the change in temperature. Since nitrogen (\( \text{N}_2 \)) is a linear molecule, use \( C_{V,m} = \frac{5}{2} R \). Use \( R = 8.314 \, \text{J/mol}\cdot\text{K} \) for calculations.
Transcribed Image Text:**Problem Statement:** A 0.513 mol sample of \( \text{N}_2(g) \) initially at 298 K and 1.00 atm is held at constant volume while enough heat is applied to raise the temperature of the gas by 11.1 K. Assuming ideal gas behavior, calculate the amount of heat (\( q \)) in joules required to affect this temperature change and the total change in internal energy, \( \Delta U \). Note that some books use \( \Delta E \) as the symbol for internal energy instead of \( \Delta U \). **Formula Details:** - The provided table shows the molar heat capacity at constant volume (\( C_{V,m} \)) for different types of gases: | Type of gas | Molar heat capacity at constant volume (\( C_{V,m} \)) | |----------------------|---------------------------------------------------------| | atoms | \( \frac{3}{2} R \) | | linear molecules | \( \frac{5}{2} R \) | | nonlinear molecules | \( 3 R \) | where \( R \) is the ideal gas constant. **Results:** - \( q =\ \underline{\hspace{100pt}} \) J - \( \Delta U =\ \underline{\hspace{100pt}} \) J **Note:** To solve, use \( q = n \cdot C_{V,m} \cdot \Delta T \) where: - \( n \) is the number of moles, - \( C_{V,m} \) is the specific heat at constant volume for nitrogen (\( \text{N}_2 \)), - \( \Delta T \) is the change in temperature. Since nitrogen (\( \text{N}_2 \)) is a linear molecule, use \( C_{V,m} = \frac{5}{2} R \). Use \( R = 8.314 \, \text{J/mol}\cdot\text{K} \) for calculations.
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