Real-World Examples of the Combined Gas Law in Action

📚 Quick Study Guide

• 🌡️ The Combined Gas Law relates pressure ($P$), volume ($V$), and temperature ($T$) for a fixed amount of gas.
• 📝 The formula is: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$, where the subscripts 1 and 2 denote initial and final states, respectively.
• 📏 Temperature MUST be in Kelvin (K). To convert from Celsius (°C), use: $K = °C + 273.15$.
• ⚙️ The number of moles of gas remains constant.
• 💡 This law is derived from combining 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 ($\frac{P_1}{T_1} = \frac{P_2}{T_2}$).
• 💨 Remember to keep your units consistent! Pressure can be in atm, Pa, or mmHg, volume can be in L or $m^3$, as long as both sides of the equation match.

🧪 Practice Quiz

1. A gas occupies 10 L at standard temperature and pressure (STP). If the temperature is increased to 273°C and the pressure is doubled, what is the new volume?
   1. 5 L
   2. 10 L
   3. 20 L
   4. 40 L
2. A balloon contains 5 L of air at 20°C and 1 atm. If the pressure is increased to 2 atm and the temperature is decreased to -20°C, what is the new volume of the balloon?
   1. 2.29 L
   2. 10 L
   3. 5 L
   4. 2.75 L
3. 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 kPa
   2. 300 kPa
   3. 400 kPa
   4. 600 kPa
4. A cylinder contains 20 L of gas at 25°C and 150 kPa. If the volume is decreased to 10 L and the temperature is increased to 50°C, what is the new pressure?
   1. 150 kPa
   2. 200 kPa
   3. 325 kPa
   4. 300 kPa
5. A gas occupies 5 L at 27°C and 2 atm. If the pressure is decreased to 1 atm and the temperature is increased to 327°C, what is the new volume?
   1. 5 L
   2. 10 L
   3. 15 L
   4. 20 L
6. A container of gas has a volume of 3.0 L at a pressure of 2.0 atm and a temperature of 200 K. If the volume is changed to 6.0 L and the temperature is increased to 400 K, what is the new pressure?
   1. 1.0 atm
   2. 2.0 atm
   3. 3.0 atm
   4. 4.0 atm
7. A gas occupies a volume of 10.0 L at STP. If the conditions are changed to 546 K and 2 atm, what is the new volume?
   1. 5.0 L
   2. 10.0 L
   3. 15.0 L
   4. 20.0 L