Gas Laws Test Review Answer Key Chemistry

Gas Laws Test Review: A Comprehensive Guide with Answers

Understanding gas laws is fundamental to success in chemistry. This comprehensive review covers all the key concepts, equations, and problem-solving strategies you'll need to ace your gas laws test. We'll delve into each law individually, providing example problems and solutions to solidify your understanding. Let's get started!

Understanding the Ideal Gas Law: PV=nRT

The Ideal Gas Law, PV = nRT, is the cornerstone of gas law calculations. It relates pressure (P), volume (V), number of moles (n), temperature (T), and the ideal gas constant (R). Understanding each variable and its units is crucial.

• Pressure (P): Measured in atmospheres (atm), kilopascals (kPa), millimeters of mercury (mmHg), or torr. Remember to be consistent with units throughout your calculations.

• Volume (V): Measured in liters (L).

• Number of Moles (n): Represents the amount of gas present. Calculated using the molar mass of the gas.

• Temperature (T): Always expressed in Kelvin (K). Remember to convert Celsius to Kelvin using the formula: K = °C + 273.15.

• Ideal Gas Constant (R): The value of R depends on the units used for pressure and volume. Common values include:

  • 0.0821 L·atm/mol·K
  • 8.314 L·kPa/mol·K
  • 62.36 L·mmHg/mol·K

Example Problem 1: Ideal Gas Law Calculation

A sample of nitrogen gas occupies 5.00 L at 25°C and 1.00 atm. How many moles of nitrogen are present?

Solution:

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

2. Identify known values: V = 5.00 L, T = 298.15 K, P = 1.00 atm, R = 0.0821 L·atm/mol·K

3. Rearrange the Ideal Gas Law to solve for n: n = PV/RT

4. Substitute and solve: n = (1.00 atm)(5.00 L) / (0.0821 L·atm/mol·K)(298.15 K) = 0.204 mol

Boyle's Law: The Inverse Relationship Between Pressure and Volume

Boyle's Law states that at constant temperature, the volume of a gas is inversely proportional to its pressure. This means if pressure increases, 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.

Example Problem 2: Boyle's Law Application

A gas occupies 2.50 L at a pressure of 1.20 atm. If the pressure is increased to 1.80 atm at constant temperature, what is the new volume?

Solution:

1. Identify known values: P₁ = 1.20 atm, V₁ = 2.50 L, P₂ = 1.80 atm

2. Rearrange Boyle's Law to solve for V₂: V₂ = P₁V₁/P₂

3. Substitute and solve: V₂ = (1.20 atm)(2.50 L) / (1.80 atm) = 1.67 L

Charles's Law: The Direct Relationship Between Volume and Temperature

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

V₁/T₁ = V₂/T₂

Example Problem 3: Charles's Law Calculation

A balloon has a volume of 2.00 L at 20°C. What is its volume at 100°C if the pressure remains constant?

Solution:

1. Convert Celsius to Kelvin: T₁ = 20°C + 273.15 = 293.15 K, T₂ = 100°C + 273.15 = 373.15 K

2. Identify known values: V₁ = 2.00 L, T₁ = 293.15 K, T₂ = 373.15 K

3. Rearrange Charles's Law to solve for V₂: V₂ = V₁T₂/T₁

4. Substitute and solve: V₂ = (2.00 L)(373.15 K) / (293.15 K) = 2.55 L

Gay-Lussac's Law: The Direct Relationship Between Pressure and Temperature

Gay-Lussac's Law states that at constant volume, the pressure of a gas is directly proportional to its absolute temperature. This means if temperature increases, pressure increases, and vice versa. The equation is:

P₁/T₁ = P₂/T₂

Example Problem 4: Gay-Lussac's Law Problem

A sealed container of gas has a pressure of 1.50 atm at 25°C. What is the pressure if the temperature is increased to 50°C at constant volume?

