The enthalpy of vapourisation of liquid diethyl ether `(C_(2)H_(5))_(2)O` is `26.0 kJ mol^(-1)` at its boiling point (`25.0^(@)C`). Calculate `DeltaS^(@)` for the conversion of
(a) liquid to vapour and
(b) vapour to liquid at `35^(@)C`.

Explanation

(a) For vaporisation of diethyl ether: `therefore Delta_(vap)S^(@) = (Delta_(vap)H^(@))/(T)`
`Delta_(vap)H^(@) = 26.0 kJ mol^(-1), T = 273 + 35 = 308 K`
`therefore Delta_(vap)S^(@) = (26.0 xx 10^(3)Jmol^(-1))/(308K) = 84.4 J K^(-1) mol^(-1)` .
(b) The conversion of vapour into liquid is condensation. The enthalpy of condensation is negative of enthalpy of vaporisation. `Delta_(vap)H^(@) = -Delta_(cond)H^(@)`
`therefore` For condensation of diethyl ether (i.e., conversion of vapour to liquid)
`Delta_(cond)S^(@) = (Delta_(cond)H^(@))/(T) = (-26.0 xx 10^(3)mol^(-1))/(308) = -84.4 J K^(-1) mol^(-1)`.