Gas Laws Worksheet #2 Answer Key

Gas Laws Worksheet #2: A Comprehensive Guide with Answers

This comprehensive guide provides detailed explanations and answers for a hypothetical Gas Laws Worksheet #2. Since I cannot access specific worksheets, this guide will cover the fundamental gas laws – Boyle's Law, Charles's Law, Gay-Lussac's Law, the Combined Gas Law, and the Ideal Gas Law – with example problems mirroring the type of questions typically found in such worksheets. This will equip you with the knowledge and skills to tackle any Gas Laws Worksheet effectively.

Understanding the Fundamental Gas Laws

Before diving into the worksheet problems, let's review the core principles governing the behavior of gases:

1. Boyle's Law: Pressure and Volume

Boyle's Law states that the pressure of a gas is inversely proportional to its volume at a constant temperature. Mathematically, this is represented as:

P₁V₁ = P₂V₂

Where:

• P₁ = Initial pressure
• V₁ = Initial volume
• P₂ = Final pressure
• V₂ = Final volume

Key takeaway: If you increase the pressure on a gas, its volume will decrease proportionally, and vice versa, provided the temperature remains constant.

2. Charles's Law: Volume and Temperature

Charles's Law states that the volume of a gas is directly proportional to its absolute temperature at a constant pressure. Expressed mathematically:

V₁/T₁ = V₂/T₂

Where:

• V₁ = Initial volume
• T₁ = Initial absolute temperature (in Kelvin)
• V₂ = Final volume
• T₂ = Final absolute temperature (in Kelvin)

Crucial Note: Always convert Celsius temperatures to Kelvin (K = °C + 273.15) before applying Charles's Law.

Key takeaway: As the temperature of a gas increases, its volume increases proportionally, and vice versa, assuming the pressure stays the same.

3. Gay-Lussac's Law: Pressure and Temperature

Gay-Lussac's Law describes the relationship between the pressure and temperature of a gas at constant volume:

P₁/T₁ = P₂/T₂

Where:

• P₁ = Initial pressure
• T₁ = Initial absolute temperature (in Kelvin)
• P₂ = Final pressure
• T₂ = Final absolute temperature (in Kelvin)

Key takeaway: Increasing the temperature of a gas at a constant volume will proportionally increase its pressure, and conversely. Remember to use Kelvin for temperature.

4. The Combined Gas Law

The Combined Gas Law merges Boyle's, Charles's, and Gay-Lussac's Laws into a single equation, applicable when none of the three parameters (pressure, volume, temperature) are held constant:

P₁V₁/T₁ = P₂V₂/T₂

This equation is highly versatile and crucial for solving many gas law problems.

5. The Ideal Gas Law

The Ideal Gas Law is a more comprehensive equation that accounts for the amount of gas present, expressed in moles (n):

PV = nRT

Where:

• P = Pressure
• V = Volume
• n = Number of moles
• R = Ideal gas constant (value varies depending on the units used; common values include 0.0821 L·atm/mol·K and 8.314 J/mol·K)
• T = Absolute temperature (in Kelvin)

The ideal gas law provides a more accurate representation of gas behavior, particularly at low pressures and high temperatures. However, it assumes ideal gas conditions, which may not always be perfectly met in real-world scenarios.

Hypothetical Gas Laws Worksheet #2: Solved Problems

Let's work through some example problems, mirroring the types of questions you might find on a typical Gas Laws Worksheet #2:

Problem 1 (Boyle's Law): A gas occupies 5.0 L at a pressure of 1.0 atm. What volume will it occupy at a pressure of 2.0 atm, assuming constant temperature?

Solution: Use Boyle's Law: P₁V₁ = P₂V₂

• 1.0 atm * 5.0 L = 2.0 atm * V₂
• V₂ = (1.0 atm * 5.0 L) / 2.0 atm = 2.5 L

Answer: The gas will occupy 2.5 L at 2.0 atm pressure.

Problem 2 (Charles's Law): A balloon contains 2.0 L of gas at 25°C. What will its volume be if the temperature is increased to 50°C, assuming constant pressure?

Solution: Remember to convert Celsius to Kelvin:

• T₁ = 25°C + 273.15 = 298.15 K
• T₂ = 50°C + 273.15 = 323.15 K

Use Charles's Law: V₁/T₁ = V₂/T₂

• 2.0 L / 298.15 K = V₂ / 323.15 K
• V₂ = (2.0 L * 323.15 K) / 298.15 K ≈ 2.16 L

Answer: The balloon's volume will be approximately 2.16 L at 50°C.

Problem 3 (Gay-Lussac's Law): A sealed container holds gas at a pressure of 1.5 atm at 20°C. What will the pressure be if the temperature is raised to 100°C, assuming constant volume?

Solution: Convert Celsius to Kelvin:

• T₁ = 20°C + 273.15 = 293.15 K
• T₂ = 100°C + 273.15 = 373.15 K

Use Gay-Lussac's Law: P₁/T₁ = P₂/T₂

• 1.5 atm / 293.15 K = P₂ / 373.15 K
• P₂ = (1.5 atm * 373.15 K) / 293.15 K ≈ 1.91 atm

Answer: The pressure will be approximately 1.91 atm at 100°C.

Problem 4 (Combined Gas Law): A gas sample has a volume of 3.0 L at 27°C and 1.0 atm pressure. What will its volume be at 127°C and 2.0 atm pressure?

Solution: Convert Celsius to Kelvin:

• T₁ = 27°C + 273.15 = 300.15 K
• T₂ = 127°C + 273.15 = 400.15 K

Use the Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂

• (1.0 atm * 3.0 L) / 300.15 K = (2.0 atm * V₂) / 400.15 K
• V₂ = (1.0 atm * 3.0 L * 400.15 K) / (300.15 K * 2.0 atm) ≈ 2.0 L

Answer: The volume will be approximately 2.0 L at the new conditions.

Problem 5 (Ideal Gas Law): What is the volume occupied by 2.0 moles of an ideal gas at 25°C and 1.5 atm pressure? Use R = 0.0821 L·atm/mol·K.

Solution: Convert Celsius to Kelvin: T = 25°C + 273.15 = 298.15 K

Use the Ideal Gas Law: PV = nRT

• (1.5 atm) * V = (2.0 mol) * (0.0821 L·atm/mol·K) * (298.15 K)
• V = [(2.0 mol) * (0.0821 L·atm/mol·K) * (298.15 K)] / (1.5 atm) ≈ 32.6 L

Answer: The volume occupied by the gas is approximately 32.6 L.

Advanced Gas Law Problems and Considerations

Worksheet #2 might also include more complex scenarios, such as:

• Gas Mixtures: Problems involving Dalton's Law of Partial Pressures, where the total pressure of a gas mixture is the sum of the partial pressures of its components.
• Stoichiometry: Problems combining gas laws with stoichiometric calculations, requiring you to use molar masses and balanced chemical equations.
• Real Gases: Problems that deviate from ideal gas behavior, requiring the use of correction factors (e.g., van der Waals equation).

To effectively tackle these advanced problems, ensure a strong grasp of the fundamental gas laws and related concepts. Practice solving various problem types to build confidence and proficiency. Remember to always carefully analyze the problem statement, identify the relevant gas law, and ensure consistent units throughout your calculations. Paying attention to detail and practicing regularly will significantly improve your understanding and ability to solve even the most challenging gas law problems.

This comprehensive guide provides a solid foundation for tackling Gas Laws Worksheet #2 and beyond. Remember to consult your textbook and class notes for further clarification and to practice with additional problems. Consistent practice is key to mastering the concepts and building your problem-solving skills.