15.35 L Of A Gas Is At A Pressure Of 198.0 KPa. At What Pressure Would The Gas Have A Volume Of 13.78 L?

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The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. 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. In this article, we will use the ideal gas law to solve a problem involving a gas with a given initial volume and pressure, and determine the pressure at which the gas would have a different volume.

Given Information

  • Initial volume (V1) = 15.35 L
  • Initial pressure (P1) = 198.0 kPa
  • Final volume (V2) = 13.78 L
  • We need to find the final pressure (P2)

Using the Ideal Gas Law

Since the number of moles (n) and the temperature (T) remain constant in this problem, we can use the combined gas law, which is a rearrangement of the ideal gas law:

P1V1/T1 = P2V2/T2

However, since the temperature is not given, we will assume that it remains constant and use the simplified form of the combined gas law:

P1V1 = P2V2

Solving for P2

Now, we can plug in the given values and solve for P2:

P1V1 = P2V2 (198.0 kPa)(15.35 L) = P2(13.78 L)

To solve for P2, we can divide both sides of the equation by V2:

P2 = (P1V1) / V2 = (198.0 kPa)(15.35 L) / (13.78 L)

Calculating P2

Now, we can calculate the value of P2:

P2 = (198.0 kPa)(15.35 L) / (13.78 L) = 223.5 kPa

Conclusion

In this article, we used the ideal gas law to solve a problem involving a gas with a given initial volume and pressure, and determined the pressure at which the gas would have a different volume. We assumed that the temperature remained constant and used the simplified form of the combined gas law to solve for the final pressure. The final pressure was calculated to be 223.5 kPa.

Real-World Applications

The ideal gas law has numerous real-world applications in fields such as chemistry, physics, and engineering. It is used to calculate the pressure and volume of gases in various systems, such as refrigeration cycles, heat exchangers, and chemical reactors. Understanding the ideal gas law is essential for designing and optimizing these systems.

Limitations of the Ideal Gas Law

While the ideal gas law is a powerful tool for understanding the behavior of gases, it has several limitations. It assumes that the gas molecules are point particles with no volume, which is not true for real gases. It also assumes that the gas molecules interact with each other only through elastic collisions, which is not the case for real gases. Additionally, the ideal gas law does not take into account the effects of temperature and pressure on the gas molecules.

Future Research Directions

Despite its limitations, the ideal gas law remains a fundamental concept in chemistry and physics. Future research directions include developing more accurate models of gas behavior, such as the van der Waals equation, and exploring the applications of the ideal gas law in new fields, such as nanotechnology and biotechnology.

References

  • Atkins, P. W. (2010). Physical chemistry. Oxford University Press.
  • Chang, R. (2010). Physical chemistry for the life sciences. Cambridge University Press.
  • Levine, I. N. (2014). Physical chemistry. McGraw-Hill Education.

Glossary

  • Ideal gas law: A mathematical equation that describes the behavior of gases under various conditions.
  • Combined gas law: A rearrangement of the ideal gas law that takes into account changes in temperature and pressure.
  • Gas constant: A constant that relates the pressure and volume of a gas to its temperature.
  • Mole: A unit of measurement that represents the amount of a substance in terms of its molecular weight.
  • Temperature: A measure of the average kinetic energy of the molecules in a substance.
    Q&A: Understanding the Ideal Gas Law =====================================

In our previous article, we discussed the ideal gas law and its application to a problem involving a gas with a given initial volume and pressure. In this article, we will answer some frequently asked questions about the ideal gas law and provide additional insights into its application.

Q: What is the ideal gas law?

A: The ideal gas law is a mathematical equation that describes the behavior of gases under various conditions. 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 molecules are point particles with no volume, that the gas molecules interact with each other only through elastic collisions, and that the temperature and pressure of the gas remain constant.

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

A: The ideal gas law has several limitations. It does not take into account the effects of temperature and pressure on the gas molecules, and it assumes that the gas molecules are point particles with no volume. Additionally, the ideal gas law does not account for the interactions between gas molecules and the container walls.

Q: When is the ideal gas law applicable?

A: The ideal gas law is applicable when the gas is at low pressure and high temperature, and when the gas molecules are far apart. In these conditions, the gas behaves like an ideal gas, and the ideal gas law can be used to accurately predict its behavior.

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

A: The ideal gas law is used in a wide range of real-world applications, including the design of refrigeration systems, heat exchangers, and chemical reactors. It is also used in the calculation of the pressure and volume of gases in various systems, such as pipelines and storage tanks.

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:

  • Assuming that the gas is at constant temperature and pressure, when in fact it is not.
  • Failing to account for the effects of temperature and pressure on the gas molecules.
  • Using the ideal gas law to calculate the behavior of gases at high pressure and low temperature, when in fact it is not applicable.

Q: What are some alternative models to the ideal gas law?

A: Some alternative models to the ideal gas law include the van der Waals equation, the Redlich-Kwong equation, and the Peng-Robinson equation. These models take into account the effects of temperature and pressure on the gas molecules, and are more accurate than the ideal gas law in certain conditions.

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 using the equation PV = nRT to calculate the pressure and volume of the gas. This can be done by rearranging the equation to solve for the unknown variable, and then plugging in the given values.

Q: What are some real-world examples of the application of the ideal gas law?

A: Some real-world examples of the application of the ideal gas law include:

  • The design of refrigeration systems, which use the ideal gas law to calculate the pressure and volume of the refrigerant gas.
  • The calculation of the pressure and volume of gases in pipelines and storage tanks.
  • The design of chemical reactors, which use the ideal gas law to calculate the pressure and volume of the reactants and products.

Conclusion

In this article, we have answered some frequently asked questions about the ideal gas law and provided additional insights into its application. We have also discussed some common mistakes to avoid when using the ideal gas law, and some alternative models to the ideal gas law. By understanding the ideal gas law and its limitations, we can use it to accurately predict the behavior of gases in various conditions.