General Chemistry 1: Gases - Daltons Law of Partial Pressures Collecting Gas over Water

What Is This?

Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of gases is the sum of the partial pressures of each individual gas. Collecting Gas over Water involves measuring the volume of a gas collected over water and correcting for the water vapor pressure. This topic appears in exams to test your understanding of gas laws and your ability to apply them to practical scenarios.

Why It Matters

This topic is frequently tested in chemistry exams, particularly in high school and undergraduate levels. It typically carries moderate marks (5-10 points) and tests your analytical and problem-solving skills. Understanding this topic is crucial for careers in chemistry, environmental science, and engineering.

Core Concepts

1. Dalton's Law of Partial Pressures: The total pressure of a gas mixture is the sum of the partial pressures of each gas.
2. Partial Pressure: The pressure a gas would exert if it alone occupied the volume of the mixture at the same temperature.
3. Vapor Pressure of Water: The pressure exerted by water vapor at a given temperature, which must be subtracted from the total pressure when collecting gas over water.
4. Ideal Gas Law: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
5. Correction for Water Vapor: The measured pressure must be adjusted for the vapor pressure of water to find the true pressure of the collected gas.

Prerequisites

1. Basic Understanding of Pressure: Know what pressure is and how it is measured.
2. Ideal Gas Law: Be familiar with the formula PV = nRT and its components.
3. Temperature Conversions: Know how to convert between Celsius and Kelvin.

The Rule-Book (How It Works)

Primary Rule

Dalton's Law of Partial Pressures: P_total = P_1 + P_2 + P_3 + ... + P_n

Sub-rules and Edge Cases

1. Partial Pressure Calculation: P_i = (n_i / n_total) * P_total
2. Vapor Pressure Correction: P_dry = P_measured - P_water_vapor
3. Ideal Gas Law Application: Use PV = nRT to find the number of moles or volume of the gas.

Visual Pattern

Imagine a container with different gases. Each gas contributes to the total pressure like layers in a cake. The total height (pressure) is the sum of the heights (partial pressures) of each layer.

Exam / Job / Audit Weighting

• Frequency: Moderate
• Difficulty Rating: Intermediate
• Question Type: Multiple Choice, Calculation-based, Short Answer

Difficulty Level

Intermediate

Must-Know Rules, Formulas, Standards, or Principles

1. Dalton's Law: P_total = P_1 + P_2 + P_3 + ... + P_n
2. Vapor Pressure Correction: P_dry = P_measured - P_water_vapor
3. Ideal Gas Law: PV = nRT

Worked Examples (Step-by-Step)

Easy

Question: A mixture of gases contains 2.0 moles of nitrogen and 1.0 mole of oxygen. The total pressure is 3.0 atm. What is the partial pressure of nitrogen?

Step-by-Step:
1. Total moles = 2.0 (N_2) + 1.0 (O_2) = 3.0 moles
2. Partial pressure of nitrogen = (2.0 / 3.0) * 3.0 atm = 2.0 atm

Answer: 2.0 atm

Medium

Question: A gas is collected over water at 25°C and 750 mmHg. The vapor pressure of water at 25°C is 23.8 mmHg. What is the dry pressure of the gas?

Step-by-Step:
1. P_measured = 750 mmHg
2. P_water_vapor = 23.8 mmHg
3. P_dry = 750 mmHg - 23.8 mmHg = 726.2 mmHg

Answer: 726.2 mmHg

Hard

Question: A mixture of gases contains 3.0 moles of CO_2, 2.0 moles of O_2, and 1.0 mole of N_2. The total pressure is 5.0 atm. What is the partial pressure of O_2?

Step-by-Step:
1. Total moles = 3.0 (CO_2) + 2.0 (O_2) + 1.0 (N_2) = 6.0 moles
2. Partial pressure of O_2 = (2.0 / 6.0) * 5.0 atm = 1.67 atm

Answer: 1.67 atm

Common Exam Traps & Mistakes

1. Forgetting Vapor Pressure Correction: Not subtracting the vapor pressure of water.
2. Wrong Answer: Using the measured pressure directly.

3. Correct Approach: Always subtract the vapor pressure of water.

4. Incorrect Temperature Conversion: Not converting Celsius to Kelvin.

5. Wrong Answer: Using Celsius in the Ideal Gas Law.

6. Correct Approach: Convert Celsius to Kelvin (K = °C + 273.15).

7. Miscalculating Total Moles: Incorrectly summing the moles of gases.

8. Wrong Answer: Incorrect partial pressure due to wrong total moles.

9. Correct Approach: Double-check the sum of moles.

10. Ignoring Units: Not converting units correctly.

11. Wrong Answer: Incorrect pressure due to unit mismatch.
12. Correct Approach: Ensure all units are consistent.

Shortcut Strategies & Exam Hacks

• Memory Aid: Remember "P_total = Sum of P_i" for Dalton's Law.
• Elimination Strategy: If a choice doesn't account for vapor pressure, eliminate it.
• Pattern Recognition: Look for questions involving gas mixtures and water vapor.
• Formula Shortcut: Use PV = nRT for quick volume or mole calculations.

