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(a) A rigid tank contains 1.80 moles of helium, which can be treated as an ideal gas, at a pressure of 20.4 atm. While the tank and gas maintain a constant volume and temperature, a number of moles are removed from the tank, reducing the pressure to 4.50 atm. How many moles are removed? -0.397 What is the ideal gas law? Which quantities in the law are changing, and which are constant? Can you solve for the constant quantities, and use them to relate the changing quantities to each other? mol (b) What If? In a separate experiment beginning from the same initial conditions, including a temperature T, of 25.0°C, half the number of moles found in part (a) are withdrawn while the temperature is allowed to vary and the pressure undergoes the same change from 20.4 atm to 4.50 atm. What is the final temperature (in °C) of the gas? 141.53 X °C

(a) A rigid tank contains 1.80 moles of helium, which can be treated as an ideal gas, at a pressure of 20.4 atm. While the tank and gas maintain a constant volume and temperature, a number of moles are removed from the tank, reducing the pressure to 4.50 atm. How many moles are removed? -0.397 What is the ideal gas law? Which quantities in the law are changing, and which are constant? Can you solve for the constant quantities, and use them to relate the changing quantities to each other? mol (b) What If? In a separate experiment beginning from the same initial conditions, including a temperature T, of 25.0°C, half the number of moles found in part (a) are withdrawn while the temperature is allowed to vary and the pressure undergoes the same change from 20.4 atm to 4.50 atm. What is the final temperature (in °C) of the gas? 141.53 X °C

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### Ideal Gas Law Problems **Example (a):** A rigid tank contains **1.80 moles** of helium, which can be treated as an ideal gas, at a pressure of **20.4 atm**. While the tank and gas maintain a constant volume and temperature, a number of moles are removed from the tank, reducing the pressure to **4.50 atm**. How many moles are removed? #### Incorrect Attempt: - Answer: -0.397 mol ❌ **Feedback:** What is the ideal gas law? Which quantities in the law are changing, and which are constant? Can you solve for the constant quantities and use them to relate the changing quantities to each other? **Ideal Gas Law Relationship:** PV = nRT Since the volume and temperature are constant, we can relate the pressures and the moles directly: (P1 / P2) = (n1 / n2) --- **Example (b):** **What If?** In a separate experiment beginning from the same initial conditions, including a temperature \( T_i \) of **25.0°C**, half the number of moles found in part (a) are withdrawn while the temperature is allowed to vary and the pressure undergoes the same change from **20.4 atm** to **4.50 atm**. What is the final temperature (in °C) of the gas? #### Incorrect Attempt: - Answer: 141.53 °C ❌ **Feedback:** Revisit the ideal gas law, paying attention to how temperature relates to pressure and volume when the number of moles changes. **Visualization:** Although no graphs or diagrams are provided in this exercise, an explanation of the problem setup includes understanding the direct relationship between pressure and moles at constant temperature and volume, as well as how temperature adjusts when some of the gas is removed but the pressure change remains constant. --- ### Need Help? Click the "Read It" button below for additional explanation and guidance on solving ideal gas law problems. [Read It](#) --- This example illustrates the importance of correctly applying the ideal gas law and understanding the relationships between the variables involved in gas behavior changes.
Transcribed Image Text:### Ideal Gas Law Problems **Example (a):** A rigid tank contains **1.80 moles** of helium, which can be treated as an ideal gas, at a pressure of **20.4 atm**. While the tank and gas maintain a constant volume and temperature, a number of moles are removed from the tank, reducing the pressure to **4.50 atm**. How many moles are removed? #### Incorrect Attempt: - Answer: -0.397 mol ❌ **Feedback:** What is the ideal gas law? Which quantities in the law are changing, and which are constant? Can you solve for the constant quantities and use them to relate the changing quantities to each other? **Ideal Gas Law Relationship:** PV = nRT Since the volume and temperature are constant, we can relate the pressures and the moles directly: (P1 / P2) = (n1 / n2) --- **Example (b):** **What If?** In a separate experiment beginning from the same initial conditions, including a temperature \( T_i \) of **25.0°C**, half the number of moles found in part (a) are withdrawn while the temperature is allowed to vary and the pressure undergoes the same change from **20.4 atm** to **4.50 atm**. What is the final temperature (in °C) of the gas? #### Incorrect Attempt: - Answer: 141.53 °C ❌ **Feedback:** Revisit the ideal gas law, paying attention to how temperature relates to pressure and volume when the number of moles changes. **Visualization:** Although no graphs or diagrams are provided in this exercise, an explanation of the problem setup includes understanding the direct relationship between pressure and moles at constant temperature and volume, as well as how temperature adjusts when some of the gas is removed but the pressure change remains constant. --- ### Need Help? Click the "Read It" button below for additional explanation and guidance on solving ideal gas law problems. [Read It](#) --- This example illustrates the importance of correctly applying the ideal gas law and understanding the relationships between the variables involved in gas behavior changes.
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