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23 January, 15:36

A 1.40 L sample of O2 at 645 Torr and 25 °C, and a 0.751 L sample of N2 at 1.13 atm and 25 °C, are both transferred to the same 2.00 L container at 25 °C. What are the partial pressures of the two gases and the total pressure inside the 2.00 L container? Show your work.

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  1. 23 January, 19:28
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    P (O₂) = 0.595 atm P (N₂) = 0.424 atm Total Pressure = 1.019 atm

    Explanation:

    To solve this problem we use PV=nRT for both gases in their containers, in order to calculate the moles of each one:

    O₂:

    645 Torr ⇒ 645 / 760 = 0.85 atm

    25°C ⇒ 25 + 273.16 = 298.16 K

    0.85 atm * 1.40 L = n * 0.082 atm·L·mol⁻¹·K⁻¹ * 298.16 K

    n = 0.0487 mol O₂

    N₂:

    1.13 atm * 0.751 L = n * 0.082 atm·L·mol⁻¹·K⁻¹ * 298.16 K

    n = 0.0347 mol N₂

    Now we can calculate the partial pressure for each gas in the new container, because the number of moles did not change:

    O₂:

    P (O₂) * 2.00 L = 0.0487 mol O₂ * 0.082 atm·L·mol⁻¹·K⁻¹ * 298.16 K

    P (O₂) = 0.595 atm

    N₂:

    P (N₂) * 2.00 L = 0.0347 mol N₂ * 0.082 atm·L·mol⁻¹·K⁻¹ * 298.16 K

    P (N₂) = 0.424 atm

    Finally we add the partial pressures of all gases to calculate the total pressure:

    Pt = 0.595 atm + 0.424 atm = 1.019 atm
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