Gaseous benzene reacts with hydrogen gas in presence of a nickel catalyst to form gaseous cyclohexane according to the reaction:
`C_(6)H_(6) (g) + 3H_(2) (h) rArr C_(6) H_(12) (g)`
A mixture of `C_(6)H_(6)` and excess `H_(2)` has a pressure of 60 mm of Hg in an unknown volume. After the gas has been passed over a nickel catalyst and all the benzene converted to cyclohexane, the pressure of the gas was 30 mm of Hg in the same volume and temperature. The fraction of `C_(6)H_(6)` (by volume) present in the original mixture is :

Options

A. `½`
B. `¼`
C. `.^(1)//_(5)`
D. `.^(1)//_(6)`

Answer

D

Explanation

Suppose initially, pressure of `C_(6) H_(6) (g) = P_(1) nm` and that of `H_(2) (g)= P_(2) mm`.
`:. P_(1) + P_(2) = 60 mm` … (1)
After the reaction Pressure of `C_(6) H_(6) (g) = 0`
Pressure of `H_(2) (g) = P_(2) - 3P_(1)` Pressure of `C_(6)H_(12) (g) = P_(1)`
Total pressure `= P_(2) - 3P_(1) + P_(1) = 30 mm`
Or, `P_(2) - 2P_(1) = 30 mm` … (2)
Solving (1) & (2) we get :`P_(1) = 10mm, P_(2) = 50 mm`
Fraction of `C_(6)H_(6) (g)` by volume = Fraction of moles = Fraction of pressures `= (10)/(60) = (1)/(6)`