Physics

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A container of volume 19.4 cm3 is initially filled with air. The container is then evacuated at 0oC to a pressure of 6.0 mPa. How many molecules are in the container after evacuation if we assume that air is an ideal gas?

  • Physics -

    Since the gas is ideal, we can use the Ideal Gas Law:
    PV = nRT
    where
    P = pressure in atm
    V = volume in L
    n = number of moles of air
    R = universal gas constant = 0.0821 L-atm/mol-K
    T = temperature in K

    We first convert the given in the appropriate units:
    V = 19.4 cm^3
    cm^3 is also equal to mL. Thus there are 1000 cm^3 for every 1 L, or
    V = 19.4 / 1000 = 0.0194 L

    P = 6 mPa
    The conversion is: 101325 Pa = 1 atm, thus
    P = (6 / 1000) / 101325 =

    T = 0 C
    We just add 273 to make it Kelvin:
    T = 0 + 273 = 273 K

    Substituting to the equation:
    PV = nRT
    n = PV/RT
    n = (5.92 10^-8)(0.0194) / (0.0821)(273)
    n = 5.125 * 10^-11 moles

    Note that this is only the moles. To get the number of molecules, note that 1 mol = 6.022 * 10^23 representative particles. Thus,
    5.125 * 10^-11 * 5.125 * 10^-11
    = 3.087 * 10^13 molecules
    Check the significant figures.

    Hope this helps :3

  • Physics -

    *lol sorry, in the last calculation that should be
    5.125 * 10^-11 * 6.022 * 10^23
    but the answer is still the same. :)

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