Solution:

1. Convert Celsius to Kelvin: T₁ = 25°C + 273.15 = 298.15 K, T₂ = 50°C + 273.15 = 323.15 K

2. Identify known values: P₁ = 1.50 atm, T₁ = 298.15 K, T₂ = 323.15 K

3. Rearrange Gay-Lussac's Law to solve for P₂: P₂ = P₁T₂/T₁

4. Substitute and solve: P₂ = (1.50 atm)(323.15 K) / (298.15 K) = 1.63 atm

Avogadro's Law: The Relationship Between Volume and Number of Moles

Avogadro's Law states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas present. This means if the number of moles increases, the volume increases, and vice versa. The equation is:

V₁/n₁ = V₂/n₂

Example Problem 5: Avogadro's Law Application

A sample of helium gas occupies 10.0 L at STP (Standard Temperature and Pressure: 0°C and 1 atm). If the number of moles is doubled at constant temperature and pressure, what is the new volume?

Solution:

1. Identify known values: V₁ = 10.0 L, n₁ = initial number of moles, n₂ = 2n₁

2. Rearrange Avogadro's Law to solve for V₂: V₂ = V₁(n₂/n₁)

3. Substitute and solve: V₂ = 10.0 L (2n₁/n₁) = 20.0 L

Combined Gas Law: Combining Multiple Gas Laws

The Combined Gas Law combines Boyle's, Charles's, and Gay-Lussac's laws into a single equation:

P₁V₁/T₁ = P₂V₂/T₂

This equation is useful when dealing with changes in pressure, volume, and temperature simultaneously.

Example Problem 6: Combined Gas Law Problem

A gas occupies 5.00 L at 27°C and 1.00 atm. What is its volume if the temperature is increased to 127°C and the pressure is increased to 2.00 atm?

Solution:

1. Convert Celsius to Kelvin: T₁ = 27°C + 273.15 = 300.15 K, T₂ = 127°C + 273.15 = 400.15 K

2. Identify known values: P₁ = 1.00 atm, V₁ = 5.00 L, T₁ = 300.15 K, P₂ = 2.00 atm, T₂ = 400.15 K

3. Rearrange the Combined Gas Law to solve for V₂: V₂ = (P₁V₁T₂) / (P₂T₁)

4. Substitute and solve: V₂ = (1.00 atm)(5.00 L)(400.15 K) / (2.00 atm)(300.15 K) = 3.33 L

Dalton's Law of Partial Pressures: Dealing with Gas Mixtures

Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases. The partial pressure of a gas is the pressure it would exert if it occupied the volume alone. Mathematically:

P_Total = P₁ + P₂ + P₃ + ...

Example Problem 7: Dalton's Law Application

A container holds a mixture of nitrogen (P_N₂ = 0.60 atm), oxygen (P_O₂ = 0.25 atm), and carbon dioxide (P_CO₂ = 0.15 atm). What is the total pressure in the container?

Solution:

P_Total = P_N₂ + P_O₂ + P_CO₂ = 0.60 atm + 0.25 atm + 0.15 atm = 1.00 atm

Understanding Non-Ideal Gases: Deviations from Ideal Behavior

The Ideal Gas Law works well for many gases under normal conditions. However, real gases deviate from ideal behavior at high pressures and low temperatures. This is because ideal gas molecules are assumed to have negligible volume and no intermolecular forces. Real gas molecules have finite volume and experience attractive forces, particularly at low temperatures where kinetic energy is reduced.

Key Takeaways and Test Preparation Strategies

This review covered the fundamental gas laws, their applications, and problem-solving techniques. To prepare for your test:

• Practice, practice, practice: Work through numerous problems of varying difficulty.
• Understand the underlying concepts: Don't just memorize equations; understand the relationships between pressure, volume, temperature, and the number of moles.
• Pay attention to units: Consistency in units is crucial for accurate calculations.
• Review your notes and textbook: Ensure you understand all the definitions, concepts, and equations.
• Create flashcards: Use flashcards to memorize key formulas and definitions.
• Form a study group: Collaborate with classmates to discuss challenging concepts and solve practice problems together.
• Seek help when needed: Don't hesitate to ask your teacher or tutor for assistance if you're struggling with any aspect of the material.

By following these strategies and mastering the concepts outlined in this review, you'll be well-prepared to succeed on your gas laws test. Remember that understanding the fundamental principles and practicing regularly are key to achieving a strong grasp of this important topic in chemistry. Good luck!