How to Use Charles's Law to Solve Gas Problems

Okay, let's break down Charles's Law and how to use it to solve gas problems. Charles's Law describes how gases tend to expand when heated. A modern statement of Charles's Law is:

For a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature.

🌡️ Charles's Law Formula

The formula for Charles's Law is: $$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$ Where:

• $V_1$ = Initial volume
• $T_1$ = Initial temperature (in Kelvin)
• $V_2$ = Final volume
• $T_2$ = Final temperature (in Kelvin)

Important: Temperature must be in Kelvin (K). To convert Celsius (°C) to Kelvin (K), use the formula: $$K = °C + 273.15$$

📝 Steps to Solve Gas Problems Using Charles's Law

1. Identify the knowns and unknowns: List the given values for $V_1$, $T_1$, and either $V_2$ or $T_2$. Identify what you need to find.
2. Convert temperature to Kelvin: If the temperature is given in Celsius, convert it to Kelvin.
3. Apply Charles's Law: Use the formula $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ to solve for the unknown variable.

🧪 Example 1: Volume Change

Problem: A gas occupies 3.0 L at 27°C. If the temperature is increased to 227°C, what is the new volume, assuming constant pressure? Solution:

1. Identify knowns and unknowns:
   • $V_1 = 3.0 \text{ L}$
   • $T_1 = 27°C$
   • $T_2 = 227°C$
   • $V_2 = ?$ (unknown)
2. Convert temperature to Kelvin:
   • $T_1 = 27 + 273.15 = 300.15 \text{ K}$
   • $T_2 = 227 + 273.15 = 500.15 \text{ K}$
3. Apply Charles's Law: $$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$ $$\frac{3.0}{300.15} = \frac{V_2}{500.15}$$ $$V_2 = \frac{3.0 \times 500.15}{300.15} = 5.0 \text{ L}$$

Therefore, the new volume is 5.0 L.

🔥 Example 2: Temperature Change

Problem: A balloon has a volume of 1.0 L at 25°C. If you want to increase the volume to 2.0 L, what temperature (in Celsius) is required, assuming constant pressure? Solution:

1. Identify knowns and unknowns:
   • $V_1 = 1.0 \text{ L}$
   • $T_1 = 25°C$
   • $V_2 = 2.0 \text{ L}$
   • $T_2 = ?$ (unknown)
2. Convert temperature to Kelvin:
   • $T_1 = 25 + 273.15 = 298.15 \text{ K}$
3. Apply Charles's Law: $$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$ $$\frac{1.0}{298.15} = \frac{2.0}{T_2}$$ $$T_2 = \frac{2.0 \times 298.15}{1.0} = 596.3 \text{ K}$$
4. Convert Kelvin back to Celsius: $$T_2 (°C) = 596.3 - 273.15 = 323.15 °C$$

Therefore, the required temperature is approximately 323.15°C. By following these steps and understanding the formula, you can confidently solve gas problems using Charles's Law. 🚀