High School

Consider two 5.0 L chambers. In one chamber, there are 5.00 g of O₂, and in the other, there are 5.00 g of He. Which chamber has the higher pressure at room temperature?

Answer :

To determine which gas exerts a higher pressure, we can use the ideal gas law equation:

[tex]PV = nRT[/tex]

Where:

  • [tex]P[/tex] is the pressure,
  • [tex]V[/tex] is the volume,
  • [tex]n[/tex] is the number of moles of the gas,
  • [tex]R[/tex] is the ideal gas constant, and
  • [tex]T[/tex] is the temperature.

In this question, both gases are in identical 5.0 L chambers at room temperature, so the volume ([tex]V[/tex]) and temperature ([tex]T[/tex]) can be considered as constants, and we are comparing the pressure based on the number of moles ([tex]n[/tex]) of each gas. The ideal gas constant ([tex]R[/tex]) is also a constant value, so the pressure will depend directly on the number of moles of gas present:

  1. Calculate the number of moles for each gas:

    • For O₂ (oxygen):

      • The molar mass of O₂ is approximately 32.00 g/mol.
      • The number of moles, [tex]n[/tex], is calculated as:

      [tex]n = \frac{5.00 \text{ g}}{32.00 \text{ g/mol}} = 0.15625 \text{ mol}[/tex]

    • For He (helium):

      • The molar mass of He is approximately 4.00 g/mol.
      • The number of moles, [tex]n[/tex], is calculated as:

      [tex]n = \frac{5.00 \text{ g}}{4.00 \text{ g/mol}} = 1.25 \text{ mol}[/tex]

  2. Compare the number of moles:

    Helium (He) has more moles (1.25 mol) compared to oxygen (O₂) (0.15625 mol) for the same mass of gas.

  3. Conclude the pressure comparison:

    Since the number of moles is directly proportional to pressure in the ideal gas law (assuming constant temperature and volume), the chamber with helium (He) will exert a higher pressure than the chamber with oxygen (O₂).

In conclusion, the chamber containing helium (He) has the higher pressure at room temperature.

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