Charles Law Worksheet Answer Key

Charles's Law Worksheet: A Comprehensive Guide with Answers and Explanations

Understanding Charles's Law is crucial for anyone studying gas laws in chemistry or physics. This worksheet provides a comprehensive guide to Charles's Law, including practice problems with detailed answers and explanations, ensuring a thorough understanding of this fundamental principle. We'll explore the relationship between volume and temperature of a gas at constant pressure, covering various scenarios and problem-solving techniques. This guide serves as a valuable resource for students, teachers, and anyone looking to master Charles's Law.

Introduction to Charles's Law

Charles's Law, also known as the law of volumes, describes the relationship between the volume and temperature of a gas when the pressure and the amount of gas (number of moles) are held constant. It states that the volume of a gas is directly proportional to its absolute temperature. This means that if the temperature of a gas increases, its volume will also increase proportionally, and vice-versa, provided the pressure remains constant.

Mathematically, Charles's Law is expressed as:

V₁/T₁ = V₂/T₂

Where:

• V₁ is the initial volume of the gas
• T₁ is the initial absolute temperature of the gas (in Kelvin)
• V₂ is the final volume of the gas
• T₂ is the final absolute temperature of the gas (in Kelvin)

It's crucial to remember that temperature must always be expressed in Kelvin (K). To convert Celsius (°C) to Kelvin (K), use the formula: K = °C + 273.15. Ignoring this conversion is a common source of error in Charles's Law calculations.

Understanding the Underlying Principles

Charles's Law is a direct consequence of the kinetic molecular theory of gases. This theory postulates that gas particles are in constant, random motion and that the average kinetic energy of these particles is directly proportional to the absolute temperature. As temperature increases, the gas particles move faster, colliding more frequently and with greater force against the container walls. To maintain constant pressure, the volume must expand, allowing the particles more space to move. Conversely, decreasing the temperature slows down the particles, leading to a decrease in volume.

Solving Charles's Law Problems: A Step-by-Step Approach

Let's work through several examples to solidify your understanding of Charles's Law problem-solving. Remember to always convert temperatures to Kelvin before applying the formula.

Example 1:

A balloon has a volume of 2.0 L at a temperature of 25°C. What will be its volume if the temperature is increased to 50°C, assuming constant pressure?

Step 1: Convert temperatures to Kelvin:

• T₁ = 25°C + 273.15 = 298.15 K
• T₂ = 50°C + 273.15 = 323.15 K

Step 2: Apply Charles's Law:

V₁/T₁ = V₂/T₂

2.0 L / 298.15 K = V₂ / 323.15 K

Step 3: Solve for V₂:

V₂ = (2.0 L * 323.15 K) / 298.15 K

V₂ ≈ 2.17 L

Answer: The balloon's volume will increase to approximately 2.17 L.

Example 2:

A gas occupies 500 mL at 27°C. To what temperature (in °C) must the gas be cooled to reduce its volume to 300 mL at constant pressure?

Step 1: Convert temperatures to Kelvin:

• T₁ = 27°C + 273.15 = 300.15 K

Step 2: Apply Charles's Law:

V₁/T₁ = V₂/T₂

500 mL / 300.15 K = 300 mL / T₂

Step 3: Solve for T₂:

T₂ = (300 mL * 300.15 K) / 500 mL

T₂ ≈ 180.09 K

Step 4: Convert back to Celsius:

T₂ = 180.09 K - 273.15 = -93.06 °C

Answer: The gas must be cooled to approximately -93.06 °C.

Example 3: A more complex scenario

A sample of gas initially occupies a volume of 1.5 L at 20°C and 1 atm. If the pressure remains constant and the volume is increased to 2.0 L, what is the final temperature in both Kelvin and Celsius?

Step 1: Convert the initial temperature to Kelvin:

• T₁ = 20°C + 273.15 = 293.15 K

Step 2: Apply Charles's Law:

V₁/T₁ = V₂/T₂

1.5 L / 293.15 K = 2.0 L / T₂

Step 3: Solve for T₂ (in Kelvin):

T₂ = (2.0 L * 293.15 K) / 1.5 L

T₂ ≈ 390.87 K

Step 4: Convert T₂ to Celsius:

T₂ = 390.87 K - 273.15 = 117.72 °C

Answer: The final temperature is approximately 390.87 K or 117.72 °C.

Charles's Law: Deviations and Limitations

While Charles's Law provides a good approximation of the behavior of real gases under many conditions, it's important to acknowledge its limitations. The law assumes ideal gas behavior, meaning that:

• Gas particles have negligible volume.
• Gas particles have no intermolecular forces.
• Collisions between gas particles are perfectly elastic.

Real gases deviate from ideal behavior at high pressures and low temperatures. Under these conditions, the volume of the gas particles themselves becomes significant, and intermolecular forces become more prominent, affecting the accuracy of Charles's Law predictions. For accurate calculations under extreme conditions, more complex equations of state, such as the van der Waals equation, are necessary.

Frequently Asked Questions (FAQ)

Q1: Why must temperature be in Kelvin when using Charles's Law?

A1: Kelvin is an absolute temperature scale, meaning it starts at absolute zero (0 K), the theoretical point where all molecular motion ceases. Charles's Law is based on the direct proportionality between volume and absolute temperature. Using Celsius would introduce a non-zero intercept, invalidating the direct proportionality.

Q2: What happens if the pressure is not constant?

A2: If the pressure is not constant, Charles's Law cannot be directly applied. In such cases, you would need to use the combined gas law, which considers changes in pressure, volume, and temperature simultaneously.

Q3: Can Charles's Law be used for liquids or solids?

A3: No, Charles's Law applies only to gases. Liquids and solids have much stronger intermolecular forces and their volumes are far less sensitive to temperature changes than gases.

Q4: What are some real-world applications of Charles's Law?

A4: Charles's Law has numerous real-world applications, including:

• Hot air balloons: The heating of air within the balloon causes expansion, decreasing the air density and enabling the balloon to rise.
• Weather forecasting: Understanding how temperature affects air volume is vital for predicting atmospheric conditions.
• Tire pressure: The temperature of tires affects their pressure; on hot days, tire pressure can increase significantly.

Conclusion

Charles's Law is a fundamental principle in chemistry and physics that describes the direct relationship between the volume and temperature of a gas at constant pressure. Understanding this law, along with the ability to apply its formula and interpret its results, is essential for solving a wide range of problems related to gas behavior. While the law provides an excellent approximation under many conditions, remember to consider its limitations when dealing with real gases under extreme pressures and temperatures. By mastering the concepts and problem-solving techniques outlined in this comprehensive guide, you can confidently tackle any Charles's Law challenge. Remember to practice regularly, and don't hesitate to review the examples and explanations provided to further strengthen your understanding. Good luck!