A Tale Of Two Gases Answer Key

A Tale of Two Gases: A Comprehensive Exploration and Answer Key

This article delves deep into the fascinating world of gases, exploring key concepts, comparing and contrasting different gaseous behaviors, and providing comprehensive answers to common questions often encountered in chemistry studies. We'll dissect the properties of gases, examine ideal gas laws, and explore real-world applications. Consider this your ultimate guide to mastering the complexities of gases.

Understanding the Fundamentals: Properties of Gases

Gases are unique states of matter characterized by their ability to expand to fill any container they occupy. Unlike solids and liquids, gases have no definite shape or volume. This behavior is directly linked to the weak intermolecular forces between gas particles, allowing them to move freely and independently. Several key properties define a gas:

1. Pressure (P):

Pressure is the force exerted by gas particles colliding with the walls of their container. It's typically measured in atmospheres (atm), Pascals (Pa), or millimeters of mercury (mmHg). Higher pressure indicates more frequent and forceful collisions. Understanding pressure is crucial for many gas law applications.

2. Volume (V):

Volume represents the space occupied by a gas. It's often expressed in liters (L) or cubic meters (m³). Changes in volume directly impact pressure and temperature, as we'll see later.

3. Temperature (T):

Temperature is a measure of the average kinetic energy of gas particles. It's expressed in Kelvin (K), which is crucial for gas law calculations, as absolute zero (0 K) represents the theoretical point where all molecular motion ceases.

4. Amount (n):

The amount of gas is typically measured in moles (mol), representing Avogadro's number (6.022 x 10²³) of particles. More moles mean more particles, resulting in increased pressure at constant volume and temperature.

The Ideal Gas Law: A Cornerstone of Gas Behavior

The ideal gas law is a mathematical relationship that describes the behavior of an ideal gas, a theoretical gas whose particles have negligible volume and do not interact with each other. While no gas is truly ideal, the ideal gas law provides a good approximation for many gases under many conditions. The equation is:

PV = nRT

Where:

• P = Pressure
• V = Volume
• n = Number of moles
• R = Ideal gas constant (0.0821 L·atm/mol·K or 8.314 J/mol·K)
• T = Temperature in Kelvin

This equation is incredibly versatile and allows us to calculate any of the variables if the other three are known. Many problems involve manipulating this equation to solve for a specific unknown.

Beyond the Ideal: Real Gases and Deviations

While the ideal gas law is a useful simplification, real gases deviate from ideal behavior, particularly at high pressures and low temperatures. At high pressures, the volume of the gas particles themselves becomes significant compared to the total volume of the container. At low temperatures, intermolecular forces become more important, causing particles to stick together and reducing the number of collisions with the container walls.

The van der Waals equation is a more sophisticated model that accounts for these deviations:

(P + a(n/V)²)(V - nb) = nRT

Where:

• a and b are van der Waals constants specific to each gas, representing the intermolecular forces and the volume of the gas particles respectively.

Common Gas Law Problems and Solutions: A Detailed Guide

Let's examine several common problems associated with gas laws and provide detailed solutions:

Problem 1: A sample of gas occupies 5.0 L at 25°C and 1.0 atm. What will be its volume if the pressure is increased to 2.0 atm while the temperature remains constant?

Solution: This problem involves Boyle's Law (P₁V₁ = P₂V₂), which states that the pressure and volume of a gas are inversely proportional at constant temperature.

1. Convert temperature to Kelvin: 25°C + 273.15 = 298.15 K (although this step isn't needed here since temperature is constant)

2. Apply Boyle's Law: (1.0 atm)(5.0 L) = (2.0 atm)(V₂)

3. Solve for V₂: V₂ = (1.0 atm)(5.0 L) / (2.0 atm) = 2.5 L

Therefore, the volume will be 2.5 L.

Problem 2: A balloon contains 2.0 moles of helium gas at 25°C and 1.0 atm. What is the volume of the balloon?

Solution: This problem uses the ideal gas law (PV = nRT).

1. Convert temperature to Kelvin: 25°C + 273.15 = 298.15 K

2. Apply the ideal gas law: (1.0 atm)(V) = (2.0 mol)(0.0821 L·atm/mol·K)(298.15 K)

3. Solve for V: V = [(2.0 mol)(0.0821 L·atm/mol·K)(298.15 K)] / (1.0 atm) ≈ 49 L

Therefore, the volume of the balloon is approximately 49 L.

Problem 3: A gas sample has a volume of 10.0 L at 273 K and 1.0 atm. If the temperature is increased to 373 K and the pressure is kept constant, what will be the new volume?

Solution: This problem uses Charles's Law (V₁/T₁ = V₂/T₂), which states that the volume of a gas is directly proportional to its temperature at constant pressure.

1. Apply Charles's Law: (10.0 L)/(273 K) = (V₂)/(373 K)

2. Solve for V₂: V₂ = (10.0 L)(373 K) / (273 K) ≈ 13.7 L

Therefore, the new volume will be approximately 13.7 L.

Gas Stoichiometry: Connecting Gases to Chemical Reactions

Gas stoichiometry involves using the ideal gas law and stoichiometric principles to solve problems involving chemical reactions that produce or consume gases. A crucial step often involves converting between moles of gas and volume using the ideal gas law.

Problem 4: Consider the reaction: 2H₂(g) + O₂(g) → 2H₂O(l). If 2.00 L of hydrogen gas reacts completely at STP (Standard Temperature and Pressure: 0°C and 1.00 atm), what volume of oxygen gas is needed?

Solution:

1. Moles of H₂: Use the ideal gas law to find moles of H₂ at STP: n = PV/RT = (1.00 atm)(2.00 L) / (0.0821 L·atm/mol·K)(273.15 K) ≈ 0.0893 mol H₂

2. Moles of O₂: Use the stoichiometry of the balanced equation: 0.0893 mol H₂ × (1 mol O₂ / 2 mol H₂) = 0.0447 mol O₂

3. Volume of O₂: Use the ideal gas law to find the volume of O₂ at STP: V = nRT/P = (0.0447 mol)(0.0821 L·atm/mol·K)(273.15 K) / (1.00 atm) ≈ 1.00 L

Therefore, 1.00 L of oxygen gas is needed.

Dalton's Law of Partial Pressures: Mixtures of Gases

When multiple gases are in the same container, each gas exerts its own pressure, called its partial pressure. Dalton's Law states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas:

P_total = P₁ + P₂ + P₃ + ...

Further Exploration: Advanced Gas Concepts

Beyond the fundamentals, many other exciting concepts exist within the realm of gas chemistry, including:

• Graham's Law of Diffusion and Effusion: This law describes the relationship between the rate of diffusion or effusion of a gas and its molar mass. Lighter gases diffuse and effuse faster.
• Kinetic Molecular Theory (KMT): This theory provides a microscopic explanation of gas behavior, linking macroscopic properties to the motion of gas particles.
• Effusion: The process by which a gas escapes through a small hole into a vacuum.

Conclusion: Mastering the World of Gases

Understanding gases is fundamental to chemistry and has significant real-world applications, from weather forecasting to industrial processes. This comprehensive exploration of gas laws, problem-solving techniques, and advanced concepts equips you with a solid foundation to tackle various challenges related to gas behavior. Remember that consistent practice and a clear understanding of the underlying principles are key to mastering this essential area of chemistry. By applying these principles and working through various examples, you will develop a strong understanding of the "tale of two gases"—and many more!