A Sample Of The Inert Gas Krypton Has Its Pressure Tripled While Its Temperature Remains Constant. If The Original Volume Is 12 L, What Is The Final Volume?A. 9.0 L B. 6.0 L C. 36 L D. 48 L E. 4.0 L
The ideal gas law is a fundamental concept in chemistry that describes the behavior of ideal gases under various conditions. It is a mathematical equation that relates the pressure, volume, and temperature of a gas. The ideal gas law is expressed as:
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
- T is the temperature of the gas in Kelvin
In this article, we will explore the concept of the ideal gas law and its applications, particularly in the context of a sample of the inert gas krypton.
The Ideal Gas Law and Its Assumptions
The ideal gas law is a simplified equation that assumes that the gas molecules are point particles with no volume, and that there are no intermolecular forces between the gas molecules. These assumptions are not always true, but they provide a good approximation for many real-world situations.
The Ideal Gas Law and the Behavior of Gases
The ideal gas law can be used to predict the behavior of gases under various conditions. For example, if the pressure of a gas is increased while the temperature remains constant, the volume of the gas will decrease. Conversely, if the pressure of a gas is decreased while the temperature remains constant, the volume of the gas will increase.
The Problem: A Sample of Krypton with Tripled Pressure
Let's consider a sample of krypton with an original volume of 12 L. If the pressure of the gas is tripled while the temperature remains constant, what is the final volume of the gas?
To solve this problem, we can use the ideal gas law and the fact that the temperature remains constant. Since the pressure is tripled, the new pressure is 3P, where P is the original pressure. The volume of the gas is inversely proportional to the pressure, so the new volume will be 1/3 of the original volume.
Calculating the Final Volume
Using the ideal gas law, we can write:
P1V1 = nRT
P2V2 = nRT
Since the temperature remains constant, we can set up a proportion:
P1V1 = P2V2
Substituting the values, we get:
P1(12 L) = P2V2
Since the pressure is tripled, we can write:
P2 = 3P1
Substituting this value, we get:
P1(12 L) = 3P1V2
Dividing both sides by 3P1, we get:
V2 = 4 L
Therefore, the final volume of the gas is 4 L.
Conclusion
In conclusion, the ideal gas law is a powerful tool for predicting the behavior of gases under various conditions. By understanding the ideal gas law and its assumptions, we can solve problems involving gases and make predictions about their behavior. In this article, we used the ideal gas law to solve a problem involving a sample of krypton with tripled pressure. We found that the final volume of the gas is 4 L.
Answer
The final answer is 4.0 L.
Discussion
This problem is a classic example of the ideal gas law in action. The ideal gas law is a fundamental concept in chemistry that describes the behavior of ideal gases under various conditions. By understanding the ideal gas law and its assumptions, we can solve problems involving gases and make predictions about their behavior.
Related Questions
- What is the ideal gas law?
- What are the assumptions of the ideal gas law?
- How can the ideal gas law be used to predict the behavior of gases?
- What is the relationship between pressure and volume in the ideal gas law?
- How can the ideal gas law be used to solve problems involving gases?
References
- Atkins, P. W. (2010). Physical chemistry. Oxford University Press.
- Chang, R. (2010). Physical chemistry for the life sciences. W.H. Freeman and Company.
- Levine, I. N. (2012). Physical chemistry. McGraw-Hill Education.
Keywords
- Ideal gas law
- Krypton
- Pressure
- Volume
- Temperature
- Gas constant
- Mole
- Kelvin
Ideal Gas Law Q&A =====================
The ideal gas law is a fundamental concept in chemistry that describes the behavior of ideal gases under various conditions. In this article, we will answer some frequently asked questions about the ideal gas law.
Q: What is the ideal gas law?
A: The ideal gas law is a mathematical equation that relates the pressure, volume, and temperature of a gas. It is expressed as:
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
- 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 molecules are point particles with no volume, and that there are no intermolecular forces between the gas molecules. These assumptions are not always true, but they provide a good approximation for many real-world situations.
