Conceptual Physics Practice Page Chapter 14 Gases Gas Pressure Answers

Let's delve into the fascinating world of gases and pressure, specifically focusing on the concepts presented in Conceptual Physics Chapter 14, alongside providing practice questions and answers to solidify your understanding. Gas pressure, often an invisible force, plays a critical role in our daily lives, from inflating tires to enabling weather patterns. Understanding the principles governing gas behavior is essential for anyone interested in physics, chemistry, or even everyday phenomena. This exploration aims to unpack those principles in a clear and accessible manner.

Understanding Gas Pressure

Gas pressure arises from the constant motion of gas molecules. These molecules, whether they are oxygen, nitrogen, or a mixture of various gases, are always in motion, colliding with each other and the walls of their container. Each collision exerts a tiny force. When you add up the forces of countless collisions over a specific area, you get the pressure exerted by the gas. This pressure is typically measured in units like Pascals (Pa), atmospheres (atm), or pounds per square inch (psi).

Several factors influence gas pressure. These include:

• Temperature: Increasing the temperature of a gas increases the average kinetic energy of its molecules, making them move faster and collide more forcefully and frequently with the container walls. This leads to higher pressure, assuming the volume remains constant.

• Volume: Decreasing the volume of a gas forces the molecules into a smaller space. This increases the frequency of collisions with the container walls, resulting in higher pressure. Conversely, increasing the volume decreases the pressure.

• Number of Molecules: Adding more gas molecules to a container increases the number of collisions with the walls, leading to higher pressure. Removing molecules reduces the collisions and thus lowers the pressure.

These relationships are formally expressed in the ideal gas law: 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 temperature. The ideal gas law provides a mathematical framework for understanding how these variables are interconnected.

Key Concepts from Conceptual Physics Chapter 14

Chapter 14 of Conceptual Physics likely covers several core concepts related to gases. These may include:

1. Atmospheric Pressure: The pressure exerted by the weight of the air above us. This pressure is significant, though we often don't feel it because our bodies have adapted to it. Atmospheric pressure decreases with altitude, as there is less air above us.

2. Boyle's Law: This law states that for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional. In other words, if you double the volume of a gas, the pressure will be halved (P₁V₁ = P₂V₂).

3. Charles's Law: This law describes the relationship between volume and temperature for a fixed amount of gas at constant pressure. It states that the volume of a gas is directly proportional to its absolute temperature (V₁/T₁ = V₂/T₂).

4. Gay-Lussac's Law: This law focuses on the relationship between pressure and temperature for a fixed amount of gas at constant volume. It states that the pressure of a gas is directly proportional to its absolute temperature (P₁/T₁ = P₂/T₂).

5. The Ideal Gas Law: As mentioned earlier, this law combines Boyle's, Charles's, and Gay-Lussac's laws into a single equation (PV = nRT). It's a fundamental equation for describing the behavior of ideal gases.

6. Partial Pressures (Dalton's Law): In a mixture of gases, each gas contributes to the total pressure. Dalton's Law of Partial Pressures states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas (Ptotal = P₁ + P₂ + P₃ + ...).

7. Buoyancy of Air: Just like objects can float in water, they can also float in air. This is because air exerts an upward buoyant force on objects. The magnitude of this force depends on the volume of air displaced by the object.

8. Bernoulli's Principle: Although not exclusively about gases, Bernoulli's principle is highly relevant. It states that as the speed of a fluid (liquid or gas) increases, the pressure within the fluid decreases. This principle explains how airplanes fly and how wind can lift roofs off houses.

Practice Questions and Answers: Conceptual Physics Chapter 14

Here are some practice questions, similar to what you might find in Conceptual Physics Chapter 14, along with detailed answers to help you grasp the concepts.

Question 1: A container of gas has a volume of 2.0 L and a pressure of 3.0 atm. If the volume is increased to 4.0 L while keeping the temperature constant, what will the new pressure be?

Answer: This problem involves Boyle's Law (P₁V₁ = P₂V₂).

• P₁ = 3.0 atm
• V₁ = 2.0 L
• V₂ = 4.0 L
• P₂ = ?

