Ideal Gas Law Applications

Oct 13, 2025 by pinkandtrash.com 133 views

A 1.50 liter sample of dry air in a cylinder exerts a pressure of 3.00 atmospheres at a temperature of $$25^{\circ} C$$

Understanding the Initial Conditions

The given scenario involves a 1.50 liter sample of dry air contained within a cylinder. The air in the cylinder exerts a pressure of 3.00 atmospheres at a temperature of $$25^{\circ} C$$. To begin with, let's understand the initial conditions of the system. The volume of the air sample is given as 1.50 liters, and the pressure exerted by the air is 3.00 atmospheres. The temperature of the air is maintained at a constant $$25^{\circ} C$$.

The Ideal Gas Law

The behavior of gases can be described using the ideal gas law, which is given 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.

Converting Temperature to Kelvin

To apply the ideal gas law, we need to convert the temperature from Celsius to Kelvin. The temperature in Kelvin is given by:

T (K) = T (°C) + 273.15

Substituting the given temperature of $$25^{\circ} C$$, we get:

T (K) = 25 + 273.15 = 298.15 K

Applying the Ideal Gas Law

Now that we have the temperature in Kelvin, we can apply the ideal gas law to the given scenario. Rearranging the ideal gas law to solve for the number of moles (n), we get:

n = PV / RT

Substituting the given values, we get:

n = (3.00 atm × 1.50 L) / (0.08206 L atm/mol K × 298.15 K)

Solving for n, we get:

n = 0.0615 mol

Understanding the Change in Pressure

The piston in the cylinder is moved, resulting in a reduction in pressure to 1.00 atmosphere. We need to determine the new volume of the air sample after the change in pressure. Since the temperature remains constant, we can use the ideal gas law to relate the initial and final conditions.

Applying the Ideal Gas Law to the Final Conditions

We can apply the ideal gas law to the final conditions by rearranging the equation to solve for the new volume (V2):

V2 = nRT / P2

Substituting the values, we get:

V2 = (0.0615 mol × 0.08206 L atm/mol K × 298.15 K) / (1.00 atm)

Solving for V2, we get:

V2 = 1.50 L

The Relationship Between Pressure and Volume

The ideal gas law shows that the pressure of a gas is inversely proportional to its volume, provided that the temperature remains constant. This relationship can be expressed mathematically as:

P1V1 = P2V2

where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

Substituting the Values

Substituting the given values, we get:

(3.00 atm × 1.50 L) = (1.00 atm × V2)

Solving for V2, we get:

V2 = 4.50 L

Conclusion

In conclusion, the initial volume of the air sample is 1.50 liters, and the pressure exerted by the air is 3.00 atmospheres at a temperature of $$25^{\circ} C$$. When the piston is moved, the pressure is reduced to 1.00 atmosphere, and the new volume of the air sample is calculated to be 4.50 liters. The relationship between pressure and volume is described by the ideal gas law, which shows that the pressure of a gas is inversely proportional to its volume, provided that the temperature remains constant.

References

Ideal Gas Law: The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases. It is given 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.
Temperature Conversion: The temperature in Kelvin is given by T (K) = T (°C) + 273.15, where T (°C) is the temperature in Celsius.
Ideal Gas Law Applications: The ideal gas law can be applied to a wide range of scenarios, including the calculation of the number of moles of a gas, the determination of the volume of a gas, and the calculation of the pressure of a gas.

Frequently Asked Questions

What is the ideal gas law? The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases. It is given 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.
How is the temperature converted to Kelvin? The temperature in Kelvin is given by T (K) = T (°C) + 273.15, where T (°C) is the temperature in Celsius.
What is the relationship between pressure and volume? The ideal gas law shows that the pressure of a gas is inversely proportional to its volume, provided that the temperature remains constant. This relationship can be expressed mathematically as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
A 1.50 liter sample of dry air in a cylinder exerts a pressure of 3.00 atmospheres at a temperature of $$25^{\circ} C$$

Q&A: Understanding the Ideal Gas Law and Its Applications

Q: What is the ideal gas law? A: The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases. It is given 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: How is the ideal gas law used in real-world applications? A: The ideal gas law is used in a wide range of applications, including the calculation of the number of moles of a gas, the determination of the volume of a gas, and the calculation of the pressure of a gas. It is also used in the design of gas cylinders, pipelines, and other equipment that involves the handling of gases.

Q: What is the relationship between pressure and volume? A: The ideal gas law shows that the pressure of a gas is inversely proportional to its volume, provided that the temperature remains constant. This relationship can be expressed mathematically as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

Q: How is the temperature converted to Kelvin? A: The temperature in Kelvin is given by T (K) = T (°C) + 273.15, where T (°C) is the temperature in Celsius.

Q: What is the significance of the gas constant (R)? A: The gas constant (R) is a fundamental constant that relates the pressure, volume, and temperature of a gas. It is used in the ideal gas law to calculate the number of moles of a gas, the volume of a gas, and the pressure of a gas.

Q: Can the ideal gas law be applied to real gases? A: While the ideal gas law is a useful approximation for many gases, it is not always accurate for real gases. Real gases can exhibit non-ideal behavior, such as non-linear relationships between pressure and volume, and non-ideal temperature dependencies.

Q: What are some common applications of the ideal gas law? A: The ideal gas law has many common applications, including:

Calculating the number of moles of a gas in a gas cylinder or pipeline
Determining the volume of a gas in a gas cylinder or pipeline
Calculating the pressure of a gas in a gas cylinder or pipeline
Designing gas cylinders, pipelines, and other equipment that involves the handling of gases
Understanding the behavior of gases in various industrial processes, such as chemical reactions and phase transitions

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:

Failing to convert the temperature to Kelvin
Failing to use the correct units for the gas constant (R)
Failing to account for non-ideal behavior in real gases
Failing to use the correct equation for the ideal gas law, such as PV = nRT

Conclusion

The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases. It is used in a wide range of applications, including the calculation of the number of moles of a gas, the determination of the volume of a gas, and the calculation of the pressure of a gas. By understanding the ideal gas law and its applications, you can better appreciate the behavior of gases and make more accurate calculations in a variety of fields.

References

Ideal Gas Law: The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases. It is given 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.
Temperature Conversion: The temperature in Kelvin is given by T (K) = T (°C) + 273.15, where T (°C) is the temperature in Celsius.
Gas Constant (R): The gas constant (R) is a fundamental constant that relates the pressure, volume, and temperature of a gas. It is used in the ideal gas law to calculate the number of moles of a gas, the volume of a gas, and the pressure of a gas.

Frequently Asked Questions

What is the ideal gas law? The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases. It is given 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.
How is the ideal gas law used in real-world applications? The ideal gas law is used in a wide range of applications, including the calculation of the number of moles of a gas, the determination of the volume of a gas, and the calculation of the pressure of a gas.
What is the relationship between pressure and volume? The ideal gas law shows that the pressure of a gas is inversely proportional to its volume, provided that the temperature remains constant. This relationship can be expressed mathematically as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.