Gas Laws Worksheet 2 Answer Key

Gas Laws Worksheet 2: Answer Key and Comprehensive Guide

This comprehensive guide provides answers and detailed explanations for a typical Gas Laws Worksheet 2, covering Boyle's Law, Charles's Law, Gay-Lussac's Law, and the Combined Gas Law. We'll delve into the principles behind each law, explore common problem-solving strategies, and offer tips for mastering these essential concepts in chemistry.

Understanding the Gas Laws

Before diving into the answers, let's revisit the fundamental gas laws. These laws describe the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of an ideal gas. Remember that an ideal gas is a theoretical gas that perfectly obeys these laws. Real gases deviate slightly from ideal behavior, especially at high pressures and low temperatures.

1. Boyle's Law: Pressure and Volume

Boyle's Law states that at constant temperature and amount of gas, the volume of a gas is inversely proportional to its pressure. This means that if you increase the pressure, the volume decreases, and vice versa. Mathematically, it's represented as:

P₁V₁ = P₂V₂

where:

• P₁ and V₁ are the initial pressure and volume
• P₂ and V₂ are the final pressure and volume

2. Charles's Law: Volume and Temperature

Charles's Law states that at constant pressure and amount of gas, the volume of a gas is directly proportional to its absolute temperature (in Kelvin). This implies that if you increase the temperature, the volume increases proportionally, and vice versa. The formula is:

V₁/T₁ = V₂/T₂

where:

• V₁ and T₁ are the initial volume and temperature (in Kelvin)
• V₂ and T₂ are the final volume and temperature (in Kelvin)

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

Gay-Lussac's Law states that at constant volume and amount of gas, the pressure of a gas is directly proportional to its absolute temperature (in Kelvin). Similar to Charles's Law, increasing the temperature increases the pressure proportionally. The equation is:

P₁/T₁ = P₂/T₂

where:

• P₁ and T₁ are the initial pressure and temperature (in Kelvin)
• P₂ and T₂ are the final pressure and temperature (in Kelvin)

4. Combined Gas Law: Pressure, Volume, and Temperature

The Combined Gas Law combines Boyle's, Charles's, and Gay-Lussac's Laws into a single equation that describes the relationship between pressure, volume, and temperature when the amount of gas remains constant:

(P₁V₁)/T₁ = (P₂V₂)/T₂

This equation is extremely useful for solving a wide range of gas law problems.

Sample Gas Laws Worksheet 2 Problems and Solutions

Now, let's tackle some sample problems that are typically found in a Gas Laws Worksheet 2. Remember to always convert temperatures to Kelvin (K) by adding 273.15 to the Celsius temperature (°C).

Problem 1 (Boyle's Law): A gas occupies a volume of 5.0 L at a pressure of 1.0 atm. What will be its volume if the pressure is increased to 2.5 atm at constant temperature?

Solution:

Using Boyle's Law: P₁V₁ = P₂V₂

• P₁ = 1.0 atm
• V₁ = 5.0 L
• P₂ = 2.5 atm
• V₂ = ?

(1.0 atm)(5.0 L) = (2.5 atm)(V₂)

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

Answer: The volume will be 2.0 L.

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

Solution:

First, convert temperatures to Kelvin:

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

Using Charles's Law: V₁/T₁ = V₂/T₂

• V₁ = 2.0 L
• T₁ = 298.15 K
• V₂ = ?
• T₂ = 323.15 K

(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 volume will be approximately 2.16 L.

Problem 3 (Gay-Lussac's Law): A gas in a rigid container has a pressure of 1.5 atm at 20°C. What will be its pressure if the temperature is increased to 100°C at constant volume?

Solution:

Convert temperatures to Kelvin:

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

Using Gay-Lussac's Law: P₁/T₁ = P₂/T₂

• P₁ = 1.5 atm
• T₁ = 293.15 K
• P₂ = ?
• T₂ = 373.15 K

(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.

Problem 4 (Combined Gas Law): A gas has a volume of 3.0 L at a pressure of 1.2 atm and a temperature of 27°C. What will be its volume if the pressure is increased to 1.8 atm and the temperature is decreased to 10°C?

Solution:

Convert temperatures to Kelvin:

• T₁ = 27°C + 273.15 = 300.15 K
• T₂ = 10°C + 273.15 = 283.15 K

Using the Combined Gas Law: (P₁V₁)/T₁ = (P₂V₂)/T₂

• P₁ = 1.2 atm
• V₁ = 3.0 L
• T₁ = 300.15 K
• P₂ = 1.8 atm
• V₂ = ?
• T₂ = 283.15 K

(1.2 atm * 3.0 L) / 300.15 K = (1.8 atm * V₂) / 283.15 K

V₂ = (1.2 atm * 3.0 L * 283.15 K) / (300.15 K * 1.8 atm) ≈ 1.68 L

Answer: The volume will be approximately 1.68 L.

Advanced Gas Law Problems and Concepts

Beyond the basic gas laws, more complex problems may involve:

• Ideal Gas Law (PV = nRT): This law incorporates the number of moles (n) of gas and the ideal gas constant (R = 0.0821 L·atm/mol·K). It's essential for problems involving the mass or molar mass of the gas.

• Partial Pressures (Dalton's Law): This law states that the total pressure of a mixture of gases is the sum of the partial pressures of each individual gas.

• Gas Stoichiometry: This involves using the gas laws in conjunction with stoichiometric calculations to determine the amounts of reactants and products in chemical reactions involving gases.

• Real Gases: Understanding the deviations of real gases from ideal behavior requires considering intermolecular forces and the finite volume of gas molecules. Equations like the van der Waals equation are used to model real gas behavior more accurately.

Tips for Mastering Gas Laws

• Understand the Concepts: Don't just memorize the formulas; understand the relationships between pressure, volume, and temperature.

• Use Consistent Units: Always use consistent units throughout your calculations (e.g., atm for pressure, L for volume, K for temperature).

• Practice, Practice, Practice: The best way to master gas laws is to solve numerous problems. Work through examples and try different variations.

• Seek Help When Needed: Don't hesitate to ask your teacher or tutor for assistance if you're struggling with a particular concept.

• Utilize Online Resources: Many online resources offer additional practice problems and explanations of gas laws.

By mastering these gas laws and problem-solving strategies, you'll build a strong foundation in chemistry and develop crucial analytical skills applicable to many scientific fields. Remember to always check your units and double-check your calculations to ensure accuracy in your answers. This detailed guide should equip you to confidently tackle any Gas Laws Worksheet 2 and beyond.