If The Volume Of A Gas Is Decreased From 8.0 L To 4.0 L While Keeping The Temperature Constant, What Happens To The Pressure?A. The Pressure Is Halved B. The Pressure Remains The Same C. The Pressure Increases By Four Times D. The Pressure Is Doubled
Introduction
In chemistry, the behavior of gases is governed by the ideal gas law, which states that the product of the pressure and volume of a gas is equal to the product of the gas constant and the temperature. Mathematically, this can be expressed as:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
In this article, we will explore the relationship between the volume and pressure of a gas, and how changes in volume affect the pressure of a gas.
The Effect of Decreasing Volume on Pressure
Let's consider a scenario where the volume of a gas is decreased from 8.0 L to 4.0 L while keeping the temperature constant. We want to determine what happens to the pressure of the gas as a result of this change.
To answer this question, we can use the ideal gas law and the fact that the temperature remains constant. Since the temperature is constant, we can rearrange the ideal gas law to solve for pressure:
P = nRT / V
We know that the volume is decreased from 8.0 L to 4.0 L, so we can substitute these values into the equation:
P1 = nRT / 8.0 L P2 = nRT / 4.0 L
Since the temperature is constant, the number of moles of gas (n) and the gas constant (R) remain the same. Therefore, we can cancel out these constants and simplify the equation:
P1 / P2 = 8.0 L / 4.0 L
Simplifying the equation, we get:
P1 / P2 = 2
This means that the pressure of the gas is doubled when the volume is decreased from 8.0 L to 4.0 L.
Conclusion
In conclusion, when the volume of a gas is decreased from 8.0 L to 4.0 L while keeping the temperature constant, the pressure of the gas is doubled. This is because the pressure of a gas is inversely proportional to its volume, as described by the ideal gas law.
Key Takeaways
- The pressure of a gas is inversely proportional to its volume.
- When the volume of a gas is decreased, the pressure of the gas increases.
- The ideal gas law (PV = nRT) describes the relationship between the pressure, volume, and temperature of a gas.
Frequently Asked Questions
Q: What happens to the pressure of a gas when its volume is increased?
A: When the volume of a gas is increased, the pressure of the gas decreases.
Q: What is the relationship between the pressure and volume of a gas?
A: The pressure of a gas is inversely proportional to its volume.
Q: What is the ideal gas law?
A: The ideal gas law is a mathematical equation that describes the relationship between the pressure, volume, and temperature of a gas.
Q: What happens to the pressure of a gas when its temperature is increased?
A: When the temperature of a gas is increased, the pressure of the gas increases.
References
- Atkins, P. W., & de Paula, J. (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.
Glossary
- Ideal gas law: A mathematical equation that describes the relationship between the pressure, volume, and temperature of a gas.
- Pressure: The force exerted by a gas on its container.
- Volume: The amount of space occupied by a gas.
- Temperature: A measure of the average kinetic energy of the particles in a gas.
Q&A: Understanding the Relationship Between Volume and Pressure of a Gas ====================================================================
Introduction
In our previous article, we explored the relationship between the volume and pressure of a gas, and how changes in volume affect the pressure of a gas. In this article, we will answer some frequently asked questions about the relationship between volume and pressure of a gas.
Q: What happens to the pressure of a gas when its volume is increased?
A: When the volume of a gas is increased, the pressure of the gas decreases. This is because the pressure of a gas is inversely proportional to its volume, as described by the ideal gas law (PV = nRT).
Q: What is the relationship between the pressure and volume of a gas?
A: The pressure of a gas is inversely proportional to its volume. This means that as the volume of a gas increases, the pressure of the gas decreases, and vice versa.
Q: What is the ideal gas law?
A: The ideal gas law is a mathematical equation that describes the relationship between the pressure, volume, and temperature of a gas. It is expressed as:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
Q: What happens to the pressure of a gas when its temperature is increased?
A: When the temperature of a gas is increased, the pressure of the gas increases. This is because the temperature of a gas is directly proportional to its pressure, as described by the ideal gas law (PV = nRT).
Q: Can the pressure of a gas be increased without changing its volume?
A: Yes, the pressure of a gas can be increased without changing its volume. This can be done by increasing the temperature of the gas, which will cause the pressure to increase.
Q: Can the volume of a gas be increased without changing its pressure?
A: Yes, the volume of a gas can be increased without changing its pressure. This can be done by decreasing the temperature of the gas, which will cause the volume to increase.
Q: What is the effect of decreasing the number of moles of a gas on its pressure?
A: Decreasing the number of moles of a gas will decrease its pressure. This is because the pressure of a gas is directly proportional to the number of moles of gas, as described by the ideal gas law (PV = nRT).
Q: What is the effect of increasing the number of moles of a gas on its pressure?
A: Increasing the number of moles of a gas will increase its pressure. This is because the pressure of a gas is directly proportional to the number of moles of gas, as described by the ideal gas law (PV = nRT).
Q: Can the pressure of a gas be increased without changing its temperature?
A: Yes, the pressure of a gas can be increased without changing its temperature. This can be done by decreasing the volume of the gas, which will cause the pressure to increase.
Q: Can the volume of a gas be increased without changing its temperature?
A: Yes, the volume of a gas can be increased without changing its temperature. This can be done by decreasing the pressure of the gas, which will cause the volume to increase.
Conclusion
In conclusion, the relationship between the volume and pressure of a gas is complex and depends on several factors, including the temperature and number of moles of the gas. By understanding these relationships, we can better understand the behavior of gases and make predictions about their behavior under different conditions.
Key Takeaways
- The pressure of a gas is inversely proportional to its volume.
- The pressure of a gas is directly proportional to its temperature.
- The pressure of a gas is directly proportional to the number of moles of gas.
- The volume of a gas can be increased without changing its pressure.
- The pressure of a gas can be increased without changing its temperature.
Frequently Asked Questions
Q: What is the ideal gas law?
A: The ideal gas law is a mathematical equation that describes the relationship between the pressure, volume, and temperature of a gas.
Q: What is the relationship between the pressure and volume of a gas?
A: The pressure of a gas is inversely proportional to its volume.
Q: What is the effect of decreasing the temperature of a gas on its pressure?
A: Decreasing the temperature of a gas will decrease its pressure.
Q: What is the effect of increasing the number of moles of a gas on its pressure?
A: Increasing the number of moles of a gas will increase its pressure.
Q: Can the pressure of a gas be increased without changing its volume?
A: Yes, the pressure of a gas can be increased without changing its volume.
Q: Can the volume of a gas be increased without changing its pressure?
A: Yes, the volume of a gas can be increased without changing its pressure.
References
- Atkins, P. W., & de Paula, J. (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.
Glossary
- Ideal gas law: A mathematical equation that describes the relationship between the pressure, volume, and temperature of a gas.
- Pressure: The force exerted by a gas on its container.
- Volume: The amount of space occupied by a gas.
- Temperature: A measure of the average kinetic energy of the particles in a gas.