The enthalpy of tetramerization on X in gas phase `(4X(g) ® X_(4)(g)) " is" -100` kJ/mol at 300K. The enthalpy of vaporisation for liquid X and `X_(4)` are respectively 30kJ/mol and 72 kJ/mol respectively. DS for tetramerization of X in liquid phase is `-125` J/K mol at 300K. What is the DG at 300K for tetramerization of X in liquid phase?

Options

A. `-52` kJ/mol
B. `-89.5` kJ/mol
C. `-14.5` kJ/mol
D. none of these

Answer

C

Explanation

The required `R xx n` is
`4X_((l)) rarr X_(4(l))` …(1)
The given reaction are
`X_((l)) rarr X_((g)) , Delta H = 30` …(2)
`X_(4(l)) rarr X_(4(g)), Delta H = 72` …(3)
`4X_((g)) rarr X_(4(g)) , Delta H = - 100` …(4)
So `Delta H` for reaction (1)
`=4(Delta H_(2)) + Delta H_(4) - Delta H_(3)`
`= 4(30) + 4(72) - 100= 308` kJ/mole
`Delta S = - 125` J/K mole
So, `Delta G = Delta H - T Delta S = -52- ((300) - (-125))/(100) = 14.5kJ//mol`