Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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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.

---

#### 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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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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