What Is The Pressure Of 0.540 Mol Of An Ideal Gas At 35.5 L And 223 K?Use $PV = NRT$ And $R = 8.314 \frac{L \cdot KPa}{mol \cdot K}$.A. 0.715 KPa B. 2.45 KPa C. 28.2 KPa D. 62.7 KPa
Understanding the Ideal Gas Law
The ideal gas law is a fundamental concept in chemistry that describes the behavior of ideal gases. It is a mathematical equation that relates the pressure, volume, and temperature of a gas. The ideal gas law is expressed by the equation:
PV = nRT
Where:
- P is the pressure of the gas in Pascals (Pa)
- V is the volume of the gas in cubic meters (m³)
- n is the number of moles of the gas
- R is the gas constant in Pascals per cubic meter per mole per Kelvin (Pa·m³/mol·K)
- T is the temperature of the gas in Kelvin (K)
Given Values
In this problem, we are given the following values:
- n = 0.540 mol
- V = 35.5 L
- T = 223 K
- R = 8.314 L·kPa/mol·K
Converting Units
Before we can plug in the values into the ideal gas law equation, we need to convert the units of the given values to match the units of the gas constant.
- V = 35.5 L (no conversion needed)
- T = 223 K (no conversion needed)
- R = 8.314 L·kPa/mol·K (no conversion needed)
Plugging in Values
Now that we have the given values in the correct units, we can plug them into the ideal gas law equation:
PV = nRT
P = nRT / V
P = (0.540 mol) (8.314 L·kPa/mol·K) (223 K) / (35.5 L)
P = 2.45 kPa
Conclusion
Therefore, the pressure of 0.540 mol of an ideal gas at 35.5 L and 223 K is 2.45 kPa.
Answer
The correct answer is B. 2.45 kPa.
Discussion
The ideal gas law is a powerful tool for predicting the behavior of gases under different conditions. By understanding the ideal gas law, we can make predictions about the pressure, volume, and temperature of a gas. In this problem, we used the ideal gas law to calculate the pressure of a gas given its volume, temperature, and number of moles. This is a common application of the ideal gas law in chemistry and physics.
Real-World Applications
The ideal gas law has many real-world applications, including:
- Calculating the pressure of a gas in a container
- Predicting the behavior of gases in different conditions
- Designing equipment for handling gases
- Understanding the behavior of gases in chemical reactions
Limitations of the Ideal Gas Law
While the ideal gas law is a powerful tool, it has some limitations. The ideal gas law assumes that the gas is:
- Ideal: The gas behaves like an ideal gas, with no intermolecular forces or molecular size.
- Monatomic: The gas is composed of single atoms, with no molecular structure.
- Perfectly elastic: The gas molecules are perfectly elastic, with no energy loss.
Frequently Asked Questions
Q: What is the ideal gas law?
A: The ideal gas law is a mathematical equation that describes the behavior of ideal gases. It is expressed by the equation:
PV = nRT
Where:
- P is the pressure of the gas in Pascals (Pa)
- V is the volume of the gas in cubic meters (m³)
- n is the number of moles of the gas
- R is the gas constant in Pascals per cubic meter per mole per Kelvin (Pa·m³/mol·K)
- T is the temperature of the gas in Kelvin (K)
Q: What are the assumptions of the ideal gas law?
A: The ideal gas law assumes that the gas is:
- Ideal: The gas behaves like an ideal gas, with no intermolecular forces or molecular size.
- Monatomic: The gas is composed of single atoms, with no molecular structure.
- Perfectly elastic: The gas molecules are perfectly elastic, with no energy loss.
Q: What are the limitations of the ideal gas law?
A: The ideal gas law is only an approximation, and it has some limitations. In reality, gases do not behave like ideal gases, and the ideal gas law is only useful for making predictions and understanding the behavior of gases.
Q: How is the ideal gas law used in real-world applications?
A: The ideal gas law has many real-world applications, including:
- Calculating the pressure of a gas in a container
- Predicting the behavior of gases in different conditions
- Designing equipment for handling gases
- Understanding the behavior of gases in chemical reactions
Q: What is the gas constant (R)?
A: The gas constant (R) is a physical constant that relates the pressure, volume, and temperature of a gas. It is expressed in units of Pascals per cubic meter per mole per Kelvin (Pa·m³/mol·K).
Q: What is the value of the gas constant (R)?
A: The value of the gas constant (R) is:
R = 8.314 L·kPa/mol·K
Q: How is the ideal gas law used to calculate pressure?
A: The ideal gas law can be used to calculate pressure by rearranging the equation to solve for pressure:
P = nRT / V
Q: What is the unit of pressure in the ideal gas law?
A: The unit of pressure in the ideal gas law is Pascals (Pa).
Q: What is the unit of volume in the ideal gas law?
A: The unit of volume in the ideal gas law is cubic meters (m³).
Q: What is the unit of temperature in the ideal gas law?
A: The unit of temperature in the ideal gas law is Kelvin (K).
Q: What is the unit of the gas constant (R)?
A: The unit of the gas constant (R) is Pascals per cubic meter per mole per Kelvin (Pa·m³/mol·K).
Q: How is the ideal gas law used to calculate volume?
A: The ideal gas law can be used to calculate volume by rearranging the equation to solve for volume:
V = nRT / P
Q: What is the unit of volume in the ideal gas law when calculating volume?
A: The unit of volume in the ideal gas law when calculating volume is cubic meters (m³).
Q: How is the ideal gas law used to calculate temperature?
A: The ideal gas law can be used to calculate temperature by rearranging the equation to solve for temperature:
T = PV / nR
Q: What is the unit of temperature in the ideal gas law when calculating temperature?
A: The unit of temperature in the ideal gas law when calculating temperature is Kelvin (K).