Conceptual Physics Practice Page Chapter 14 Gases Gas Pressure Answers

Conceptual Physics Practice Page Chapter 14: Gases - Gas Pressure: A Deep Dive with Answers

This article provides comprehensive answers and explanations for the practice problems found in Chapter 14 of Conceptual Physics, focusing on the topic of gases and gas pressure. Understanding gas pressure is fundamental to grasping many physics concepts, from atmospheric pressure to the workings of internal combustion engines. We'll delve into the key principles, provide detailed solutions to common problems, and explore the underlying scientific reasoning. This guide aims to not just give you the answers, but to build a solid understanding of gas behavior.

Understanding Gas Pressure: The Basics

Before we dive into the practice problems, let's refresh our understanding of gas pressure. Gas pressure is essentially the force exerted by gas molecules colliding with the walls of their container. These collisions are constant and random, creating a net outward force. The magnitude of this pressure depends on several factors:

• Number of gas molecules: More molecules mean more collisions, leading to higher pressure.
• Temperature: Higher temperatures mean faster-moving molecules, resulting in more forceful collisions and higher pressure.
• Volume: A smaller volume confines the molecules, increasing the frequency of collisions and therefore the pressure.

Key Concepts & Laws Governing Gas Behavior

Several crucial laws govern the behavior of gases under different conditions. Understanding these laws is crucial to solving the practice problems:

• Boyle's Law: At constant temperature, the volume of a gas is inversely proportional to its pressure (PV = constant). If you increase the pressure, the volume decreases proportionally, and vice versa.

• Charles's Law: At constant pressure, the volume of a gas is directly proportional to its absolute temperature (V/T = constant). As temperature increases, volume increases, and vice versa.

• Gay-Lussac's Law: At constant volume, the pressure of a gas is directly proportional to its absolute temperature (P/T = constant). An increase in temperature leads to a proportional increase in pressure.

• Ideal Gas Law: This combines Boyle's, Charles's, and Gay-Lussac's laws into a single equation: PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is the absolute temperature. This law describes the behavior of ideal gases, which are theoretical gases that obey these laws perfectly. Real gases deviate slightly from ideal behavior at high pressures and low temperatures.

• Dalton's Law of Partial Pressures: The total pressure of a mixture of gases is the sum of the partial pressures of each individual gas. Each gas exerts its own pressure independently of the others.

Practice Problems and Detailed Solutions

Now, let's tackle some representative practice problems from Conceptual Physics Chapter 14, focusing on gas pressure. We will provide step-by-step solutions and explanations to build your understanding. (Note: Specific problem numbers will be replaced with general examples to avoid direct plagiarism and to allow for broader application of the concepts.)

Problem 1: Boyle's Law Application

• Problem: A gas occupies a volume of 5 liters at a pressure of 2 atmospheres. If the pressure is increased to 4 atmospheres while maintaining a constant temperature, what will be the new volume of the gas?

• Solution: We use Boyle's Law: P₁V₁ = P₂V₂.

  • P₁ = 2 atm, V₁ = 5 L, P₂ = 4 atm
  • We need to find V₂.
  • (2 atm)(5 L) = (4 atm)(V₂)
  • V₂ = (2 atm * 5 L) / 4 atm = 2.5 L

• Answer: The new volume of the gas will be 2.5 liters.

Problem 2: Charles's Law Application

• Problem: A balloon has a volume of 10 liters at 20°C. If the temperature is increased to 40°C at constant pressure, what will be the new volume of the balloon? (Remember to use absolute temperature in Kelvin: K = °C + 273.15)

• Solution: We use Charles's Law: V₁/T₁ = V₂/T₂.

  • V₁ = 10 L, T₁ = 20°C + 273.15 = 293.15 K, T₂ = 40°C + 273.15 = 313.15 K
  • We need to find V₂.
  • (10 L) / (293.15 K) = V₂ / (313.15 K)
  • V₂ = (10 L * 313.15 K) / 293.15 K ≈ 10.68 L

• Answer: The new volume of the balloon will be approximately 10.68 liters.

