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A sample of carbon dioxide gas in a rigid container has a pressure of 11.4 psi at 75 °C. What will the new temperature be (in °C) if the pressure is changed to 28.2 psi? 8-5.

A sample of carbon dioxide gas in a rigid container has a pressure of 11.4 psi at 75 °C. What will the new temperature be (in °C) if the pressure is changed to 28.2 psi? 8-5.

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 8-5: Gas Laws and Temperature Calculation** A sample of carbon dioxide gas in a rigid container has a pressure of 11.4 psi at 75 °C. What will the new temperature be (in °C) if the pressure is changed to 28.2 psi? This problem involves applying the gas laws to determine the change in temperature when the pressure of the gas is altered, assuming the volume remains constant. **Solution Outline:** 1. **Concept**: Use the Gay-Lussac's Law which relates pressure and temperature directly when volume is constant: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \). 2. **Given Data**: - Initial pressure (\(P_1\)) = 11.4 psi - Initial temperature (\(T_1\)) = 75 °C - Final pressure (\(P_2\)) = 28.2 psi 3. **Convert Temperature to Kelvin**: - \(T_1\) in Kelvin = 75 + 273.15 = 348.15 K 4. **Calculate New Temperature (\(T_2\))**: - Using the formula \( \frac{11.4}{348.15} = \frac{28.2}{T_2} \) - Rearranging gives \( T_2 = \frac{28.2 \times 348.15}{11.4} \) 5. **Convert \(T_2\) back to Celsius**: - Result in Kelvin - 273.15 = Result in °C **Conclusion**: The calculated temperature will be the answer based on the given pressure change for the carbon dioxide gas in the rigid container.
Transcribed Image Text:**Problem 8-5: Gas Laws and Temperature Calculation** A sample of carbon dioxide gas in a rigid container has a pressure of 11.4 psi at 75 °C. What will the new temperature be (in °C) if the pressure is changed to 28.2 psi? This problem involves applying the gas laws to determine the change in temperature when the pressure of the gas is altered, assuming the volume remains constant. **Solution Outline:** 1. **Concept**: Use the Gay-Lussac's Law which relates pressure and temperature directly when volume is constant: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \). 2. **Given Data**: - Initial pressure (\(P_1\)) = 11.4 psi - Initial temperature (\(T_1\)) = 75 °C - Final pressure (\(P_2\)) = 28.2 psi 3. **Convert Temperature to Kelvin**: - \(T_1\) in Kelvin = 75 + 273.15 = 348.15 K 4. **Calculate New Temperature (\(T_2\))**: - Using the formula \( \frac{11.4}{348.15} = \frac{28.2}{T_2} \) - Rearranging gives \( T_2 = \frac{28.2 \times 348.15}{11.4} \) 5. **Convert \(T_2\) back to Celsius**: - Result in Kelvin - 273.15 = Result in °C **Conclusion**: The calculated temperature will be the answer based on the given pressure change for the carbon dioxide gas in the rigid container.
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