Use The Ideal Gas Law Formula \($PV = NRT, \, R = 0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}$\) To Determine The Volume Of 1.00 Mole Of A Gas Under The Following Conditions:- $T = 273 \, \text{K}, \, P = 2.00 \,

Introduction to the Ideal Gas Law Formula

The ideal gas law formula, ${PV = nRT}$, is a fundamental concept in chemistry that describes the behavior of gases under various conditions. This formula is a combination of several gas laws, including Boyle's Law, Charles' Law, and Avogadro's Law. The ideal gas law formula is widely used to calculate the volume, pressure, temperature, and number of moles of a gas. In this article, we will use the ideal gas law formula to determine the volume of 1.00 mole of a gas under specific conditions.

The Ideal Gas Law Formula: A Comprehensive Overview

The ideal gas law formula is given by:

${PV = nRT}$

where:

• ${P}$ is the pressure of the gas in atmospheres (atm)
• ${V}$ is the volume of the gas in liters (L)
• ${n}$ is the number of moles of the gas
• ${R}$ is the gas constant, which is equal to 0.0821 L ${\cdot}$ atm / mol ${\cdot}$ K
• ${T}$ is the temperature of the gas in Kelvin (K)

Calculating the Volume of a Gas Using the Ideal Gas Law Formula

To calculate the volume of a gas using the ideal gas law formula, we need to know the pressure, temperature, and number of moles of the gas. In this example, we are given the following conditions:

• ${T = 273 \, \text{K}}$
• ${P = 2.00 \, \text{atm}}$
• ${n = 1.00 \, \text{mol}}$

We can now plug these values into the ideal gas law formula to calculate the volume of the gas.

Step-by-Step Calculation of the Volume of the Gas

1. Identify the given values: We are given the temperature (${T = 273 \, \text{K}}$), pressure (${P = 2.00 \, \text{atm}}$), and number of moles (${n = 1.00 \, \text{mol}}$).
2. Plug the values into the ideal gas law formula: We can now plug these values into the ideal gas law formula to get:

${P \times V = n \times R \times T}$

${2.00 \, \text{atm} \times V = 1.00 \, \text{mol} \times 0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} \times 273 \, \text{K}}$ 3. Solve for the volume: To solve for the volume, we can rearrange the equation to get:

${V = \frac{n \times R \times T}{P}}$

${V = \frac{1.00 \, \text{mol} \times 0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} \times 273 \, \text{K}}{2.00 \, \text{atm}}}$ 4. Calculate the volume: Now, we can calculate the volume by plugging in the values:

${V = \frac{1.00 \, \text{mol} \times 0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} \times 273 \, \text{K}}{2.00 \, \text{atm}}}$

${V = \frac{22.31 \, \text{L} \cdot \text{K}}{2.00 \, \text{atm}}}$

${V = 11.155 \, \text{L}}$

Conclusion

In this article, we used the ideal gas law formula to determine the volume of 1.00 mole of a gas under specific conditions. We plugged in the given values into the ideal gas law formula and solved for the volume. The calculated volume was 11.155 L. This example demonstrates the importance of the ideal gas law formula in chemistry and its applications in real-world scenarios.

Applications of the Ideal Gas Law Formula

The ideal gas law formula has numerous applications in chemistry and other fields. Some of the applications include:

• Calculating the volume of a gas: The ideal gas law formula can be used to calculate the volume of a gas under various conditions.
• Determining the pressure of a gas: The ideal gas law formula can be used to determine the pressure of a gas under various conditions.
• Calculating the number of moles of a gas: The ideal gas law formula can be used to calculate the number of moles of a gas under various conditions.
• Understanding the behavior of gases: The ideal gas law formula provides a comprehensive understanding of the behavior of gases under various conditions.

Limitations of the Ideal Gas Law Formula

While the ideal gas law formula is a powerful tool in chemistry, it has some limitations. Some of the limitations include:

• Assumes ideal behavior: The ideal gas law formula assumes that the gas behaves ideally, which is not always the case.
• Does not account for intermolecular forces: The ideal gas law formula does not account for intermolecular forces, which can affect the behavior of gases.
• Does not account for non-ideal behavior: The ideal gas law formula does not account for non-ideal behavior, such as the behavior of gases at high pressures or low temperatures.