Plugging the values into the equation:

(3. 0 atm)(2.0 L) = P₂(4.0 L)

P₂ = (3.0 atm * 2.0 L) / 4.0 L

P₂ = 1.5 atm

Therefore, the new pressure will be 1.5 atm.

Question 2: A balloon contains 1.0 L of air at 27°C. If the temperature is increased to 54°C, what will the new volume of the balloon be, assuming the pressure remains constant?

Answer: This problem involves Charles's Law (V₁/T₁ = V₂/T₂). Remember that temperature must be in Kelvin.

• V₁ = 1.0 L
• T₁ = 27°C + 273.15 = 300.15 K
• T₂ = 54°C + 273.15 = 327.15 K
• V₂ = ?

Plugging the values into the equation:

(1. 0 L) / (300.15 K) = V₂ / (327.15 K)

V₂ = (1.0 L * 327.15 K) / 300.15 K

V₂ = 1.09 L

Therefore, the new volume of the balloon will be approximately 1.09 L.

Question 3: A rigid container holds a gas at a pressure of 2.0 atm and a temperature of 20°C. If the temperature is increased to 60°C, what will the new pressure be?

Answer: This problem involves Gay-Lussac's Law (P₁/T₁ = P₂/T₂). Again, temperature must be in Kelvin.

• P₁ = 2.0 atm
• T₁ = 20°C + 273.15 = 293.15 K
• T₂ = 60°C + 273.15 = 333.15 K
• P₂ = ?

Plugging the values into the equation:

(2. 0 atm) / (293.15 K) = P₂ / (333.15 K)

P₂ = (2.0 atm * 333.15 K) / 293.15 K

P₂ = 2.28 atm

Therefore, the new pressure will be approximately 2.28 atm.

Question 4: A container holds 2 moles of oxygen gas and 3 moles of nitrogen gas. If the total pressure in the container is 5.0 atm, what is the partial pressure of the oxygen gas?

Answer: This problem involves Dalton's Law of Partial Pressures. The partial pressure of a gas is proportional to its mole fraction in the mixture.

• Total moles = 2 moles (O₂) + 3 moles (N₂) = 5 moles
• Mole fraction of O₂ = 2 moles / 5 moles = 0.4
• Total pressure = 5.0 atm

Partial pressure of O₂ = (Mole fraction of O₂) * (Total pressure)

Partial pressure of O₂ = (0.4) * (5.0 atm)

Partial pressure of O₂ = 2.0 atm

Therefore, the partial pressure of the oxygen gas is 2.0 atm.

Question 5: Explain why a hot air balloon rises.

Answer: A hot air balloon rises due to the principle of buoyancy. When the air inside the balloon is heated, it becomes less dense than the cooler air outside the balloon. Because the hot air is less dense, it experiences a greater buoyant force. The buoyant force is an upward force exerted by the surrounding air. When the buoyant force is greater than the weight of the balloon and the air inside, the balloon rises. This is the same reason why a piece of wood floats on water – the buoyant force exerted by the water is greater than the weight of the wood.

Question 6: How does atmospheric pressure change with altitude, and why?

Answer: Atmospheric pressure decreases with increasing altitude. This is because atmospheric pressure is caused by the weight of the air above a given point. At higher altitudes, there is less air above, and therefore less weight pressing down, resulting in lower pressure. Imagine a stack of books; the book at the bottom experiences the weight of all the books above it, while the book at the top only experiences its own weight. Similarly, air at sea level experiences the weight of the entire atmosphere above it, while air at a high altitude experiences the weight of only the air above that altitude.

Question 7: What is the difference between gauge pressure and absolute pressure?

Answer: Absolute pressure is the total pressure exerted by a gas, including atmospheric pressure. It is measured relative to a perfect vacuum. Gauge pressure, on the other hand, is the difference between the absolute pressure and atmospheric pressure. Gauge pressure is what most pressure gauges measure. For example, if a tire pressure gauge reads 30 psi, that's the gauge pressure. The absolute pressure would be 30 psi plus the atmospheric pressure (approximately 14.7 psi at sea level), for a total of 44.7 psi. Mathematically:

Absolute Pressure = Gauge Pressure + Atmospheric Pressure

Question 8: Explain Bernoulli's principle and give a real-world example of its application.

