2. Summarize what Boyle's Law and Cha and solve the following problems: a. Given an initial pressure of 67.5mmHg and 500ML, what is the final pressure in a 125mL container? b. Given 3.5L at 295K of a gas, what is the final volume when heated to 310K? es s Law (using equations) c. Verify your answers by indicating proportional or inversely proportional changes in factors.
2. Summarize what Boyle's Law and Cha and solve the following problems: a. Given an initial pressure of 67.5mmHg and 500ML, what is the final pressure in a 125mL container? b. Given 3.5L at 295K of a gas, what is the final volume when heated to 310K? es s Law (using equations) c. Verify your answers by indicating proportional or inversely proportional changes in factors.
Chemistry
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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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![**Boyle's Law and Charles's Law Problems**
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**Summary and Problem Solving Exercises**
**2. Summarize Boyle’s Law and Charles’s Law (using equations) and solve the following problems:**
**a.** Given an initial pressure of 67.5 mmHg and 500 mL, what is the final pressure in a 125 mL container?
**b.** Given 3.5 L at 295 K of a gas, what is the final volume when heated to 310 K?
**c.** Verify your answers by indicating proportional or inversely proportional changes in factors.
---
**Detailed Explanation:**
1. **Boyle’s Law** states that the pressure of a given mass of gas is inversely proportional to its volume at a constant temperature. Mathematically, it is expressed as:
\[ P_1V_1 = P_2V_2 \]
Where \( P_1 \) and \( V_1 \) are the initial pressure and volume, and \( P_2 \) and \( V_2 \) are the final pressure and volume, respectively.
2. **Charles’s Law** states that the volume of a gas is directly proportional to its temperature (in Kelvin) at constant pressure. Mathematically, it is expressed as:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Where \( V_1 \) and \( T_1 \) are the initial volume and temperature, and \( V_2 \) and \( T_2 \) are the final volume and temperature, respectively.
Let's apply these laws to solve the given problems.
---
**Part a:** Using Boyle’s Law to find the final pressure.
Given:
- Initial pressure (\( P_1 \)) = 67.5 mmHg
- Initial volume (\( V_1 \)) = 500 mL
- Final volume (\( V_2 \)) = 125 mL
Using the formula:
\[ P_1V_1 = P_2V_2 \]
\[ 67.5 \, \text{mmHg} \times 500 \, \text{mL} = P_2 \times 125 \, \text{mL} \]
\[ P_2 = \frac{67.5 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F03726909-0b7c-4f74-a5a1-45086bfb2ab5%2Ff1b4ad94-c6f9-4f3d-8a85-1f477746f3a5%2Ftwyep8.jpeg&w=3840&q=75)
Transcribed Image Text:**Boyle's Law and Charles's Law Problems**
---
**Summary and Problem Solving Exercises**
**2. Summarize Boyle’s Law and Charles’s Law (using equations) and solve the following problems:**
**a.** Given an initial pressure of 67.5 mmHg and 500 mL, what is the final pressure in a 125 mL container?
**b.** Given 3.5 L at 295 K of a gas, what is the final volume when heated to 310 K?
**c.** Verify your answers by indicating proportional or inversely proportional changes in factors.
---
**Detailed Explanation:**
1. **Boyle’s Law** states that the pressure of a given mass of gas is inversely proportional to its volume at a constant temperature. Mathematically, it is expressed as:
\[ P_1V_1 = P_2V_2 \]
Where \( P_1 \) and \( V_1 \) are the initial pressure and volume, and \( P_2 \) and \( V_2 \) are the final pressure and volume, respectively.
2. **Charles’s Law** states that the volume of a gas is directly proportional to its temperature (in Kelvin) at constant pressure. Mathematically, it is expressed as:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Where \( V_1 \) and \( T_1 \) are the initial volume and temperature, and \( V_2 \) and \( T_2 \) are the final volume and temperature, respectively.
Let's apply these laws to solve the given problems.
---
**Part a:** Using Boyle’s Law to find the final pressure.
Given:
- Initial pressure (\( P_1 \)) = 67.5 mmHg
- Initial volume (\( V_1 \)) = 500 mL
- Final volume (\( V_2 \)) = 125 mL
Using the formula:
\[ P_1V_1 = P_2V_2 \]
\[ 67.5 \, \text{mmHg} \times 500 \, \text{mL} = P_2 \times 125 \, \text{mL} \]
\[ P_2 = \frac{67.5 \
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