Conclusion

In conclusion, the ideal gas law formula is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It has numerous applications in chemistry and other fields, including calculating the volume of a gas, determining the pressure of a gas, and calculating the number of moles of a gas. However, it has some limitations, including assuming ideal behavior, not accounting for intermolecular forces, and not accounting for non-ideal behavior.

Introduction

The ideal gas law formula is a fundamental concept in chemistry that describes the behavior of gases under various conditions. In this article, we will answer some of the most frequently asked questions about the ideal gas law formula.

Q: What is the ideal gas law formula?

A: The ideal gas law formula is given by:

${PV = nRT}$

where:

• ${P}$ is the pressure of the gas in atmospheres (atm)
• ${V}$ is the volume of the gas in liters (L)
• ${n}$ is the number of moles of the gas
• ${R}$ is the gas constant, which is equal to 0.0821 L ${\cdot}$ atm / mol ${\cdot}$ K
• ${T}$ is the temperature of the gas in Kelvin (K)

Q: What are the units of the ideal gas law formula?

A: The units of the ideal gas law formula are:

• Pressure (${P}$): atmospheres (atm)
• Volume (${V}$): liters (L)
• Number of moles (${n}$): moles (mol)
• Gas constant (${R}$): L ${\cdot}$ atm / mol ${\cdot}$ K
• Temperature (${T}$): Kelvin (K)

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 equal to 0.0821 L ${\cdot}$ atm / mol ${\cdot}$ K.

Q: How is the ideal gas law formula used in real-world applications?

A: The ideal gas law formula is used in a wide range of real-world applications, including:

• Calculating the volume of a gas
• Determining the pressure of a gas
• Calculating the number of moles of a gas
• Understanding the behavior of gases under various conditions

Q: What are some of the limitations of the ideal gas law formula?

A: Some of the limitations of the ideal gas law formula include:

• Assuming ideal behavior
• Not accounting for intermolecular forces
• Not accounting for non-ideal behavior

Q: Can the ideal gas law formula be used to calculate the volume of a gas at high pressures or low temperatures?

A: No, the ideal gas law formula is not suitable for calculating the volume of a gas at high pressures or low temperatures. In such cases, the non-ideal behavior of the gas must be taken into account.

Q: How can the ideal gas law formula be modified to account for non-ideal behavior?

A: The ideal gas law formula can be modified to account for non-ideal behavior by using the van der Waals equation or other equations of state that take into account the intermolecular forces and non-ideal behavior of the gas.

Q: What is the difference between the ideal gas law formula and the van der Waals equation?

A: The ideal gas law formula assumes that the gas behaves ideally, whereas the van der Waals equation takes into account the intermolecular forces and non-ideal behavior of the gas.

Conclusion

In conclusion, the ideal gas law formula is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It has numerous applications in real-world scenarios, but it also has some limitations. By understanding the ideal gas law formula and its limitations, we can better appreciate the behavior of gases and make more accurate predictions about their behavior.

Additional Resources

For further information on the ideal gas law formula and its applications, please refer to the following resources:

• Textbooks: Chemistry textbooks, such as "Chemistry: The Central Science" by Theodore L. Brown, H. Eugene LeMay, and Bruce E. Bursten.
• Online Resources: Online resources, such as the Khan Academy and the Chemistry LibreTexts.
• Scientific Articles: Scientific articles, such as those published in the Journal of Chemical Physics and the Journal of Physical Chemistry.

Glossary

• Ideal Gas: A gas that behaves ideally, meaning that it obeys the ideal gas law formula.
• Non-Ideal Gas: A gas that does not behave ideally, meaning that it does not obey the ideal gas law formula.
• Gas Constant: A fundamental constant that relates the pressure, volume, and temperature of a gas.
• Van der Waals Equation: An equation of state that takes into account the intermolecular forces and non-ideal behavior of a gas.