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Question: The normal boiling point of toluene is nearly \({110.7^ \circ }\;C\) and its boiling point elevation...

The normal boiling point of toluene is nearly 110.7  C{110.7^ \circ }\;C and its boiling point elevation constant is 3.32  K  kg  mol13.32\;K\;kg\;mo{l^{ - 1}}. The enthalpy of vaporization of toluene is nearly
(A) 17  KJ  mol117\;KJ\;mo{l^{ - 1}}
(B) 21  KJ  mol121\;KJ\;mo{l^{ - 1}}
(C) 51  KJ  mol151\;KJ\;mo{l^{ - 1}}
(D) 68  KJ  mol168\;KJ\;mo{l^{ - 1}}

Explanation

Solution

The enthalpy of vaporisation and the boiling point elevation constant are related by the equation derived from the references from Raoult’s law. We need to find the enthalpy of evaporation through that relationship. All other parameters are given such as boiling point and the boiling point elevation constant.

Complete step by step solution: We know that the relation between molal elevation constant Kb{K_b} and enthalpy of vaporisation is given by
Kb=MRTb21000Evap{K_b} = \dfrac{{MRT_b^2}}{{1000{E_{vap}}}} where Kb{K_b} is the molal elevation constant
M is the molar mass of the molecule
Tb{T_b} is the boiling point
R is the universal gas constant
Evap{E_{vap}} is the enthalpy of evaporation
So we have been provided with the following information
Kb{K_b}=3.32  K  kg  mol13.32\;K\;kg\;mo{l^{ - 1}}
Tb=110.7  C{T_b} = {110.7^ \circ }\;C =110.7+273=383.7  K = 110.7 + 273 = 383.7\;K
R=8.314  Nm  K1R = 8.314\;Nm\;{K^{ - 1}}
Boiling point elevation constant is given by
Kb=MRTb21000Evap{K_b} = \dfrac{{MRT_b^2}}{{1000{E_{vap}}}}
So putting the given values in the equation we get
Evap=92×8.314×(383.7)21000×3.32{E_{vap}} = \dfrac{{92 \times 8.314 \times {{(383.7)}^2}}}{{1000 \times 3.32}}
Evap=33.834  KJ  mol1\Rightarrow {E_{vap}} = 33.8 \approx 34\;KJ\;mo{l^{ - 1}}
Therefore the enthalpy of vaporisation is approximately 34  KJ  mol134\;KJ\;mo{l^{ - 1}}

Hence, none of the options is correct.

Note: Here the temperatures are present in degree celsius which should be converted to kelvin before applying into the formula. Also, the enthalpy of evaporation of a liquid is proportional to the thermodynamic temperature at which the liquid boils. This is termed as Trouton’s rule. In the given concept it is useful to write the concentration in terms of molality instead of mole fraction while the derivation of the equation.