Combined Gas Law: Importance of Units and Significant Figures

📚 Understanding the Combined Gas Law

The Combined Gas Law is a fundamental principle in chemistry that relates pressure, volume, and temperature for a fixed amount of gas. It's a combination of Boyle's Law, Charles's Law, and Gay-Lussac's Law. Mastering this law is crucial for solving various gas-related problems.

📜 History and Background

The Combined Gas Law wasn't discovered by a single person but evolved from the individual gas laws established in the 17th and 18th centuries. Boyle's Law (1662) described the inverse relationship between pressure and volume, Charles's Law (1787) related volume and temperature, and Gay-Lussac's Law (1802) linked pressure and temperature. The Combined Gas Law integrates these relationships into a single equation.

⚗️ Key Principles

The Combined Gas Law is expressed as:

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

Where:

• 🔍 $P$ represents pressure.
• 📏 $V$ represents volume.
• 🌡️ $T$ represents absolute temperature (in Kelvin).

Importance of Units:

• ⚖️ Pressure: Can be in Pascals (Pa), atmospheres (atm), mmHg, or torr. Consistency is key!
• 💧 Volume: Commonly in liters (L) or milliliters (mL). Again, maintain consistency.
• 🌡️ Temperature: MUST be in Kelvin (K). Convert Celsius to Kelvin using the formula: $K = °C + 273.15$.

Significant Figures:

• 🔢 Identify the least precise measurement in the problem.
• ➗ Perform the calculation.
• ✅ Round the final answer to the same number of significant figures as the least precise measurement.

🧪 Real-world Examples

Example 1: A gas occupies 10.0 L at standard temperature and pressure (STP). If the temperature is increased to 50.0 °C and the pressure is doubled, what is the new volume?

Solution:

1. 📝 $P_1 = 1 \text{ atm}$, $V_1 = 10.0 \text{ L}$, $T_1 = 273.15 \text{ K}$
2. 🌡️ $P_2 = 2 \text{ atm}$, $V_2 = ?$, $T_2 = 50.0 + 273.15 = 323.15 \text{ K}$
3. ➗ $\frac{(1 \text{ atm})(10.0 \text{ L})}{273.15 \text{ K}} = \frac{(2 \text{ atm})(V_2)}{323.15 \text{ K}}$
4. ✅ Solving for $V_2$: $V_2 = \frac{(1 \text{ atm})(10.0 \text{ L})(323.15 \text{ K})}{(2 \text{ atm})(273.15 \text{ K})} = 5.91 \text{ L}$ (3 sig figs)

🎯 Conclusion

The Combined Gas Law is a powerful tool for predicting the behavior of gases under varying conditions. Paying close attention to units and significant figures is essential for accurate calculations. Always convert temperature to Kelvin and ensure consistent units for pressure and volume. By mastering these concepts, you can confidently solve a wide range of gas law problems.

✍️ Practice Quiz

Solve the following problems, paying close attention to units and significant figures:

1. 🎈 A gas occupies 5.0 L at 25 °C and 1.0 atm. What volume will it occupy at 50 °C and 2.0 atm?
2. 🔥 A gas has a volume of 10.0 L at STP. If the pressure is increased to 3.0 atm and the temperature to 100 °C, what is the new volume?
3. 🧊 A container of gas has a volume of 2.0 L at a pressure of 2.5 atm and a temperature of 20 °C. If the volume is increased to 4.0 L and the temperature is increased to 40 °C, what is the new pressure?