Mixed Gas Laws Worksheet Answer Key: Complete Guide
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Understanding mixed gas laws can be complex, but with the right resources, it can become much easier to grasp. In this complete guide, we will explore mixed gas laws and provide a comprehensive answer key to help you with your understanding. This guide aims to be a useful tool for both students and educators alike, as it offers insights into the calculations and applications of the various gas laws.
What are Mixed Gas Laws?
Mixed gas laws refer to the combination of individual gas laws that describe how gases behave under different conditions. The primary gas laws include:
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Boyle’s Law: This law states that the pressure of a gas is inversely proportional to its volume when temperature is held constant. Mathematically, this is represented as: [ P_1V_1 = P_2V_2 ]
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Charles’s Law: This law states that the volume of a gas is directly proportional to its absolute temperature when pressure is held constant: [ \frac{V_1}{T_1} = \frac{V_2}{T_2} ]
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Gay-Lussac’s Law: This law states that the pressure of a gas is directly proportional to its absolute temperature when volume is held constant: [ \frac{P_1}{T_1} = \frac{P_2}{T_2} ]
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Ideal Gas Law: This is a combination of all the individual laws mentioned above, represented as: [ PV = nRT ] Where:
- ( P ) = pressure
- ( V ) = volume
- ( n ) = number of moles
- ( R ) = ideal gas constant
- ( T ) = temperature in Kelvin
How to Solve Mixed Gas Law Problems
When working with mixed gas laws, it is essential to identify which gas law applies to the problem at hand. Here’s a general approach to solving these problems:
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Read the Problem Carefully: Identify what is given and what needs to be calculated.
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Choose the Correct Gas Law: Based on the information provided, decide whether to use Boyle’s Law, Charles’s Law, Gay-Lussac’s Law, or the Ideal Gas Law.
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Convert Units if Necessary: Ensure that all your units are compatible, particularly temperature, which must be in Kelvin.
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Insert Values into the Formula: Substitute known values into the chosen gas law equation.
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Solve for the Unknown: Rearrange the formula to solve for the desired variable and calculate the answer.
Example Problems
Let’s explore a few example problems, along with their solutions, that utilize mixed gas laws:
Example 1: Boyle's Law
Problem: A gas occupies a volume of 4.0 L at a pressure of 2.0 atm. What will be the volume of the gas if the pressure is increased to 4.0 atm?
Solution: Using Boyle's Law: [ P_1V_1 = P_2V_2 ] Substituting the values: [ (2.0 , \text{atm})(4.0 , \text{L}) = (4.0 , \text{atm})(V_2) ] Calculating gives: [ 8.0 = 4.0V_2 \implies V_2 = \frac{8.0}{4.0} = 2.0 , \text{L} ]
Example 2: Charles's Law
Problem: If 3.0 L of gas is at 300 K, what will be the new volume at 600 K, assuming the pressure remains constant?
Solution: Using Charles's Law: [ \frac{V_1}{T_1} = \frac{V_2}{T_2} ] Substituting values: [ \frac{3.0 , \text{L}}{300 , \text{K}} = \frac{V_2}{600 , \text{K}} ] Solving gives: [ V_2 = \frac{3.0 \times 600}{300} = 6.0 , \text{L} ]
Example 3: Ideal Gas Law
Problem: What is the pressure exerted by 2.0 moles of gas occupying a volume of 10.0 L at a temperature of 300 K? (Use R = 0.0821 L·atm/(K·mol))
Solution: Using the Ideal Gas Law: [ PV = nRT ] Rearranging for pressure ( P ): [ P = \frac{nRT}{V} ] Substituting the values: [ P = \frac{(2.0 , \text{mol})(0.0821 , \text{L·atm/(K·mol)})(300 , \text{K})}{10.0 , \text{L}} = 4.926 , \text{atm} \approx 4.93 , \text{atm} ]
Key Takeaways
- Understand Individual Laws: Knowing each gas law and its specific application is crucial for solving mixed gas problems.
- Practice Makes Perfect: The more problems you solve, the more familiar you will become with the laws and calculations.
- Unit Consistency: Always ensure that you are using consistent units, especially for temperature.
Answer Key Table
Here's a summary table for quick reference of the laws and their equations:
<table> <tr> <th>Gas Law</th> <th>Equation</th> </tr> <tr> <td>Boyle’s Law</td> <td>P<sub>1</sub>V<sub>1</sub> = P<sub>2</sub>V<sub>2</sub></td> </tr> <tr> <td>Charles’s Law</td> <td>V<sub>1</sub>/T<sub>1</sub> = V<sub>2</sub>/T<sub>2</sub></td> </tr> <tr> <td>Gay-Lussac’s Law</td> <td>P<sub>1</sub>/T<sub>1</sub> = P<sub>2</sub>/T<sub>2</sub></td> </tr> <tr> <td>Ideal Gas Law</td> <td>PV = nRT</td> </tr> </table>
Through this guide, we hope you have gained a deeper understanding of mixed gas laws and how to apply them effectively. Whether for academic purposes or practical applications, mastering these concepts can significantly enhance your knowledge of chemistry.