## Introduction

Welcome to our comprehensive guide on Boyle's Law and Charles Law! In this article, we will provide you with a complete answer key and work for the Boyle's Law and Charles Law worksheet. These two fundamental laws of gas behavior are essential for understanding the relationship between pressure, volume, and temperature. By solving the worksheet problems step by step, you will gain a solid grasp of these concepts and be well-prepared for any upcoming exams or assignments.

### Understanding Boyle's Law

Boyle's Law, named after the renowned physicist Robert Boyle, states that the pressure of a gas is inversely proportional to its volume, given that the temperature remains constant. Mathematically, it can be expressed as:

P1 x V1 = P2 x V2

Where P1 and V1 represent the initial pressure and volume, and P2 and V2 represent the final pressure and volume, respectively. By using this equation, we can solve various gas-related problems, such as calculating pressure or volume changes when one of these variables is known.

### Applying Boyle's Law

Let's dive into the worksheet problems to apply Boyle's Law. Remember to work through each step and show your calculations for a comprehensive understanding of the concepts. Here are some sample problems:

### Problem 1:

A gas sample has an initial volume of 2.0 L and a pressure of 3.0 atm. If the volume is reduced to 1.5 L, what will be the new pressure?

Solution:

P1 x V1 = P2 x V2

(3.0 atm) x (2.0 L) = P2 x (1.5 L)

6.0 atm = P2 x 1.5 L

P2 = 6.0 atm / 1.5 L

P2 = 4.0 atm

The new pressure will be 4.0 atm.

### Problem 2:

A gas sample initially occupies a volume of 8.0 mL at a pressure of 2.0 atm. If the pressure is increased to 4.0 atm, what will be the new volume?

Solution:

P1 x V1 = P2 x V2

(2.0 atm) x (8.0 mL) = (4.0 atm) x V2

16.0 mL = 4.0 atm x V2

V2 = 16.0 mL / 4.0 atm

V2 = 4.0 mL

The new volume will be 4.0 mL.

### Understanding Charles Law

Charles Law, named after the French physicist Jacques Charles, describes the relationship between the volume and temperature of a gas when pressure is held constant. It states that the volume of a gas is directly proportional to its temperature in Kelvin. Mathematically, it can be expressed as:

V1 / T1 = V2 / T2

Where V1 and T1 represent the initial volume and temperature, and V2 and T2 represent the final volume and temperature, respectively. By using this equation, we can solve various problems related to temperature and volume changes in gases.

### Applying Charles Law

Let's now tackle the Charles Law problems in the worksheet. Remember to convert all temperatures to Kelvin for accurate calculations. Here are a couple of sample problems:

### Problem 1:

A gas occupies a volume of 500 mL at a temperature of 25°C. If the temperature is increased to 100°C, what will be the new volume?

Solution:

V1 / T1 = V2 / T2

V2 = (V1 x T2) / T1

V2 = (500 mL x 373 K) / 298 K

V2 = 623.82 mL

The new volume will be 623.82 mL.

### Problem 2:

A gas sample has a volume of 2.0 L at a temperature of 300 K. If the temperature is decreased to 200 K, what will be the new volume?

Solution:

V1 / T1 = V2 / T2

V2 = (V1 x T2) / T1

V2 = (2.0 L x 200 K) / 300 K

V2 = 1.33 L

The new volume will be 1.33 L.

### Conclusion

By working through the Boyle's Law and Charles Law worksheet problems with the provided answers and step-by-step solutions, you have gained a solid understanding of these fundamental gas laws. Remember to practice more problems to reinforce your knowledge and apply these laws to various real-world scenarios. With your newfound expertise, you will be well-prepared to tackle any gas-related questions that come your way!