(1) Calculate moles of N_{2}:

$\overline{){\mathbf{PV}}{\mathbf{=}}{\mathbf{nRT}}}\phantom{\rule{0ex}{0ex}}\mathbf{n}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{PV}}{\mathbf{RT}}\mathbf{=}\frac{(1\overline{)\mathrm{atm}})(4\overline{)L})}{(0.08206{\displaystyle \frac{\overline{)L\mathrm{atm}}}{\mathrm{mol}\overline{)K}}})(273\overline{)K})}$

n = 0.1786

(2) Calculate moles of H_{2}:

$\overline{){\mathbf{PV}}{\mathbf{=}}{\mathbf{nRT}}}\phantom{\rule{0ex}{0ex}}\mathbf{n}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{PV}}{\mathbf{RT}}\mathbf{=}\frac{\mathbf{(}\mathbf{1}\mathbf{}\overline{)\mathbf{atm}}\mathbf{)}\mathbf{(}\mathbf{2}\mathbf{}\overline{)\mathbf{L}}\mathbf{)}}{\mathbf{(}\mathbf{0}\mathbf{.}\mathbf{08206}\mathbf{}{\displaystyle \frac{\overline{)L\mathrm{atm}}}{\mathrm{mol}\overline{)K}}}\mathbf{)}\mathbf{(}\mathbf{273}\mathbf{}\overline{)\mathbf{K}}\mathbf{)}}$

A 4.0-L vessel containing N_{2} at STP and a 2.0-L vessel containing H_{2} at STP are connected by a valve. If the valve is opened allowing the two gases to mix, what is the mole fraction of hydrogen in the mixture?

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