Problem 3: Combined Gas Law Application

• Problem: A gas has a volume of 2 liters at a pressure of 1 atmosphere and a temperature of 27°C. What will be its volume if the pressure is increased to 2 atmospheres and the temperature is increased to 57°C?

• Solution: This problem requires the combined gas law, which is a combination of Boyle's and Charles's laws: (P₁V₁)/T₁ = (P₂V₂)/T₂.

  • P₁ = 1 atm, V₁ = 2 L, T₁ = 27°C + 273.15 = 300.15 K
  • P₂ = 2 atm, T₂ = 57°C + 273.15 = 330.15 K
  • We need to find V₂.
  • (1 atm * 2 L) / 300.15 K = (2 atm * V₂) / 330.15 K
  • V₂ = (1 atm * 2 L * 330.15 K) / (300.15 K * 2 atm) ≈ 1.1 L

• Answer: The new volume will be approximately 1.1 liters.

Problem 4: Dalton's Law of Partial Pressures

• Problem: A container holds a mixture of oxygen (partial pressure 0.8 atm) and nitrogen (partial pressure 0.7 atm). What is the total pressure in the container?

• Solution: Dalton's Law states that the total pressure is the sum of the partial pressures: P_total = P_oxygen + P_nitrogen

  • P_oxygen = 0.8 atm
  • P_nitrogen = 0.7 atm
  • P_total = 0.8 atm + 0.7 atm = 1.5 atm

• Answer: The total pressure in the container is 1.5 atm.

Problem 5: Ideal Gas Law Application

• Problem: A sample of gas contains 2 moles of gas at a temperature of 300 K and a pressure of 1 atm. What is the volume of the gas? (Use R = 0.0821 L·atm/mol·K)

• Solution: We use the Ideal Gas Law: PV = nRT.

  • P = 1 atm, n = 2 mol, R = 0.0821 L·atm/mol·K, T = 300 K
  • We need to find V.
  • (1 atm)V = (2 mol)(0.0821 L·atm/mol·K)(300 K)
  • V = (2 mol * 0.0821 L·atm/mol·K * 300 K) / 1 atm ≈ 49.26 L

• Answer: The volume of the gas is approximately 49.26 liters.

Further Exploration and Advanced Concepts

This is just a starting point. A deeper understanding of gases requires exploring more advanced concepts:

• Kinetic Molecular Theory: This theory explains gas behavior at a microscopic level, describing gases as collections of constantly moving particles.

• Real Gases vs. Ideal Gases: Real gases deviate from ideal behavior, especially at high pressures and low temperatures. The van der Waals equation is a more accurate model for real gases.

• Diffusion and Effusion: These processes describe the movement of gases from areas of high concentration to areas of low concentration. Graham's Law relates the rate of effusion to the molar mass of the gas.

Frequently Asked Questions (FAQ)

• Q: What is absolute zero?

  • A: Absolute zero is the lowest possible temperature, theoretically 0 Kelvin (-273.15°C), where all molecular motion ceases.

• Q: Why do we use Kelvin in gas law calculations?

  • A: Kelvin is an absolute temperature scale, meaning it starts at absolute zero. Using Kelvin avoids negative values that could lead to incorrect results in gas law equations.

• Q: What is the difference between pressure and force?

  • A: Pressure is force per unit area (P = F/A). Pressure describes how concentrated a force is.

Conclusion

Understanding gas pressure and the laws governing gas behavior is crucial in various fields of science and engineering. By working through practice problems and grasping the underlying principles, you'll gain a strong foundation in this fundamental area of physics. Remember that consistent practice and a thorough understanding of the concepts are key to mastering this topic. Don't hesitate to revisit the concepts and work through additional problems to solidify your understanding. The more you practice, the more confident and proficient you will become in solving gas pressure problems.