1.

An organic compound `C_xH_(2y)O_y` was burnt with twice the amount of oxygen needed for complete combustion to `CO_2` and `H_2O`. The hot gases when cooled to `0^@C` and 1 atm pressure, measured `2.24` litre. The water collected during cooling weighed 0.9 gm. the vapour pressure of pure water at `20^@C` is 17.5 mm Hg and is lowered by 0.104 mm when 50 gm of the organic compound is dissolved in 1000 gm of water. Give the molecular formula of the organic compound.

Answer» Correct Answer - `C_(5)H_(10)O_(5)`
`C_xH_(2y)O_y+2xO_2 hArrxCO_2+yH_2O+xO_2`
After cooling only `CO_(2)` and `O_(2)` are present because water is in liquid form.
Thus, moles of gases after cooling =`x + x =2x`
Volume of gases after cooling =`2.24 L`
`2x=2.24 L`
`x=1.12 L`
Number of moles of `CO_(2)=1.12/2.24 =0.5 mol`
Hence, the empirical formula of organic compound is `C(H_(2)O)`
Given, Vapour pressure of pure water `(P^(@))=17.5 mm Hg`
Lowering of vapour pressure `(P^(@)-P)=0.104 mm Hg`
weight of solute `(W_(2)) =50 g`
weight of solvent `(W_(1)) =1000 g`
`(P^(@)-P)/ P^(@)=(W_(2) xx Mw_(1))/(Mw_(1) xx W_(1))`
`0.104/17.5=(50 xx 18)/(Mw_(2) xx 1000)`
`Mw_(2)=(900 xx 17.5)/104=151.4 g`
Empirical formula weight =`C(H_(2)O)`
=`12 +2 +16 =30`
Molecular weight (m)=151.4 g`
`n=("Molecular weight")/("Empirical formula weight")`
=`151.4/30 =5.04 =5`
Thus, molecular formula =`[C(H_(2)O]_(5)=C_(5)H_(10)O_(5)`


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