Q: How can the ideal gas law be used to predict the behavior of gases?
A: The ideal gas law can be used to predict the behavior of gases under various conditions. For example, if the pressure of a gas is increased while the temperature remains constant, the volume of the gas will decrease. Conversely, if the pressure of a gas is decreased while the temperature remains constant, the volume of the gas will increase.
Q: What is the relationship between pressure and volume in the ideal gas law?
A: The pressure and volume of a gas are inversely proportional. This means that if the pressure of a gas is increased, the volume of the gas will decrease, and vice versa.
Q: How can the ideal gas law be used to solve problems involving gases?
A: The ideal gas law can be used to solve problems involving gases by rearranging the equation to solve for the unknown variable. For example, if the pressure, volume, and temperature of a gas are known, the number of moles of the gas can be calculated using the ideal gas law.
Q: What is the gas constant (R)?
A: The gas constant (R) is a constant that relates the pressure, volume, and temperature of a gas. It is approximately equal to 0.0821 L atm/mol K.
Q: What is the difference between the ideal gas law and the real gas law?
A: The ideal gas law is a simplified equation that assumes that the gas molecules are point particles with no volume, and that there are no intermolecular forces between the gas molecules. The real gas law, on the other hand, takes into account the actual behavior of real gases, including the effects of intermolecular forces and molecular volume.
Q: When is the ideal gas law a good approximation?
A: The ideal gas law is a good approximation when the gas molecules are far apart and there are no significant intermolecular forces between them. This is typically the case at high temperatures and low pressures.
Q: When is the real gas law a good approximation?
A: The real gas law is a good approximation when the gas molecules are close together and there are significant intermolecular forces between them. This is typically the case at low temperatures and high pressures.
Q: How can the ideal gas law be used in real-world applications?
A: The ideal gas law can be used in a variety of real-world applications, including:
- Calculating the volume of a gas in a container
- Determining the pressure of a gas in a container
- Calculating the number of moles of a gas
- Predicting the behavior of gases under various conditions
Conclusion
In conclusion, the ideal gas law is a fundamental concept in chemistry that describes the behavior of ideal gases under various conditions. By understanding the ideal gas law and its assumptions, we can solve problems involving gases and make predictions about their behavior. The ideal gas law is a powerful tool that can be used in a variety of real-world applications.
Answer Key
- Q1: The ideal gas law is a mathematical equation that relates the pressure, volume, and temperature of a gas.
- Q2: The ideal gas law assumes that the gas molecules are point particles with no volume, and that there are no intermolecular forces between the gas molecules.
- Q3: The ideal gas law can be used to predict the behavior of gases under various conditions.
- Q4: The pressure and volume of a gas are inversely proportional.
- Q5: The ideal gas law can be used to solve problems involving gases by rearranging the equation to solve for the unknown variable.
- Q6: The gas constant (R) is a constant that relates the pressure, volume, and temperature of a gas.
- Q7: The ideal gas law is a simplified equation that assumes that the gas molecules are point particles with no volume, and that there are no intermolecular forces between the gas molecules.
- Q8: The ideal gas law is a good approximation when the gas molecules are far apart and there are no significant intermolecular forces between them.
- Q9: The real gas law is a good approximation when the gas molecules are close together and there are significant intermolecular forces between them.
- Q10: The ideal gas law can be used in a variety of real-world applications, including calculating the volume of a gas in a container, determining the pressure of a gas in a container, calculating the number of moles of a gas, and predicting the behavior of gases under various conditions.
References
- Atkins, P. W. (2010). Physical chemistry. Oxford University Press.
- Chang, R. (2010). Physical chemistry for the life sciences. W.H. Freeman and Company.
- Levine, I. N. (2012). Physical chemistry. McGraw-Hill Education.
Keywords
- Ideal gas law
- Gas constant
- Pressure
- Volume
- Temperature
- Mole
- Kelvin
- Real gas law
- Inter molecular forces
- Molecular volume