Combined Gas Law: A Simple Explanation for High School Chemistry

📚 Understanding the Combined Gas Law

The Combined Gas Law expresses the relationship between pressure, volume, and temperature for a fixed amount of gas. It's super useful when you have a gas undergoing changes in all three of these properties!

🧪 The Formula

Here's the formula you need to know:

$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

Where:

• 📊 $P_1$ = Initial Pressure
• 📦 $V_1$ = Initial Volume
• 🌡️ $T_1$ = Initial Temperature (in Kelvin!)
• 📈 $P_2$ = Final Pressure
• 🛢️ $V_2$ = Final Volume
• 🔥 $T_2$ = Final Temperature (in Kelvin!)

🧑‍🏫 Teacher's Guide: Combined Gas Law Lesson Plan

This lesson plan provides a structured approach to teaching the Combined Gas Law to high school chemistry students.

🎯 Objectives:

• ✅ Students will be able to state the Combined Gas Law and explain its relationship to Boyle's, Charles's, and Gay-Lussac's Laws.
• ⚗️ Students will be able to apply the Combined Gas Law to solve problems involving changes in pressure, volume, and temperature of a gas.
• 📐 Students will be able to convert temperature values between Celsius and Kelvin scales.

🧰 Materials:

• 🖥️ Projector and computer for presentations
• 📝 Whiteboard or chalkboard and markers/chalk
• 📃 Printed worksheets with practice problems (see below)
• 🌡️ Thermometers (optional, for demonstrations)
• 🎈 Balloons (optional, for demonstrations)

Warm-up (5 mins):

• 🤔 Begin by reviewing Boyle's Law ($P_1V_1 = P_2V_2$), Charles's Law ($\frac{V_1}{T_1} = \frac{V_2}{T_2}$), and Gay-Lussac's Law ($\frac{P_1}{T_1} = \frac{P_2}{T_2}$).
• ❓ Ask students what happens when all three variables (P, V, T) change simultaneously.

Main Instruction (30 mins):

• 🧑‍🏫 Introduce the Combined Gas Law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$. Explain that it combines Boyle's, Charles's, and Gay-Lussac's Laws into a single equation.
• 📝 Emphasize that temperature MUST be in Kelvin. Show how to convert from Celsius to Kelvin: $K = \, ^\circ C + 273.15$.
• ✍️ Work through several example problems step-by-step on the board. Encourage student participation. Example: A gas occupies 10.0 L at STP. What volume will it occupy at 100°C and 660 torr? (Remember STP is 1 atm and 273.15 K)
• ➗ Stress the importance of correct units and unit conversions.

Assessment (10 mins):

• ✍️ Have students work individually or in pairs on a short quiz or worksheet with Combined Gas Law problems.
• ✅ Collect the quizzes/worksheets and provide feedback.

💡 Key Tips & Tricks

• 🔑 Units Matter! Make sure pressure and volume units are consistent on both sides of the equation. Temperature MUST be in Kelvin.
• ✔️ Isolate the Variable: Algebra is your friend! Rearrange the equation to solve for the unknown variable before plugging in numbers.
• 🔍 Read Carefully: Pay close attention to what the problem is asking! What are you trying to find?

🧮 Example Problem

A container of gas has a volume of 5.0 L at a pressure of 200 kPa and a temperature of 300 K. If the pressure is increased to 400 kPa and the temperature is increased to 400 K, what is the new volume of the gas?

Solution:

1. Identify the knowns: $P_1 = 200 \text{ kPa}$, $V_1 = 5.0 \text{ L}$, $T_1 = 300 \text{ K}$, $P_2 = 400 \text{ kPa}$, $T_2 = 400 \text{ K}$
2. Identify the unknown: $V_2$
3. Apply the Combined Gas Law: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$
4. Solve for $V_2$: $V_2 = \frac{P_1V_1T_2}{P_2T_1}$
5. Plug in the values: $V_2 = \frac{(200 \text{ kPa})(5.0 \text{ L})(400 \text{ K})}{(400 \text{ kPa})(300 \text{ K})} = 3.33 \text{ L}$

📝 Practice Quiz

1. A gas occupies 2.0 L at standard temperature and pressure (STP). What volume will it occupy at 300 K and 150 kPa?
2. A balloon has a volume of 1.0 L at 25°C and 100 kPa. If the temperature is increased to 50°C and the pressure is decreased to 90 kPa, what is the new volume of the balloon?
3. A gas occupies 5.0 L at 27°C and 1 atm. If the gas is compressed to 2.5 L and heated to 77°C, what is the new pressure?
4. A container of gas has a volume of 10.0 L at 200 K and 200 kPa. If the volume is increased to 15.0 L and the temperature is increased to 300 K, what is the new pressure?
5. A gas occupies 3.0 L at 250 K and 120 kPa. If the pressure is increased to 240 kPa and the temperature is decreased to 200 K, what is the new volume?
6. A balloon has a volume of 2.0 L at 30°C and 101.3 kPa. If the temperature is decreased to 10°C and the pressure remains constant, what is the new volume of the balloon?
7. A gas occupies 7.0 L at 300 K and 150 kPa. If the volume is decreased to 3.5 L and the temperature remains constant, what is the new pressure?