Help with perfect gas question?

Question

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.

Answer 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