Á balloon is filled to a volume of 6.65 × 10´ mL at a temperature of 15.0°C. The balloon is then cooled at constant pressure to a temperature of 1.07 × 10“ K. What is the final volume of the balloon? Volume = mL
Á balloon is filled to a volume of 6.65 × 10´ mL at a temperature of 15.0°C. The balloon is then cooled at constant pressure to a temperature of 1.07 × 10“ K. What is the final volume of the balloon? Volume = mL
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 balloon is filled to a volume of \( 6.65 \times 10^2 \) mL at a temperature of 15.0°C. The balloon is then cooled at constant pressure to a temperature of \( 1.07 \times 10^2 \) K. What is the final volume of the balloon?
**Volume =** \_\_\_\_ mL
---
In this problem, the relationship between the initial and final volumes and temperatures of a gas is explored at constant pressure, which applies Charles's Law. This law can be expressed as:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Where:
- \( V_1 \) is the initial volume.
- \( T_1 \) is the initial temperature in Kelvin.
- \( V_2 \) is the final volume.
- \( T_2 \) is the final temperature in Kelvin.
To solve the problem:
1. Convert the initial temperature from Celsius to Kelvin:
\[ T_1 = 15.0°C + 273.15 = 288.15 \, K \]
2. Set up the equation using Charles's Law to find \( V_2 \):
\[ \frac{6.65 \times 10^2 \, \text{mL}}{288.15 \, K} = \frac{V_2}{1.07 \times 10^2 \, K} \]
3. Solve for \( V_2 \):
\[ V_2 = \frac{(6.65 \times 10^2 \, \text{mL})(1.07 \times 10^2 \, K)}{288.15 \, K} \]
Calculate to find the final volume of the balloon.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3dae5a27-a228-455d-8cc9-f5b577430088%2Ff5db1ed7-4818-4b77-b0e9-c99270591d00%2Fh8xae25_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A balloon is filled to a volume of \( 6.65 \times 10^2 \) mL at a temperature of 15.0°C. The balloon is then cooled at constant pressure to a temperature of \( 1.07 \times 10^2 \) K. What is the final volume of the balloon?
**Volume =** \_\_\_\_ mL
---
In this problem, the relationship between the initial and final volumes and temperatures of a gas is explored at constant pressure, which applies Charles's Law. This law can be expressed as:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Where:
- \( V_1 \) is the initial volume.
- \( T_1 \) is the initial temperature in Kelvin.
- \( V_2 \) is the final volume.
- \( T_2 \) is the final temperature in Kelvin.
To solve the problem:
1. Convert the initial temperature from Celsius to Kelvin:
\[ T_1 = 15.0°C + 273.15 = 288.15 \, K \]
2. Set up the equation using Charles's Law to find \( V_2 \):
\[ \frac{6.65 \times 10^2 \, \text{mL}}{288.15 \, K} = \frac{V_2}{1.07 \times 10^2 \, K} \]
3. Solve for \( V_2 \):
\[ V_2 = \frac{(6.65 \times 10^2 \, \text{mL})(1.07 \times 10^2 \, K)}{288.15 \, K} \]
Calculate to find the final volume of the balloon.
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