Question-Type Taxonomy

1. Multiple Choice: Common in high school and undergraduate exams.
2. Example: What is the partial pressure of gas X in a mixture?

3. Favored By: SAT, AP Chemistry

4. Calculation-based: Requires numerical answers.

5. Example: Calculate the dry pressure of a gas collected over water.

6. Favored By: University-level chemistry exams

7. Short Answer: Explain a concept or process.

8. Example: Describe how to correct for water vapor pressure.
9. Favored By: Comprehensive exams, lab reports

Practice Set (MCQs)

Question 1

Question: A gas mixture contains 1.0 mole of H_2 and 2.0 moles of N_2. The total pressure is 4.0 atm. What is the partial pressure of H_2? Options: A) 1.0 atm B) 2.0 atm C) 3.0 atm D) 4.0 atm

Correct Answer: A) 1.0 atm Explanation: Total moles = 1.0 (H_2) + 2.0 (N_2) = 3.0 moles. Partial pressure of H_2 = (1.0 / 3.0) * 4.0 atm = 1.33 atm. Why the Distractors Are Tempting: B) and C) are incorrect calculations; D) is the total pressure, not partial.

Question 2

Question: A gas is collected over water at 20°C and 760 mmHg. The vapor pressure of water at 20°C is 17.5 mmHg. What is the dry pressure of the gas? Options: A) 742.5 mmHg B) 760 mmHg C) 777.5 mmHg D) 780 mmHg

Correct Answer: A) 742.5 mmHg Explanation: P_dry = 760 mmHg - 17.5 mmHg = 742.5 mmHg. Why the Distractors Are Tempting: B) is the measured pressure; C) and D) are incorrect calculations.

Question 3

Question: A mixture of gases contains 2.0 moles of CO_2 and 3.0 moles of O_2. The total pressure is 6.0 atm. What is the partial pressure of CO_2? Options: A) 2.0 atm B) 3.0 atm C) 4.0 atm D) 6.0 atm

Correct Answer: A) 2.0 atm Explanation: Total moles = 2.0 (CO_2) + 3.0 (O_2) = 5.0 moles. Partial pressure of CO_2 = (2.0 / 5.0) * 6.0 atm = 2.4 atm. Why the Distractors Are Tempting: B) and C) are incorrect calculations; D) is the total pressure.

Question 4

Question: A gas is collected over water at 30°C and 750 mmHg. The vapor pressure of water at 30°C is 31.8 mmHg. What is the dry pressure of the gas? Options: A) 718.2 mmHg B) 750 mmHg C) 781.8 mmHg D) 800 mmHg

Correct Answer: A) 718.2 mmHg Explanation: P_dry = 750 mmHg - 31.8 mmHg = 718.2 mmHg. Why the Distractors Are Tempting: B) is the measured pressure; C) and D) are incorrect calculations.

Question 5

Question: A mixture of gases contains 1.0 mole of H_2, 2.0 moles of N_2, and 3.0 moles of O_2. The total pressure is 7.0 atm. What is the partial pressure of N_2? Options: A) 1.0 atm B) 2.0 atm C) 3.0 atm D) 4.0 atm

Correct Answer: B) 2.0 atm Explanation: Total moles = 1.0 (H_2) + 2.0 (N_2) + 3.0 (O_2) = 6.0 moles. Partial pressure of N_2 = (2.0 / 6.0) * 7.0 atm = 2.33 atm. Why the Distractors Are Tempting: A) and C) are incorrect calculations; D) is the total pressure.

30-Second Cheat Sheet

• Dalton's Law: P_total = Sum of P_i
• Partial Pressure: P_i = (n_i / n_total) * P_total
• Vapor Pressure Correction: P_dry = P_measured - P_water_vapor
• Ideal Gas Law: PV = nRT
• Temperature Conversion: K = °C + 273.15

Learning Path

1. Beginner Foundation: Understand basic gas laws and pressure concepts.
2. Core Rules: Learn Dalton's Law and vapor pressure correction.
3. Practice: Solve problems involving gas mixtures and water vapor.
4. Timed Drills: Practice under exam conditions.
5. Mock Tests: Take full-length practice exams.

Related Topics

1. Ideal Gas Law: Often appears alongside Dalton's Law in gas mixture problems.
2. Gas Stoichiometry: Involves calculating moles and volumes of gases in reactions.
3. Gas Collection Methods: Understanding different methods of gas collection and their corrections.