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The dissolution of ammonium chloride in water is an endothermic reaction, yet it is a spontaneous process. This is due to the fact that:
A.\[\Delta H\] is +ve, \[\Delta S\] is –ve.
B.\[\Delta H\] is -ve, \[\Delta S\] is +ve.
C.\[\Delta H\] is +ve, \[\Delta S\] is +ve and \[\Delta H < T\Delta S\]
D. \[\Delta H\] is +ve and\[\;\Delta H\; > T{\text{ }}\Delta S\].

Answer Verified Verified
Hint: An endothermic reaction is a reaction in which heat is absorbed and the system feels cold. A spontaneous process is a process which goes in the forward direction and a non-spontaneous process is a process which goes in a backward direction.\[\Delta H\] and \[\Delta S\] are thermodynamic parameters.

Complete step by step answer:
According to Gibbs free energy equation:
\[\Delta G{\text{ }} = {\text{ }}\Delta H - T\Delta S\]
\[\Delta G\] = Gibbs free energy change
\[\Delta H\] = enthalpy change
\[T\] = temperature
\[\Delta S\] = entropy change
The conditions for a process to be spontaneous are:
\[\Delta G < 0\] or \[\Delta G\] should always be negative.
For an endothermic reaction \[\Delta H{\text{ }} > {\text{ }}0\]or \[\Delta H\] is positive.
So for \[\Delta G\] to be negative, \[\Delta S\]must be positive and the \[T{\text{ }}\Delta S\] must be greater than \[\Delta H\] as the latter is positive.
Now considering the dissolution of \[N{H_4}Cl\], it is an endothermic reaction. Thus \[\Delta H{\text{ }} > {\text{ }}0\]or \[\Delta H\] is positive.
So \[\Delta S\] must be positive and the value of \[T{\text{ }}\Delta S\]must be greater than\[\Delta H\]. The dissolution of \[N{H_4}Cl\] results in a favorable increase of entropy which overcomes the enthalpy change during the dissolution. As a result \[T{\text{ }}\Delta S\] become negative and the total of \[\Delta H - T\Delta S\] is negative. Hence \[\Delta G\]is negative. This accounts for the favorable dissolution of ammonium chloride in water.


Note:
Unlike endothermic reaction, an exothermic reaction \[\Delta H\]is always negative and it makes the reaction go spontaneous. The change in entropy does not affect the spontaneity of the exothermic reaction.