Boyle's Law Worksheet Answer Key: Quick Solutions Inside!
Table of Contents :
Boyle's Law is a fundamental principle in the field of gas physics that describes the relationship between the pressure and volume of a gas. The law states that, for a given mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. In simpler terms, as the volume of a gas increases, its pressure decreases, and vice versa. In this article, we will provide a comprehensive overview of Boyle's Law, present an answer key to common worksheet problems, and offer some quick solutions for easy understanding.
Understanding Boyle's Law 📚
What is Boyle's Law? 🤔
Boyle's Law can be mathematically expressed with the equation:
[ P_1 \times V_1 = P_2 \times V_2 ]
Where:
- ( P_1 ) = Initial Pressure
- ( V_1 ) = Initial Volume
- ( P_2 ) = Final Pressure
- ( V_2 ) = Final Volume
Key Concepts 🗝️
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Inverse Relationship: As the volume (V) of a gas increases, the pressure (P) decreases. This means that if one quantity goes up, the other must go down to keep the equation balanced.
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Temperature and Quantity of Gas: Boyle's Law holds true only if the temperature and the number of gas molecules remain constant.
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Real-World Applications: Boyle's Law is vital in various fields, including meteorology, engineering, and medicine, where understanding the behavior of gases under pressure is crucial.
Sample Worksheet Problems and Solutions 🔍
To better understand Boyle's Law, let’s look at some typical worksheet problems along with their answers.
Problem 1
A gas occupies a volume of 4.0 L at a pressure of 2.0 atm. What will be the volume of the gas when the pressure is increased to 4.0 atm?
Solution
Using Boyle's Law:
[ P_1 \times V_1 = P_2 \times V_2 ] [ 2.0 , \text{atm} \times 4.0 , \text{L} = 4.0 , \text{atm} \times V_2 ] [ 8.0 = 4.0 \times V_2 ] [ V_2 = \frac{8.0}{4.0} = 2.0 , \text{L} ]
Problem 2
If a gas has a volume of 10.0 L at a pressure of 1.5 atm, what will be the new pressure if the volume is reduced to 5.0 L?
Solution
Using the same equation:
[ P_1 \times V_1 = P_2 \times V_2 ] [ 1.5 , \text{atm} \times 10.0 , \text{L} = P_2 \times 5.0 , \text{L} ] [ 15.0 = 5.0 \times P_2 ] [ P_2 = \frac{15.0}{5.0} = 3.0 , \text{atm} ]
Problem 3
A gas occupies a volume of 20.0 L at a pressure of 1.0 atm. What will be the volume when the pressure is decreased to 0.5 atm?
Solution
Using Boyle's Law:
[ P_1 \times V_1 = P_2 \times V_2 ] [ 1.0 , \text{atm} \times 20.0 , \text{L} = 0.5 , \text{atm} \times V_2 ] [ 20.0 = 0.5 \times V_2 ] [ V_2 = \frac{20.0}{0.5} = 40.0 , \text{L} ]
Problem 4
A 15.0 L balloon is at a pressure of 0.7 atm. If the balloon rises and the pressure drops to 0.3 atm, what is the new volume?
Solution
Again, applying Boyle’s Law:
[ P_1 \times V_1 = P_2 \times V_2 ] [ 0.7 , \text{atm} \times 15.0 , \text{L} = 0.3 , \text{atm} \times V_2 ] [ 10.5 = 0.3 \times V_2 ] [ V_2 = \frac{10.5}{0.3} = 35.0 , \text{L} ]
Quick Reference Table for Boyle's Law Solutions 📊
Below is a quick reference table summarizing the problems and solutions discussed:
<table> <tr> <th>Problem</th> <th>Initial Volume (L)</th> <th>Initial Pressure (atm)</th> <th>Final Volume (L)</th> <th>Final Pressure (atm)</th> </tr> <tr> <td>1</td> <td>4.0</td> <td>2.0</td> <td>2.0</td> <td>4.0</td> </tr> <tr> <td>2</td> <td>10.0</td> <td>1.5</td> <td>5.0</td> <td>3.0</td> </tr> <tr> <td>3</td> <td>20.0</td> <td>1.0</td> <td>40.0</td> <td>0.5</td> </tr> <tr> <td>4</td> <td>15.0</td> <td>0.7</td> <td>35.0</td> <td>0.3</td> </tr> </table>
Important Notes for Students 📌
- Always ensure temperature remains constant when applying Boyle's Law. If the temperature changes, the equation no longer applies.
- Practice converting units if necessary, as pressure can be given in different units such as mmHg, Torr, or kPa.
- Remember to rearrange the formula if you need to solve for a different variable than volume or pressure.
In summary, Boyle's Law provides valuable insights into the behavior of gases under varying conditions. Understanding this principle is crucial for applications in both theoretical and practical scenarios. With these sample problems and quick solutions, students can enhance their grasp of Boyle's Law and perform well on their related assessments!