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The gas in a 250.0 mL piston experiences a change in pressure from 1.00 atm to 3.05 atı What is the new volume (in mL) assuming the moles of gas and temperature are held constant?

The gas in a 250.0 mL piston experiences a change in pressure from 1.00 atm to 3.05 atı What is the new volume (in mL) assuming the moles of gas and temperature are held constant?

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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**Understanding Gas Behavior in a Piston** The gas in a 250.0 mL piston experiences a change in pressure from 1.00 atm to 3.05 atm. What is the new volume (in mL) assuming the moles of gas and temperature are held constant? ### Explanation In this scenario, we apply **Boyle’s Law**, which states that the pressure and volume of a gas have an inverse relationship, when temperature and the number of moles are constant. Mathematically, this is expressed as: \[ P_1 \times V_1 = P_2 \times V_2 \] - **Initial Conditions:** - Volume (\( V_1 \)): 250.0 mL - Pressure (\( P_1 \)): 1.00 atm - **Final Conditions:** - Pressure (\( P_2 \)): 3.05 atm - Volume (\( V_2 \)): ? To find the new volume (\( V_2 \)), rearrange Boyle's Law: \[ V_2 = \frac{P_1 \times V_1}{P_2} \] Substitute the known values: \[ V_2 = \frac{1.00 \, \text{atm} \times 250.0 \, \text{mL}}{3.05 \, \text{atm}} \] Understanding this relationship allows us to predict how gases will behave under different pressure conditions, a crucial concept in many scientific and engineering applications.
Transcribed Image Text:**Understanding Gas Behavior in a Piston** The gas in a 250.0 mL piston experiences a change in pressure from 1.00 atm to 3.05 atm. What is the new volume (in mL) assuming the moles of gas and temperature are held constant? ### Explanation In this scenario, we apply **Boyle’s Law**, which states that the pressure and volume of a gas have an inverse relationship, when temperature and the number of moles are constant. Mathematically, this is expressed as: \[ P_1 \times V_1 = P_2 \times V_2 \] - **Initial Conditions:** - Volume (\( V_1 \)): 250.0 mL - Pressure (\( P_1 \)): 1.00 atm - **Final Conditions:** - Pressure (\( P_2 \)): 3.05 atm - Volume (\( V_2 \)): ? To find the new volume (\( V_2 \)), rearrange Boyle's Law: \[ V_2 = \frac{P_1 \times V_1}{P_2} \] Substitute the known values: \[ V_2 = \frac{1.00 \, \text{atm} \times 250.0 \, \text{mL}}{3.05 \, \text{atm}} \] Understanding this relationship allows us to predict how gases will behave under different pressure conditions, a crucial concept in many scientific and engineering applications.
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