Dalton's Law Of Partial Pressure Worksheet Answers Explained
Table of Contents :
Dalton's Law of Partial Pressure is a fundamental principle in chemistry that helps us understand the behavior of gases in a mixture. This law states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas in the mixture. Understanding this concept is essential for students studying chemistry, and often requires the use of worksheets to apply the principles practically. In this article, we will delve into the explanations of answers found in typical Dalton's Law of Partial Pressure worksheets, providing clarity and insight into how to solve these problems effectively.
What is Dalton's Law of Partial Pressure?
Dalton's Law was formulated by John Dalton in the early 19th century. The law is mathematically expressed as:
P_total = P₁ + P₂ + P₃ + ... + Pn
where:
- P_total is the total pressure of the gas mixture.
- P₁, P₂, P₃, ... , Pn are the partial pressures of individual gases in the mixture.
This law applies under the assumption that the gases in the mixture do not react chemically and are ideal gases.
Understanding Partial Pressure
Partial pressure refers to the pressure that a particular gas would exert if it occupied the entire volume by itself at the same temperature. For instance, if you have a container with nitrogen and oxygen gases, the partial pressure of nitrogen is the pressure it would exert alone in that container.
Worksheet Problems and Solutions
To clarify the concept of Dalton's Law of Partial Pressure, let’s consider some common types of problems you might encounter in a worksheet.
Problem 1: Calculating Total Pressure
Suppose you have a container that contains 3 gases:
- Gas A: 2 atm
- Gas B: 3 atm
- Gas C: 1 atm
Question: What is the total pressure in the container?
Solution:
Using Dalton's Law, we simply add the partial pressures together:
[ P_{total} = P_A + P_B + P_C = 2 , \text{atm} + 3 , \text{atm} + 1 , \text{atm} = 6 , \text{atm} ]
Thus, the total pressure is 6 atm.
Problem 2: Finding a Missing Partial Pressure
Imagine you know the total pressure in a mixture is 10 atm, and you have the partial pressures for two gases:
- Gas A: 4 atm
- Gas B: ? (unknown)
- Gas C: 2 atm
Question: What is the partial pressure of Gas B?
Solution:
We rearrange the formula to solve for the unknown:
[ P_B = P_{total} - (P_A + P_C) ] [ P_B = 10 , \text{atm} - (4 , \text{atm} + 2 , \text{atm}) = 10 , \text{atm} - 6 , \text{atm} = 4 , \text{atm} ]
So, the partial pressure of Gas B is 4 atm.
Problem 3: Mixing Gases
If you mix 4 moles of oxygen (O₂) and 6 moles of nitrogen (N₂) in a container at a certain temperature, what would be the partial pressures of each gas if the total pressure is 20 atm?
Solution:
First, determine the mole fraction of each gas:
[ X_{O2} = \frac{n_{O2}}{n_{total}} = \frac{4}{4+6} = 0.4 ] [ X_{N2} = \frac{n_{N2}}{n_{total}} = \frac{6}{4+6} = 0.6 ]
Next, we can find the partial pressures:
[ P_{O2} = X_{O2} \cdot P_{total} = 0.4 \cdot 20 , \text{atm} = 8 , \text{atm} ] [ P_{N2} = X_{N2} \cdot P_{total} = 0.6 \cdot 20 , \text{atm} = 12 , \text{atm} ]
Thus, the partial pressures are 8 atm for O₂ and 12 atm for N₂.
Key Takeaways
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Understanding Mole Fractions: The mole fraction of a gas is essential for calculating partial pressures when dealing with mixtures.
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Ideal Gas Assumption: Dalton's Law works best under conditions where gases behave ideally, meaning they do not interact or react chemically with each other.
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Practical Applications: This law has practical applications in areas such as atmospheric chemistry, respiratory physiology, and various industrial processes.
Important Notes
"Always remember to ensure the units are consistent throughout your calculations, especially when dealing with pressures."
Summary Table
Here’s a summary of the formulas related to Dalton's Law for quick reference:
<table> <tr> <th>Concept</th> <th>Formula</th> <th>Description</th> </tr> <tr> <td>Total Pressure</td> <td>P_total = P₁ + P₂ + ... + Pn</td> <td>Total pressure is the sum of partial pressures of gases.</td> </tr> <tr> <td>Mole Fraction</td> <td>X_gas = n_gas / n_total</td> <td>Proportion of moles of a specific gas to the total moles in the mixture.</td> </tr> <tr> <td>Partial Pressure</td> <td>P_gas = X_gas * P_total</td> <td>Calculating the pressure exerted by a specific gas in a mixture.</td> </tr> </table>
By understanding and applying Dalton's Law of Partial Pressure, students can confidently tackle a range of problems related to gas mixtures. Practice with worksheets enhances learning and reinforces this critical concept in chemistry. Happy studying! 🎓✨