What Quantity In Moles Of Hydrogen Gas At 150.0 ∘ C 150.0^{\circ} C 150. 0 ∘ C And 23.3 Atm Would Occupy A Vessel Of 4.80 L?

by ADMIN 125 views

What quantity in moles of hydrogen gas at 150.0∘C150.0^{\circ} C and 23.3 atm would occupy a vessel of 4.80 L?

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 the pressure, volume, and temperature of hydrogen gas, and we need to find the number of moles of the gas.

Converting Temperature to Kelvin

Before we can use the ideal gas law, we need to convert the temperature from Celsius to Kelvin. The formula for this conversion is: T(K) = T(°C) + 273.15. Substituting the given temperature, we get: T(K) = 150.0°C + 273.15 = 423.15 K.

Using the Ideal Gas Law

Now that we have the temperature in Kelvin, we can use the ideal gas law to find the number of moles of hydrogen gas. Rearranging the equation to solve for n, we get: n = PV / RT. Substituting the given values, we get: n = (23.3 atm)(4.80 L) / (0.08206 L atm/mol K)(423.15 K).

Calculating the Number of Moles

Now, let's calculate the number of moles of hydrogen gas using the values we have substituted into the equation. First, we need to calculate the product of the pressure and volume: (23.3 atm)(4.80 L) = 111.84 L atm. Next, we need to calculate the product of the gas constant and temperature: (0.08206 L atm/mol K)(423.15 K) = 34.73 L atm/mol. Finally, we can divide the product of the pressure and volume by the product of the gas constant and temperature to get the number of moles: n = 111.84 L atm / 34.73 L atm/mol = 3.21 mol.

Conclusion

In this problem, we used the ideal gas law to find the number of moles of hydrogen gas at a given pressure, volume, and temperature. We converted the temperature from Celsius to Kelvin and then used the ideal gas law to calculate the number of moles. The result is 3.21 mol of hydrogen gas.

Understanding the Significance of 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 a powerful tool for predicting the behavior of gases and is used in a wide range of applications, from the design of gas tanks to the understanding of the behavior of gases in the atmosphere.

Real-World Applications of the Ideal Gas Law

The ideal gas law has many real-world applications, including:

  • Designing Gas Tanks: The ideal gas law is used to design gas tanks that can safely store gases under high pressure.
  • Understanding Atmospheric Behavior: The ideal gas law is used to understand the behavior of gases in the atmosphere, including the behavior of greenhouse gases.
  • Predicting Gas Behavior: The ideal gas law is used to predict the behavior of gases under various conditions, including temperature, pressure, and volume.

Common Mistakes to Avoid

When using the ideal gas law, there are several common mistakes to avoid, including:

  • Not Converting Temperature to Kelvin: Failing to convert temperature from Celsius to Kelvin can lead to incorrect results.
  • Not Using the Correct Values for the Gas Constant: Using the wrong value for the gas constant can lead to incorrect results.
  • Not Rounding Results Correctly: Failing to round results correctly can lead to incorrect conclusions.

Conclusion

In conclusion, the ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is a powerful tool for predicting the behavior of gases and is used in a wide range of applications. By understanding the ideal gas law and avoiding common mistakes, we can use it to make accurate predictions about the behavior of gases.

Additional Resources

For more information on the ideal gas law, including tutorials, examples, and practice problems, see the following resources:

  • ChemGuide: A comprehensive guide to the ideal gas law, including tutorials, examples, and practice problems.
  • Khan Academy: A video tutorial on the ideal gas law, including examples and practice problems.
  • Wolfram Alpha: A online calculator that can be used to solve problems involving the ideal gas law.

References

Frequently Asked Questions

The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. Here are 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 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 units of the ideal gas law?

A: The units of the ideal gas law are:

  • Pressure (P): atm (atmospheres)
  • Volume (V): L (liters)
  • Number of moles (n): mol (moles)
  • Gas constant (R): L atm/mol K (liters atmospheres per mole Kelvin)
  • Temperature (T): K (Kelvin)

Q: What is the gas constant (R)?

A: The gas constant (R) is a mathematical constant that relates the pressure, volume, and temperature of a gas. It is approximately equal to 0.08206 L atm/mol K.

Q: How do I convert temperature from Celsius to Kelvin?

A: To convert temperature from Celsius to Kelvin, you can use the following formula: T(K) = T(°C) + 273.15.

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

A: To use the ideal gas law to solve problems, you can rearrange the equation to solve for the unknown variable. For example, if you are given the pressure, volume, and temperature of a gas, you can use the equation: n = PV / RT to find the number of moles of the gas.

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 temperature to Kelvin
  • Not using the correct values for the gas constant
  • Not rounding results correctly

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

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

  • Designing gas tanks
  • Understanding atmospheric behavior
  • Predicting gas behavior

Q: How do I calculate the number of moles of a gas using the ideal gas law?

A: To calculate the number of moles of a gas using the ideal gas law, you can use the equation: n = PV / RT. Simply substitute the given values into the equation and solve for n.

Q: What is the significance of 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 a powerful tool for predicting the behavior of gases and is used in a wide range of applications.

Q: How do I use the ideal gas law to solve problems involving gases at different temperatures?

A: To use the ideal gas law to solve problems involving gases at different temperatures, you can use the equation: n = PV / RT. Simply substitute the given values into the equation and solve for n, taking into account the temperature of the gas.

Q: What are some common problems that can be solved using the ideal gas law?

A: Some common problems that can be solved using the ideal gas law include:

  • Finding the number of moles of a gas given the pressure, volume, and temperature
  • Finding the pressure of a gas given the number of moles, volume, and temperature
  • Finding the volume of a gas given the number of moles, pressure, and temperature

Q: How do I use the ideal gas law to solve problems involving gases at different pressures?

A: To use the ideal gas law to solve problems involving gases at different pressures, you can use the equation: n = PV / RT. Simply substitute the given values into the equation and solve for n, taking into account the pressure of the gas.

Q: What are some common mistakes to avoid when using the ideal gas law to solve problems involving gases at different pressures?

A: Some common mistakes to avoid when using the ideal gas law to solve problems involving gases at different pressures include:

  • Not using the correct values for the gas constant
  • Not rounding results correctly
  • Not taking into account the pressure of the gas

Q: How do I use the ideal gas law to solve problems involving gases at different volumes?

A: To use the ideal gas law to solve problems involving gases at different volumes, you can use the equation: n = PV / RT. Simply substitute the given values into the equation and solve for n, taking into account the volume of the gas.

Q: What are some common mistakes to avoid when using the ideal gas law to solve problems involving gases at different volumes?

A: Some common mistakes to avoid when using the ideal gas law to solve problems involving gases at different volumes include:

  • Not using the correct values for the gas constant
  • Not rounding results correctly
  • Not taking into account the volume of the gas

Conclusion

The ideal gas law is a fundamental concept in chemistry that describes the behavior of gases under various conditions. It is a powerful tool for predicting the behavior of gases and is used in a wide range of applications. By understanding the ideal gas law and avoiding common mistakes, you can use it to solve a wide range of problems involving gases.