Book cover for Chemistry The Science in Context

Chemistry The Science in Context

Thomas R. Gilbert

ISBN #9780393615142

5th Edition

2,675 Questions

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191,124 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter explores the properties of gases, starting with basic measurements such as pressure and volume, and extends to various gas laws that govern their behavior. By integrating Boyle’s, Charles’s, Avogadro’s, and Amontons’s laws into the ideal gas law, students learn to solve practical problems. The kinetic molecular theory provides a microscopic view of gas behavior, and corrections like the van der Waals equation address real gas deviations. Applications in scuba diving, weather prediction, and industrial processes highlight the chapter’s relevance to real-world scenarios.

Learning Objectives

1

Understand the fundamental properties and behavior of gases including pressure, volume, and temperature.

2

Apply individual gas laws (Boyle’s, Charles’s, Avogadro’s, and Amontons’s laws) and combine them to use the ideal gas law.

3

Analyze how the kinetic molecular theory explains molecular motion and collisions in gases.

4

Calculate gas properties in practical situations such as scuba diving mixtures, weather prediction, and industrial processes.

5

Evaluate the limitations of the ideal gas law and incorporate corrections using the van der Waals equation for real gases.

Key Concepts

CONCEPT

DEFINITION

Pressure

The force exerted by gas molecules per unit area on the walls of their container.

Volume

The amount of space occupied by a gas.

Boyle’s Law

A principle stating that the pressure of a gas is inversely proportional to its volume when temperature and amount remain constant.

Charles’s Law

A principle stating that the volume of a gas is directly proportional to its temperature (in Kelvin) when pressure and amount remain constant.

Avogadro’s Law

A principle stating that equal volumes of gases, at the same temperature and pressure, contain an equal number of particles.

Amontons’s Law

A principle that relates the pressure of a gas to its temperature when volume and the number of moles are constant.

Ideal Gas Law

An equation of state (PV = nRT) that combines various gas laws to relate pressure, volume, moles, and temperature for an ideal gas.

van der Waals Equation

A modification of the ideal gas law that accounts for the volume occupied by gas molecules and the intermolecular forces, used for real gas behavior.

Kinetic Molecular Theory

A theory that explains gas behavior by considering the motion and collisions of molecules.

Dalton’s Law

A law stating that in a mixture of non-reacting gases, the total pressure is equal to the sum of the partial pressures of individual gases.

Gas Density

The mass per unit volume of a gas, which can change depending on pressure and temperature.

Example Problems

Example 1

Shown in Figure $\mathrm{P} 6.1$ are three barometers. The one in the center is located at sea level. Which barometer is most likely to reflect the atmospheric pressure in Denver, $\mathrm{CO}$ where the elevation is approximately $1500 \mathrm{m} ?$ Explain your answer. (b) 1 atm (sea level)

Example 2

A rubber balloon is filled with helium gas. Which of the drawings in Figure $\mathrm{P} 6.2$ most accurately reflects the gas in the balloon on a molecular level? The blue spheres represent helium atoms. Explain your answer. Because atoms are in constant motion, the spheres represent their average position.

Example 3

Which of the three changes shown in Figure $\mathrm{P} 6.3$ best illustrates what happens when the atmospheric pressure on a helium-filled rubber balloon is increased at constant temperature? Because atoms are in constant motion, the spheres represent their average position.

Example 4

Which of the drawings in Figure $\mathrm{P} 6.3$ best illustrates what happens when the temperature of a helium-filled rubber balloon is increased at constant pressure?

Example 5

Which of the three changes shown in Figure P6.5 best illustrates what happens when the amount of gas in a helium-filled rubber balloon is increased at constant temperature and pressure?
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Step-by-Step Explanations

QUESTION

If a gas has an initial pressure (P1) of 2 atm and an initial volume (V1) of 4 L, what will the pressure (P2) be if the volume is decreased to 2 L at constant temperature?

STEP-BY-STEP ANSWER:

Step 1: Write down Boyle’s Law formula: P1 × V1 = P2 × V2.
Step 2: Substitute the known values: (2 atm) × (4 L) = P2 × (2 L).
Step 3: Solve for P2: P2 = (2 atm × 4 L) / (2 L) = 4 atm.
Final Answer: The new pressure will be 4 atm.

Using Boyle’s Law

QUESTION

A container holds 1 mole of an ideal gas at 273 K and 1 atm pressure. What is the volume of the gas? (Use R = 0.0821 L·atm/mol·K)

STEP-BY-STEP ANSWER:

Step 1: Write the Ideal Gas Law formula: PV = nRT.
Step 2: Identify the given values: P = 1 atm, n = 1 mol, T = 273 K, R = 0.0821 L·atm/mol·K.
Step 3: Rearrange the equation to solve for V: V = nRT / P.
Step 4: Substitute the values: V = (1 mol × 0.0821 L·atm/mol·K × 273 K) / 1 atm.
Step 5: Calculate the volume: V ≈ 22.4 L.
Final Answer: The volume of the gas is approximately 22.4 liters.

Applying the Ideal Gas Law

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Common Mistakes

  • Assuming that gases always behave ideally under all conditions without considering real gas deviations.
  • Confusing the relationships between temperature, volume, and pressure in different gas laws.
  • Mixing up units when applying the Ideal Gas Law, leading to calculation errors.
  • Overlooking the role of intermolecular forces and molecule size when using the van der Waals equation.