Dalton's Law Of Partial Pressure Worksheet Answers

Dalton's Law of Partial Pressure Worksheet Answers: A Comprehensive Guide

Dalton's Law of Partial Pressure is a fundamental concept in chemistry, particularly crucial for understanding gas behavior in mixtures. This law states that the total pressure exerted by a mixture of non-reactive gases is equal to the sum of the partial pressures of individual gases. Mastering this concept is essential for success in chemistry, and worksheets provide a valuable tool for practicing and solidifying your understanding. This comprehensive guide will delve into Dalton's Law, provide example problems, and offer solutions to common worksheet questions.

Understanding Dalton's Law of Partial Pressure

Before tackling worksheets, let's reinforce our understanding of the core principle. Dalton's Law states:

P_Total = P₁ + P₂ + P₃ + ... + P_n

Where:

• P_Total represents the total pressure of the gas mixture.
• P₁, P₂, P₃, ... P_n represent the partial pressures of individual gases (1, 2, 3...n) within the mixture.

Key Considerations:

• Non-reactive gases: Dalton's Law applies to mixtures of gases that do not chemically react with each other. If a reaction occurs, the resulting pressure will be different.
• Ideal gas behavior: The law assumes ideal gas behavior, meaning the gases follow the ideal gas law (PV=nRT). At high pressures or low temperatures, deviations from ideal behavior may occur.
• Partial pressure: The partial pressure of a gas is the pressure that gas would exert if it occupied the entire volume alone at the same temperature.

Types of Problems Encountered in Worksheets

Dalton's Law worksheets typically involve various problem types, including:

1. Calculating Total Pressure:

This is the most straightforward application of Dalton's Law. You are given the partial pressures of individual gases, and you need to calculate the total pressure.

Example: A container holds three gases: oxygen (O₂) at 2 atm, nitrogen (N₂) at 3 atm, and carbon dioxide (CO₂) at 1 atm. What is the total pressure inside the container?

Solution: P_Total = P_O2 + P_N2 + P_CO2 = 2 atm + 3 atm + 1 atm = 6 atm

2. Calculating Partial Pressure:

These problems involve finding the partial pressure of one gas within a mixture when you know the total pressure and the partial pressures of other gases.

Example: A mixture of gases contains helium (He) at 1.5 atm, neon (Ne) at 2 atm, and an unknown gas (X). The total pressure is 5 atm. What is the partial pressure of gas X?

Solution: P_X = P_Total - P_He - P_Ne = 5 atm - 1.5 atm - 2 atm = 1.5 atm

3. Using the Ideal Gas Law with Dalton's Law:

These problems often involve using the ideal gas law (PV = nRT) in conjunction with Dalton's Law. You might be given information about the number of moles of each gas, volume, temperature, and need to calculate either partial pressures or total pressure.

Example: A 5-liter container at 25°C contains 0.2 moles of nitrogen and 0.3 moles of oxygen. Calculate the partial pressure of each gas and the total pressure. (R = 0.0821 L·atm/mol·K)

Solution:

First, convert the temperature to Kelvin: 25°C + 273.15 = 298.15 K

Then, use the ideal gas law to calculate the partial pressure of each gas:

• Nitrogen (N₂): P_N2 = (n_N2 * R * T) / V = (0.2 mol * 0.0821 L·atm/mol·K * 298.15 K) / 5 L ≈ 0.98 atm
• Oxygen (O₂): P_O2 = (n_O2 * R * T) / V = (0.3 mol * 0.0821 L·atm/mol·K * 298.15 K) / 5 L ≈ 1.47 atm

Finally, use Dalton's Law to find the total pressure:

• Total Pressure: P_Total = P_N2 + P_O2 ≈ 0.98 atm + 1.47 atm ≈ 2.45 atm

4. Mole Fraction and Partial Pressure:

The mole fraction (χ) of a gas is the ratio of the number of moles of that gas to the total number of moles in the mixture. The partial pressure of a gas is also related to its mole fraction:

P_i = χ_i * P_Total

Where:

• P_i is the partial pressure of gas i.
• χ_i is the mole fraction of gas i.
• P_Total is the total pressure.

Example: A gas mixture contains 2 moles of nitrogen and 3 moles of oxygen. The total pressure is 5 atm. What is the partial pressure of nitrogen?

Solution:

First, calculate the mole fraction of nitrogen:

χ_N2 = moles of N₂ / total moles = 2 mol / (2 mol + 3 mol) = 0.4

Then, calculate the partial pressure of nitrogen:

P_N2 = χ_N2 * P_Total = 0.4 * 5 atm = 2 atm

Advanced Worksheet Problems & Solutions

More complex worksheets might incorporate these additional elements:

1. Gas Collection over Water:

When gases are collected over water, the collected gas is saturated with water vapor. Therefore, the total pressure includes the partial pressure of water vapor at that temperature. You'll need to subtract the water vapor pressure to find the partial pressure of the collected gas.

Example: A gas is collected over water at 25°C. The total pressure is 760 mmHg. The vapor pressure of water at 25°C is 23.8 mmHg. What is the partial pressure of the collected gas?

Solution:

P_gas = P_Total - P_{water vapor} = 760 mmHg - 23.8 mmHg = 736.2 mmHg

2. Stoichiometry and Dalton's Law:

Some problems combine stoichiometry (the study of the quantitative relationships between reactants and products) with Dalton's Law. You might need to use balanced chemical equations to calculate the moles of gas produced and then apply Dalton's Law.

Example: 2 moles of hydrogen react completely with 1 mole of oxygen to produce water vapor. The reaction occurs in a 10 L container at 298 K. Calculate the total pressure after the reaction is complete.

Solution: The balanced equation is 2H₂ + O₂ → 2H₂O. All the reactants are consumed, and only water vapor remains. The number of moles of water vapor produced is 2 moles.

Using the ideal gas law: P_Total = (n * R * T) / V = (2 mol * 0.0821 L·atm/mol·K * 298 K) / 10 L ≈ 4.89 atm

3. Real Gases and Deviations from Ideality:

Advanced problems may involve exploring the limitations of Dalton's Law when dealing with real gases that deviate significantly from ideal behavior. This requires using more complex equations of state (like the van der Waals equation) to account for intermolecular forces and gas volume. This type of problem typically falls outside the scope of introductory chemistry courses.

Tips for Success with Dalton's Law Worksheets

• Understand the concepts: Thoroughly grasp Dalton's Law and its underlying principles before attempting any worksheets.
• Review the ideal gas law: Familiarity with the ideal gas law is crucial for solving many Dalton's Law problems.
• Use units consistently: Always ensure consistent units throughout your calculations to avoid errors.
• Practice regularly: The key to mastering Dalton's Law is consistent practice. Work through numerous problems to build confidence and proficiency.
• Seek help when needed: Don't hesitate to ask for help from your teacher, classmates, or tutor if you encounter difficulties.
• Break down complex problems: If you encounter a multi-step problem, break it down into smaller, manageable parts.

By following these guidelines and diligently working through practice problems, you will build a solid understanding of Dalton's Law of Partial Pressure and excel in your chemistry studies. Remember that consistent practice is the key to mastering this essential chemical concept. The more problems you solve, the more comfortable and confident you will become in applying Dalton's Law to diverse situations. Good luck!