Calculating Pressure Changes with Gay-Lussac's Law: Worked Examples

📚 Quick Study Guide

• 🌡️ Gay-Lussac's Law describes the relationship between pressure and temperature of a gas when volume and number of moles are kept constant.
• 📝 The formula for Gay-Lussac's Law is: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$, where $P_1$ and $T_1$ are the initial pressure and temperature, and $P_2$ and $T_2$ are the final pressure and temperature.
• ⚠️ Temperature must be in Kelvin (K) for accurate calculations. To convert Celsius (°C) to Kelvin (K), use the formula: $K = °C + 273.15$.
• 💡 Remember to rearrange the formula to solve for the unknown variable. For example, if you're solving for $P_2$, the formula becomes: $P_2 = \frac{P_1 \times T_2}{T_1}$.
• 🧪 Always include units in your calculations and final answers. Pressure can be in Pascals (Pa), atmospheres (atm), or mmHg, and temperature must be in Kelvin (K).

🧪 Practice Quiz

1. Question 1: A gas in a sealed container has a pressure of 200 kPa at 300 K. If the temperature is increased to 450 K, what is the new pressure?
   1. 133.3 kPa
   2. 250 kPa
   3. 300 kPa
   4. 400 kPa
2. Question 2: A tire is inflated to a pressure of 30 psi at 20°C. After driving, the tire's temperature rises to 40°C. What is the new pressure in the tire, assuming the volume remains constant?
   1. 32.07 psi
   2. 28.00 psi
   3. 30.50 psi
   4. 35.00 psi
3. Question 3: A gas has a pressure of 1.5 atm at 25°C. If the pressure is increased to 3.0 atm, what is the new temperature in Kelvin?
   1. 149 K
   2. 250 K
   3. 596 K
   4. 300 K
4. Question 4: A container of gas at 10°C has a pressure of 101.3 kPa. What will the pressure be at 25°C?
   1. 95.4 kPa
   2. 106.5 kPa
   3. 115.2 kPa
   4. 120.0 kPa
5. Question 5: If a gas in a rigid container has a pressure of 2 atm at 273 K, what is the pressure if the temperature is doubled?
   1. 1 atm
   2. 2 atm
   3. 3 atm
   4. 4 atm
6. Question 6: A balloon is filled with gas at 22°C and 100 kPa. If the temperature is increased to 44°C, what is the new pressure?
   1. 93.1 kPa
   2. 107.5 kPa
   3. 120.0 kPa
   4. 150.0 kPa
7. Question 7: A gas cylinder contains gas at a pressure of 5 atm at 300 K. If the cylinder is heated to 600 K, what is the new pressure?
   1. 2.5 atm
   2. 5 atm
   3. 10 atm
   4. 15 atm