A sample of hydrogen gas at a pressure of 1.14 atm and a temperature of 26.4° C, occupies a volume of 15.3 L. If the gas is allowed to expand at constant temperature to a volume of 20.3 L, the pressure of the gas sample will be atm.
A sample of hydrogen gas at a pressure of 1.14 atm and a temperature of 26.4° C, occupies a volume of 15.3 L. If the gas is allowed to expand at constant temperature to a volume of 20.3 L, the pressure of the gas sample will be atm.
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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![### Gas Law Problem
#### Problem Statement:
A sample of **hydrogen** gas at a pressure of **1.14 atm** and a temperature of **26.4°C**, occupies a volume of **15.3 L**. If the gas is allowed to expand at constant temperature to a volume of **20.3 L**, the pressure of the gas sample will be ___ atm.
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#### Solution:
To solve this problem, we can use Boyle's Law, which states that for a given mass of gas at a constant temperature, the product of the pressure and the volume is constant. Mathematically, it is expressed as:
\[ P_1 \times V_1 = P_2 \times V_2 \]
Where:
- \( P_1 \) is the initial pressure
- \( V_1 \) is the initial volume
- \( P_2 \) is the final pressure
- \( V_2 \) is the final volume
Given:
- \( P_1 = 1.14 \) atm
- \( V_1 = 15.3 \) L
- \( V_2 = 20.3 \) L
We need to find \( P_2 \).
Rearranging the equation for Boyle's Law to solve for \( P_2 \):
\[ P_2 = \frac{P_1 \times V_1}{V_2} \]
Substitute the given values into the equation:
\[ P_2 = \frac{1.14 \text{ atm} \times 15.3 \text{ L}}{20.3 \text{ L}} \]
Perform the calculation to find \( P_2 \).
---
Feel free to use this information and the given data to determine the new pressure of the gas sample as it expands.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ee6479a-9360-421e-a0d3-69e759864a42%2F865f33df-42ba-4eff-94ad-2a0274dff92e%2Fxhlauok.jpeg&w=3840&q=75)
Transcribed Image Text:### Gas Law Problem
#### Problem Statement:
A sample of **hydrogen** gas at a pressure of **1.14 atm** and a temperature of **26.4°C**, occupies a volume of **15.3 L**. If the gas is allowed to expand at constant temperature to a volume of **20.3 L**, the pressure of the gas sample will be ___ atm.
---
#### Solution:
To solve this problem, we can use Boyle's Law, which states that for a given mass of gas at a constant temperature, the product of the pressure and the volume is constant. Mathematically, it is expressed as:
\[ P_1 \times V_1 = P_2 \times V_2 \]
Where:
- \( P_1 \) is the initial pressure
- \( V_1 \) is the initial volume
- \( P_2 \) is the final pressure
- \( V_2 \) is the final volume
Given:
- \( P_1 = 1.14 \) atm
- \( V_1 = 15.3 \) L
- \( V_2 = 20.3 \) L
We need to find \( P_2 \).
Rearranging the equation for Boyle's Law to solve for \( P_2 \):
\[ P_2 = \frac{P_1 \times V_1}{V_2} \]
Substitute the given values into the equation:
\[ P_2 = \frac{1.14 \text{ atm} \times 15.3 \text{ L}}{20.3 \text{ L}} \]
Perform the calculation to find \( P_2 \).
---
Feel free to use this information and the given data to determine the new pressure of the gas sample as it expands.
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