20.0 g each of helium and an unknown diatomic gas are combined in a 1500. ml container. lf the temperature is 298 K, and the pressure inside is 86.11 atm, what is the unknown gas?

1 Answer
anor277
Dec 15, 2016

We assume (possibly unreasonably) ideality, and get......Cl2, molecular chlorine, as the unknown gas..........

Explanation:

P=nRTV........

And solve for n=PVRT

= 86.11⋅atm×1.500⋅L0.0821⋅L⋅atm⋅K−1⋅mol−1×298⋅K

n=5.28⋅mol

But n=nHe+nunknown gas,

i.e. 5.28⋅mol=20⋅g4⋅g⋅mol−1+nunknown gas

And thus nunknown gas=(5.28−5)⋅mol=0.280⋅mol.

And thus molecular mass of unknown gas = 20⋅g0.280⋅mol=71.5⋅g⋅mol−1.

And clearly, since the gas is diatomic, i.e. X2, X has an atomic mass of ≅35.5⋅g⋅mol−1, and thus (finally!) X=Cl, which certainly forms a Cl2 molecule as required.

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