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, V is the volume of the gas, n is the number of moles of the gas, R is the gas constant, and T is the temperature of the gas in Kelvin.
Given Values
In this problem, we are given the following values:
- n = 0.540 mol (number of moles of the gas)
- V = 35.5 L (volume of the gas)
- T = 223 K (temperature of the gas)
- R = 8.314 L路kPa/mol路K (gas constant)
Using the Ideal Gas Law to Find Pressure
We can use the ideal gas law to find the pressure of the gas. Rearranging the equation PV = nRT to solve for P, we get:
P = nRT / V
Substituting the given values, we get:
P = (0.540 mol)(8.314 L路kPa/mol路K)(223 K) / (35.5 L)
Calculating the Pressure
Now, let's calculate the pressure using the given values:
P = (0.540 mol)(8.314 L路kPa/mol路K)(223 K) / (35.5 L) P = 62.7 kPa
Conclusion
Therefore, the pressure of 0.540 mol of an ideal gas at 35.5 L and 223 K is 62.7 kPa.
Answer
The correct answer is D. 62.7 kPa.
Discussion
The ideal gas law is a powerful tool for predicting the behavior of gases. By understanding the ideal gas law, we can calculate the pressure, volume, and temperature of a gas given any two of these properties. In this problem, we used the ideal gas law to find the pressure of a gas given the number of moles, volume, and temperature. 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
- Determining the volume of a gas in a container
- Finding the temperature of a gas in a container
- Predicting the behavior of gases in different conditions
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, meaning that it has no intermolecular forces and no volume. In reality, gases are not ideal, and the ideal gas law does not accurately describe their behavior. However, the ideal gas law is still a useful approximation for many situations.
Conclusion
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, V is the volume of the gas, n is the number of moles of the gas, R is the gas constant, and T is the temperature of the gas in Kelvin.
Q: What are the assumptions of the ideal gas law?
A: The ideal gas law assumes that the gas is ideal, meaning that it has no intermolecular forces and no volume. This is not true for real gases, which have intermolecular forces and volume.
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 L路kPa/mol路K.
Q: How is the ideal gas law used in real-world applications?
A: The ideal gas law is used in many real-world applications, including:
- Calculating the pressure of a gas in a container
- Determining the volume of a gas in a container
- Finding the temperature of a gas in a container
- Predicting the behavior of gases in different conditions
Q: What are some limitations of the ideal gas law?
A: The ideal gas law has some limitations, including:
- The assumption that the gas is ideal
- The assumption that the gas has no intermolecular forces
- The assumption that the gas has no volume
- The fact that the ideal gas law does not accurately describe the behavior of real gases
Q: How can I use the ideal gas law to solve problems?
A: To use the ideal gas law to solve problems, you can follow these steps:
- Write down the ideal gas law equation: PV = nRT
- Plug in the given values for P, V, n, and T
- Solve for the unknown variable
- Check your units to make sure they are correct
Q: What are some common mistakes to avoid when using the ideal gas law?
A: Some common mistakes to avoid when using the ideal gas law include:
- Forgetting to convert units
- Forgetting to plug in the correct values
- Forgetting to check units
- Assuming that the gas is ideal when it is not
Q: Can I use the ideal gas law to solve problems involving real gases?
A: While the ideal gas law can be used to solve problems involving real gases, it is not always accurate. Real gases have intermolecular forces and volume, which can affect their behavior. In these cases, it may be necessary to use more complex equations or models to accurately describe the behavior of the gas.
Q: What are some other equations or models that can be used to describe the behavior of gases?
A: Some other equations or models that can be used to describe the behavior of gases include:
- The van der Waals equation
- The virial equation
- The ideal gas law with corrections for intermolecular forces and volume
Conclusion
In conclusion, the ideal gas law is a fundamental concept in chemistry that describes the behavior of ideal gases. While it has some limitations, it is still a useful tool for predicting the behavior of gases in many situations. By understanding the ideal gas law and its limitations, you can use it to solve problems and make predictions about the behavior of gases.