Ideal Gas Law Worksheet Answer Key: Solutions Explained
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The Ideal Gas Law is a fundamental principle in physical chemistry that describes the behavior of gases. It relates pressure, volume, temperature, and the number of moles of a gas in a single equation, PV = nRT. This equation is essential for students and professionals alike, providing the necessary tools to solve various problems related to gases.
In this article, we will delve into the Ideal Gas Law, its applications, and provide an answer key for a sample worksheet. The solutions will be explained in detail to help learners grasp the concepts better. 🌟
Understanding the Ideal Gas Law
The Formula
The Ideal Gas Law is represented by the equation:
[ PV = nRT ]
Where:
- P = Pressure (in atmospheres or pascals)
- V = Volume (in liters or cubic meters)
- n = Number of moles of the gas
- R = Ideal gas constant (0.0821 L·atm/(K·mol) or 8.314 J/(K·mol))
- T = Temperature (in Kelvin)
Key Concepts
Before diving into the worksheet and solutions, let’s clarify some key concepts:
- Pressure (P): This is the force exerted by the gas particles colliding with the walls of their container.
- Volume (V): The space that the gas occupies. It can change with pressure and temperature.
- Temperature (T): A measure of the average kinetic energy of gas particles, always measured in Kelvin for gas law calculations.
- Number of Moles (n): This indicates the quantity of gas present.
Important Notes
Remember that the Ideal Gas Law applies only to ideal gases, which do not exist in reality. Real gases behave ideally under conditions of high temperature and low pressure. 🧪
Sample Worksheet and Answer Key
Let's consider a sample worksheet containing various problems based on the Ideal Gas Law. Below is a simplified version of what such a worksheet might include, along with detailed solutions.
Sample Problems
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Problem 1: If 2 moles of an ideal gas occupy a volume of 10 liters at a temperature of 300 K, what is the pressure of the gas?
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Problem 2: A gas has a pressure of 1.5 atm and occupies a volume of 12 liters at a temperature of 250 K. How many moles of gas are present?
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Problem 3: Calculate the temperature of 3 moles of gas at a pressure of 2.0 atm occupying a volume of 15 liters.
Solutions Explained
Solution to Problem 1
Given:
- n = 2 moles
- V = 10 L
- T = 300 K
Using the Ideal Gas Law:
[ PV = nRT ] [ P = \frac{nRT}{V} ]
Substituting the values (using R = 0.0821 L·atm/(K·mol)):
[ P = \frac{(2 \text{ moles})(0.0821 \text{ L·atm/(K·mol)})(300 K)}{10 L} ] [ P = \frac{49.26}{10} = 4.926 \text{ atm} ]
Answer: The pressure of the gas is approximately 4.93 atm. 🎉
Solution to Problem 2
Given:
- P = 1.5 atm
- V = 12 L
- T = 250 K
Using the Ideal Gas Law:
[ PV = nRT ]
Rearranging for n:
[ n = \frac{PV}{RT} ]
Substituting the values:
[ n = \frac{(1.5 \text{ atm})(12 L)}{(0.0821 \text{ L·atm/(K·mol)})(250 K)} ] [ n = \frac{18}{20.525} \approx 0.875 \text{ moles} ]
Answer: There are approximately 0.88 moles of gas present. 🧮
Solution to Problem 3
Given:
- n = 3 moles
- P = 2.0 atm
- V = 15 L
Using the Ideal Gas Law:
[ PV = nRT ]
Rearranging for T:
[ T = \frac{PV}{nR} ]
Substituting the values:
[ T = \frac{(2.0 \text{ atm})(15 L)}{(3 \text{ moles})(0.0821 \text{ L·atm/(K·mol)})} ] [ T = \frac{30}{0.2463} \approx 121.82 K ]
Answer: The temperature is approximately 121.82 K. 🌡️
Summary Table of Solutions
<table> <tr> <th>Problem</th> <th>Calculated Value</th> </tr> <tr> <td>Problem 1 Pressure</td> <td>4.93 atm</td> </tr> <tr> <td>Problem 2 Moles</td> <td>0.88 moles</td> </tr> <tr> <td>Problem 3 Temperature</td> <td>121.82 K</td> </tr> </table>
Additional Practice
To further strengthen your understanding of the Ideal Gas Law, consider creating your own problems. Adjust the variables to see how changes in pressure, volume, temperature, or the number of moles can affect the outcomes. This practice will help solidify your grasp of the Ideal Gas Law and its applications. ✍️
Mastering the Ideal Gas Law is essential for students of chemistry and physics. By understanding this fundamental concept and practicing various problems, you can enhance your skills and confidence in working with gases. 🌬️