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Chemistry Question on States of matter

Equal weights of methane and hydrogen are mixed in an empty container at 25∘25^\circ C The fraction of the total pressure exerted by hydrogen is

A

12\frac{1}{2}

B

89\frac{8}{9}

C

1817\frac{18}{17}

D

1617\frac{16}{17}

Answer

89\frac{8}{9}

Explanation

Solution

The correct option is(B): 89\frac{8}{9}.

Let .v grams of each hydrogen and methane are mixed
               Moles of H2=x2\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, Moles\, of\, H_2=\frac{x}{2}
               Moles of CH4=x16\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, Moles\, of\, CH_4=\frac{x}{16}
⇒      MolefractionofH2=x2x2+x16=89\Rightarrow \, \, \, \, \, \, Mole fraction of H_2 =\frac{\frac{x}{2}}{\frac{x}{2}+\frac{x}{16}}=\frac{8}{9}
⇒    Partial pressure of H2Total pressure=Mole fraction of H2=89\Rightarrow \, \, \, \, \frac{Partial\, pressure\, of\, H_2}{Total\, pressure }=Mole\, fraction\, of\, H_2=\frac{8}{9}