10 " mL of " a gaseous organic compound containing C, H and O only was mixed with 100 " mL of " `O_(2)` and exploded under condition which allowed the `H_(2)O` formed to condense. The volume of the gas after explosion was 90 mL. On treatment with KOH solution, a further contraction of 20 mL in volume was observed. The vapour density of the compound is 23. All volume measurements were made under the same condition.
Q.The molecular formula of the compound is

Answer

`C_(2)H_(6)O`

Explanation

`C_(x)H_(y)O_(z)+(x+(y)/(4)-(z)/(2))O_(2)rarrxCO_(2)+(y)/(2)H_(2)O`
Given vol. `10mL" "+" "100mL" " 0" "+0`
After reaction `-" "+ 100-10(x+(y)/(4)-(z)/(2))10x-`
`100-10(x+(y)/(4)-(z)/(2))+10x=90`
`(y)/(4)-(z)/(2)=1`
`y-2z=4 " "(1)`
Property of `KOH` has absorbed all `CO_(2^(.))`
`therefore 10x=20`
`x=2`
`V.D`. of compound `(C_(x)H_(y)O_(z))=23" "because V.D. = (M_(w))/(2)`
`M_(w)=46 " "M_(w)2xx23=46`
`12x+y+16z=46`
`12xx2+y+16z=46`
`y+16z=22" "...(2)`
from `(aq). (1) & (2)`
`{:(,y-2z=4),(,y+16z=22),(-, "- -"),(,bar(" -18z=-18")):}`
`z=1,y=6`
Molecular formula `= C_(2)H_(6)O`.