Answer: Bernoulli's Principle states that as the speed of a fluid (liquid or gas) increases, the pressure within the fluid decreases. This principle is based on the conservation of energy. As the fluid speeds up, its kinetic energy increases, and its potential energy (which is related to pressure) decreases.

A common example of Bernoulli's principle is the lift generated by an airplane wing. The wing is designed so that air flows faster over the top surface than over the bottom surface. This faster airflow over the top creates a region of lower pressure, while the slower airflow under the wing creates a region of higher pressure. This pressure difference generates an upward force (lift) that allows the airplane to fly.

Question 9: Why is it important to use absolute temperature (Kelvin) in gas law calculations?

Answer: It is essential to use absolute temperature (Kelvin) in gas law calculations because the gas laws (Boyle's, Charles's, Gay-Lussac's, and the Ideal Gas Law) are based on the fundamental relationship between the kinetic energy of gas molecules and temperature. The Kelvin scale starts at absolute zero (0 K), which is the theoretical temperature at which all molecular motion ceases. Using Celsius or Fahrenheit would lead to incorrect results because these scales have arbitrary zero points that do not reflect the true energy state of the gas molecules. For example, a temperature of 0°C does not mean that the gas molecules have no kinetic energy.

Question 10: A sealed container is filled with a mixture of helium and neon gas. The partial pressure of helium is 300 kPa, and the partial pressure of neon is 200 kPa. What is the total pressure inside the container?

Answer: This problem utilizes Dalton's Law of Partial Pressures. The total pressure is simply the sum of the partial pressures of each gas.

Total Pressure = Partial Pressure of Helium + Partial Pressure of Neon

Total Pressure = 300 kPa + 200 kPa

Total Pressure = 500 kPa

Therefore, the total pressure inside the container is 500 kPa.

Further Exploration of Gas Behavior

Beyond the specific laws and principles, there are other aspects of gas behavior worth considering:

• Real vs. Ideal Gases: The ideal gas law provides a good approximation for the behavior of many gases under normal conditions. However, real gases deviate from ideal behavior, especially at high pressures and low temperatures. This is because the ideal gas law assumes that gas molecules have no volume and do not interact with each other. In reality, gas molecules do have volume, and they do exert attractive and repulsive forces on each other.

• Van der Waals Equation: The Van der Waals equation is a modified version of the ideal gas law that takes into account the volume of gas molecules and the intermolecular forces between them. It provides a more accurate description of the behavior of real gases.

• Kinetic Molecular Theory: This theory provides a microscopic explanation of gas behavior. It postulates that gases are composed of a large number of tiny particles (molecules) that are in constant, random motion. The average kinetic energy of these particles is proportional to the absolute temperature of the gas.

• Applications of Gas Laws: Understanding gas laws is crucial in many practical applications, including:

  • Internal combustion engines: The compression and expansion of gases are fundamental to the operation of these engines.
  • Refrigeration: Refrigerators use the properties of gases to transfer heat from one place to another.
  • Weather forecasting: Atmospheric pressure, temperature, and humidity are all important factors in weather patterns.
  • Scuba diving: Understanding pressure changes is essential for safe scuba diving.
  • Industrial processes: Many industrial processes involve the use of gases under controlled conditions.

Conclusion

Understanding the behavior of gases and gas pressure is fundamental to many areas of science and technology. By mastering the concepts presented in Conceptual Physics Chapter 14, including Boyle's Law, Charles's Law, Gay-Lussac's Law, the Ideal Gas Law, and Dalton's Law of Partial Pressures, you can gain a deeper appreciation for the world around you. The practice questions and answers provided here should help you solidify your understanding and prepare you for further exploration of this fascinating topic. Remember to always consider the units of measurement and to use absolute temperature (Kelvin) when performing gas law calculations. Keep practicing, and you'll become a gas law expert in no time!