A mixture of ethane and ethene occupies 41 L at atm and 500 K. The mixture reacts compeletly with 10/3 mole of oxygen to produce `CO_(2)` and water. The mole fraction of ethane and ethene in the mixture are (R=0.0821L atm `K^(-1)mol^(-1)` respectively

Options

A. 0.50, 0.50
B. 0.75, 0.25
C. 0.67, 0.33
D. 0.25, 0.75

Answer

C

Explanation

412 at 1 atm, 500 K `=T_(1)`, L at 1 atm, 273 K at STP
`(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))`
`(1xx41)/(500)=(1xxV)/(273)` or `V=22.4L, L = 1` mole
`C_(4)H_(6)+7//2O_(2)to2CO_(2)+3H_(2)O`
`C_(2)H_(4)+3O_(2)to2CO_(2)+2H_(2)O`
Suppose `C_(2)H_(6)` = x moles `:. C_(2)H_(4) = 1-x` mole
`O_(2)` consumed `=(7x)/(2)+3(1-x)`
`=3+x//2=(10)/(3)`(Given)
or `x=2[(10)/(3)-3]=2//3=0.67`