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Help with perfect gas question?

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Show that a mixture of gases with molar concentrations ηA=nA /(nA + nB) and ηB = nB /(nA + nB ) behaves like a perfect gas with mean molecular weight M = ηA MA + ηB MB . (i.e. derive the expression relating total pressure pA + pB to total density ρA + ρB and identify the effective gas constant).

(η is molar concentration, n is number of molecules per unit volume, M is molecular weight, p is pressure, ρ is density)

Any help with this? Thanks.

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  1. 1  pA V = nA RT

    2  pB V = nB RT

    3  ÃÂA = nA MA / V  

    4  ÃÂB = nB MB / V

    Rearrange 3 and 4 for nA and nB

    Substitute these expressions for nA and nB into 1 and 2.

    Add 1 and 2.

    P= pA + pB

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