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A 15.0-L tank is filled with helium gas at a pressure of 1.00 x 102 atm. How many balloons (each 2.00 L) can be inflated to a pressure of 1.00 atm, assuming that the tem- perature remains constant and that the tank cannot be emptied below 1.00 atm?

A 15.0-L tank is filled with helium gas at a pressure of 1.00 x 102 atm. How many balloons (each 2.00 L) can be inflated to a pressure of 1.00 atm, assuming that the tem- perature remains constant and that the tank cannot be emptied below 1.00 atm?

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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A 15.0-L tank is filled with helium gas at a pressure of \(1.00 \times 10^2\) atm. How many balloons (each 2.00 L) can be inflated to a pressure of 1.00 atm, assuming that the temperature remains constant and that the tank cannot be emptied below 1.00 atm? **Solution Explanation:** 1. **Initial Conditions:** - Volume of tank, \( V_1 = 15.0 \, \text{L} \) - Initial pressure in the tank, \( P_1 = 100 \, \text{atm} \) 2. **Final Conditions:** - Final pressure in the tank, \( P_2 = 1.00 \, \text{atm} \) 3. **Use Boyle’s Law:** - Since temperature remains constant, we use Boyle's Law: \( P_1V_1 = P_2V_2 \) 4. **Calculate Volume of Helium at 1 atm:** - \( V_2 = \frac{P_1V_1}{P_2} = \frac{(100 \, \text{atm})(15.0 \, \text{L})}{1.00 \, \text{atm}} = 1500 \, \text{L} \) 5. **Balloon Volume:** - Each balloon has a volume of 2.00 L. 6. **Number of Balloons:** - Number of balloons = \( \frac{\text{Total Volume}}{\text{Balloon Volume}} = \frac{1500 \, \text{L}}{2.00 \, \text{L/balloon}} = 750 \, \text{balloons} \) The tank can inflate 750 balloons to a pressure of 1.00 atm.
Transcribed Image Text:A 15.0-L tank is filled with helium gas at a pressure of \(1.00 \times 10^2\) atm. How many balloons (each 2.00 L) can be inflated to a pressure of 1.00 atm, assuming that the temperature remains constant and that the tank cannot be emptied below 1.00 atm? **Solution Explanation:** 1. **Initial Conditions:** - Volume of tank, \( V_1 = 15.0 \, \text{L} \) - Initial pressure in the tank, \( P_1 = 100 \, \text{atm} \) 2. **Final Conditions:** - Final pressure in the tank, \( P_2 = 1.00 \, \text{atm} \) 3. **Use Boyle’s Law:** - Since temperature remains constant, we use Boyle's Law: \( P_1V_1 = P_2V_2 \) 4. **Calculate Volume of Helium at 1 atm:** - \( V_2 = \frac{P_1V_1}{P_2} = \frac{(100 \, \text{atm})(15.0 \, \text{L})}{1.00 \, \text{atm}} = 1500 \, \text{L} \) 5. **Balloon Volume:** - Each balloon has a volume of 2.00 L. 6. **Number of Balloons:** - Number of balloons = \( \frac{\text{Total Volume}}{\text{Balloon Volume}} = \frac{1500 \, \text{L}}{2.00 \, \text{L/balloon}} = 750 \, \text{balloons} \) The tank can inflate 750 balloons to a pressure of 1.00 atm.
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