A mixture of hydrogen and oxygen at one bar pressure contains 20% by weight of hydrogen Calculate the partial pressure of hybrogen (b) A sample of gaseous arsine `(AsH_(3))` in a `500 ML` flask at 300 torr and 223 K is heated to 473 K at which `AsH_(3)` decomposes to soild arsenic ahd `H_(2)` fas The flask is then cooled to `273 K` at which the pressure in flask is 508 torr Calculate the % of `AsH_(3)` decomposed .

Explanation

Weight of `H_(2) = 20g` in `100 g` mixture
weight of `O_(2) = 80 g`
`:.` Moles of `H_(2) = (20)/(2) =10`
`:.` Moles of `O_(2) = (80)/(32) = (5)/(2)`
`:.` Total moles ` = 10 + (5)/(2) = (25)/(2)`
`:. P'_(H_(2)) = P_(T) xx` mole fraction of `H_(2)`
`= 1 xx (10)/(25//2) = 0.8` bar
(b) `{:(AsH_(3_((g)))hArr,As_((s))+,(3)/(2)H_(2_((s))),),(n,0,0,),((n-n_(1)),n_(1),(3n_(1))/(2),):}`
`:' P = 300 torr, V =500 mL, T = 223 K`
`:._(AsH_(3) = (PV)/(RT) = (300 xx 500)/(100 xx 0.0821 xx 223) = 8.19`
Also at `273 K n_("mixture") = n_(As) + n_(H_(2))`
`= (PV)/(RT) = (508 xx 500)/(100 xx 0.0821 xx 273) = 11.33`
`:. n-n_(1) + (3n_(1))/(2) = 11.33`
By eqs (i) and (ii) `n_(1) =6.28`
`:. %` decomposition `= (n_(1))/(n) xx 100 = (6.28)/(8.19) xx 100`
`=77.7%` .