Chem Problem: density of a gas of unknown molar mass was measured as a function of pressure at 0,Determine a precise molar mass for the gas.?

The density of a gas of unknown molar mass was measured as a function of pressure at 0 ∘C, as in the table below.

1. Determine a precise molar mass for the gas. Hint: Graph d/P versus P.

2. Why is d/P not a constant as a function of pressure?

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1 Answer

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  • Dr W
    Lv 7
    1 month ago

    plot d/P vs P???

    here's how I would do it

    ******

    starting with these 2 equations

    .. PV = nRT.. .. . ... ideal gas law

    .. mw = mass / n.. . definition of molar mass (mw)

    subbing and rearranging

    .. PV = (mass / mw) RT

    .. P = (RT/mw) * (mass / V)

    since density (ρ) = mass / V

    .. P = (RT/mw) * ρ

    that's a linear equation if we plot P vs ρ slope = RT/mw

    see the attached plot

    and we know slope = RT/mw so that

    .. RT/mw = 0.4354 atm/(g/L) = 0.4354 Latm / g

    .. mw = RT * (1g / 0.4354 Latm)

    .. mw = 0.08206 Latm/molK * 273.15K * (1g / 0.4354Latm) = 51.48g/mol

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