What Is The Pressure Of 0.540 Mol Of An Ideal Gas At 35.5 L And 223 K?Use The Formula $PV = NRT$ And $R = 8.314 \, \frac{L \cdot KPa}{mol \cdot K}$.A. 0.715 KPa B. 2.45 KPa C. 28.2 KPa D. 62.7 KPa

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What is the Pressure of 0.540 mol of an Ideal Gas at 35.5 L and 223 K?

Understanding the Ideal Gas Law

The ideal gas law is a fundamental concept in chemistry that describes the behavior of ideal gases. It is a mathematical equation that relates the pressure, volume, and temperature of a gas. The ideal gas law 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.

The Gas Constant (R)

The gas constant (R) is a fundamental constant in the ideal gas law. It is a measure of the energy of a gas and is used to relate the pressure, volume, and temperature of a gas. The value of R is typically expressed in units of L路kPa/mol路K. In this problem, we are given the value of R as 8.314 L路kPa/mol路K.

Given Values

We are given the following values for this problem:

  • n = 0.540 mol (number of moles of the gas)
  • V = 35.5 L (volume of the gas)
  • T = 223 K (temperature of the gas)
  • R = 8.314 L路kPa/mol路K (gas constant)

Solving for Pressure (P)

We can use the ideal gas law equation PV = nRT to solve for the pressure (P) of the gas. Rearranging the equation to solve for P, we get:

P = nRT / V

Substituting the given values, we get:

P = (0.540 mol)(8.314 L路kPa/mol路K)(223 K) / (35.5 L)

Calculating the Pressure

Now, we can calculate the pressure (P) of the gas using the given values and the ideal gas law equation.

P = (0.540 mol)(8.314 L路kPa/mol路K)(223 K) / (35.5 L) P = 62.7 kPa

Conclusion

Therefore, the pressure of 0.540 mol of an ideal gas at 35.5 L and 223 K is 62.7 kPa.

Answer

The correct answer is D. 62.7 kPa.

Discussion

The ideal gas law is a fundamental concept in chemistry that describes the behavior of ideal gases. It is a mathematical equation that relates the pressure, volume, and temperature of a gas. The ideal gas law 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.

The gas constant (R) is a fundamental constant in the ideal gas law. It is a measure of the energy of a gas and is used to relate the pressure, volume, and temperature of a gas. The value of R is typically expressed in units of L路kPa/mol路K.

In this problem, we used the ideal gas law equation PV = nRT to solve for the pressure (P) of the gas. We were given the values of n, V, T, and R, and we used these values to calculate the pressure (P) of the gas.

The ideal gas law is a powerful tool for understanding the behavior of gases. It can be used to calculate the pressure, volume, and temperature of a gas, and it can be used to predict the behavior of gases under different conditions.

Key Takeaways

  • The ideal gas law is a fundamental concept in chemistry that describes the behavior of ideal gases.
  • The ideal gas law 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.
  • The gas constant (R) is a fundamental constant in the ideal gas law. It is a measure of the energy of a gas and is used to relate the pressure, volume, and temperature of a gas.
  • The ideal gas law can be used to calculate the pressure, volume, and temperature of a gas, and it can be used to predict the behavior of gases under different conditions.

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.
    Ideal Gas Law Q&A

Frequently Asked Questions About the Ideal Gas Law

The ideal gas law is a fundamental concept in chemistry that describes the behavior of ideal gases. It is a mathematical equation that relates the pressure, volume, and temperature of a gas. 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 describes the behavior of ideal gases. 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 is the gas constant (R)?

A: The gas constant (R) is a fundamental constant in the ideal gas law. It is a measure of the energy of a gas and is used to relate the pressure, volume, and temperature of a gas. The value of R is typically expressed in units of L路kPa/mol路K.

Q: How do I use the ideal gas law to solve problems?

A: To use the ideal gas law to solve problems, you need to know the values of the variables in the equation. You can then plug these values into the equation and solve for the unknown variable. For example, if you know the pressure, volume, and temperature of a gas, you can use the ideal gas law to calculate the number of moles of the gas.

Q: What are some common applications of the ideal gas law?

A: The ideal gas law has many common applications in chemistry and physics. Some examples include:

  • Calculating the pressure of a gas in a container
  • Determining the volume of a gas in a container
  • Calculating the temperature of a gas in a container
  • Determining the number of moles of a gas in a container
  • Calculating the energy of a gas in a container

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:

  • Not converting units correctly
  • Not using the correct value of the gas constant (R)
  • Not plugging in the correct values for the variables in the equation
  • Not solving for the correct variable

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

A: The ideal gas law has many real-world applications. Some examples include:

  • Calculating the pressure of a gas in a scuba tank
  • Determining the volume of a gas in a balloon
  • Calculating the temperature of a gas in a refrigerator
  • Determining the number of moles of a gas in a container
  • Calculating the energy of a gas in a container

Q: How does the ideal gas law relate to other areas of chemistry?

A: The ideal gas law is a fundamental concept in chemistry that relates to many other areas of chemistry. Some examples include:

  • Thermodynamics: The ideal gas law is a key concept in thermodynamics, which is the study of the relationships between heat, work, and energy.
  • Kinetics: The ideal gas law is used to calculate the rates of chemical reactions.
  • Equilibrium: The ideal gas law is used to calculate the equilibrium constants of chemical reactions.

Q: What are some common misconceptions about the ideal gas law?

A: Some common misconceptions about the ideal gas law include:

  • The ideal gas law only applies to ideal gases, not real gases.
  • The ideal gas law only applies to gases at high temperatures and low pressures.
  • The ideal gas law is only used in chemistry, not in physics.

Conclusion

The ideal gas law is a fundamental concept in chemistry that describes the behavior of ideal gases. It is a mathematical equation that relates the pressure, volume, and temperature of a gas. In this article, we have answered some frequently asked questions about the ideal gas law, including its definition, applications, and common mistakes to avoid. We hope that this article has been helpful in understanding the ideal gas law and its many applications in chemistry and physics.