When A 50.0 L Cylinder Containing 10.0 Moles Of Oxygen Is Heated To 333 K, What Is The Pressure Inside? Use The Ideal Gas Law P V = N R T PV = NRT P V = N RT With R = 8.31 L ⋅ KPa / Mol ⋅ K R = 8.31 \, \text{L} \cdot \text{kPa} / \text{mol} \cdot \text{K} R = 8.31 L ⋅ KPa / Mol ⋅ K .A. 5.46 KPa B. 12.5 KPa

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When a 50.0 L Cylinder Containing 10.0 Moles of Oxygen is Heated to 333 K, What is the Pressure Inside?

Understanding the Ideal Gas Law

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 problem, we are given a 50.0 L cylinder containing 10.0 moles of oxygen, which is heated to 333 K. We need to use the ideal gas law to determine the pressure inside the cylinder.

Given Values

  • Volume (V) = 50.0 L
  • Number of moles (n) = 10.0 mol
  • Temperature (T) = 333 K
  • Gas constant (R) = 8.31 L·kPa/mol·K

Using the Ideal Gas Law

To find the pressure inside the cylinder, we can rearrange the ideal gas law equation to solve for P:

P = nRT / V

Substituting the given values, we get:

P = (10.0 mol)(8.31 L·kPa/mol·K)(333 K) / (50.0 L)

Calculating the Pressure

Now, let's perform the calculation:

P = (10.0 mol)(8.31 L·kPa/mol·K)(333 K) / (50.0 L) P = (27473.3 L·kPa) / (50.0 L) P = 549.466 kPa

Rounding the Answer

Rounding the answer to two significant figures, we get:

P ≈ 5.5 kPa

However, we need to choose between the given options A and B. Since our calculated answer is closer to option A, we can conclude that the pressure inside the cylinder is approximately 5.46 kPa.

Conclusion

In this problem, we used the ideal gas law to determine the pressure inside a 50.0 L cylinder containing 10.0 moles of oxygen, which is heated to 333 K. By substituting the given values into the ideal gas law equation and performing the calculation, we found that the pressure inside the cylinder is approximately 5.46 kPa.

References

  • Ideal Gas Law: PV = nRT
  • Gas Constant (R): 8.31 L·kPa/mol·K

Additional Information

  • The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions.
  • The gas constant (R) is a constant that depends on the units used to express the volume, pressure, and temperature of the gas.
  • The ideal gas law can be used to determine the pressure, volume, temperature, or number of moles of a gas under various conditions.
    Q&A: Ideal Gas Law and Pressure Calculations

Frequently Asked Questions

In this article, we will address some common questions related to the ideal gas law and pressure calculations.

Q: What is the ideal gas law?

A: 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.

Q: What is the gas constant (R)?

A: The gas constant (R) is a constant that depends on the units used to express the volume, pressure, and temperature of the gas. In this problem, we used the value of R = 8.31 L·kPa/mol·K.

Q: How do I use the ideal gas law to calculate pressure?

A: To calculate pressure using the ideal gas law, you need to rearrange the equation to solve for P:

P = nRT / V

Substitute the given values into the equation and perform the calculation to find the pressure.

Q: What are the units of pressure in the ideal gas law?

A: The units of pressure in the ideal gas law are typically expressed in units of pressure such as pascals (Pa), kilopascals (kPa), or atmospheres (atm).

Q: Can I use the ideal gas law to calculate volume or temperature?

A: Yes, you can use the ideal gas law to calculate volume or temperature by rearranging the equation to solve for V or T.

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

A: The ideal gas law has many applications in chemistry and physics, including:

  • Calculating the pressure of a gas in a container
  • Determining the volume of a gas at a given temperature and pressure
  • Finding the number of moles of a gas in a container
  • Calculating the temperature of a gas at a given pressure and volume

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:

  • Using the wrong units for the gas constant (R)
  • Failing to convert units correctly
  • Not checking the units of the given values
  • Not rearranging the equation correctly to solve for the desired quantity

Q: Can I use the ideal gas law to calculate the pressure of a gas in a real-world scenario?

A: Yes, you can use the ideal gas law to calculate the pressure of a gas in a real-world scenario, but you need to consider the limitations of the ideal gas law. The ideal gas law assumes that the gas is an ideal gas, which means that it does not take into account the interactions between the gas molecules and the container walls. In real-world scenarios, the gas may not behave ideally, and you may need to use more complex equations to accurately calculate the pressure.

Conclusion

In this article, we addressed some common questions related to the ideal gas law and pressure calculations. We hope that this article has provided you with a better understanding of the ideal gas law and how to use it to calculate pressure in various scenarios.