9 " mL of " a mixture of methane and ethylene was exploded with 30 mL (excess) of oxygen. After cooling, the volume was 21.0 mL. Further treatment with caustic potash solution reduced the volume to 7.0 mL. Determine the composition of the mixture.

Answer

`(b) 50`

Explanation

`CH_(4)+2O_(2)rarrCO_(2)+2H_(2)O`
`a" "2a" "a`
`C_(n)H_(2n-2)+((3n-1)/(2))O_(2)rarrnCO_(2)+(n-1)H_(2)O`
`(20-a)((3n-1)/(2))(20-a)n(20-a)`
For methane `a+n(20-a)=40….(1)`
For oxygen
`[100-2a-((3n-1)/(2))(20-a)]=40`
`2a+((3n-1)/(2))(20-a)=60`
`2a+30n-1.5na-10+0.5a=60`
`2.5a-1.5na+30n-70`
`2.5a-1.5n(a-20)=70`
`2.5a+1.5n(20-a)=70 " "...(2)`
from `(1)&(2)`
`a=10`
`n=3`
`C_(3)H_(4)`
`%` composition `rarr 50%`