Question

When ammonium chloride is added to water and stirred, it dissolves spontaneously and the resulting solution feels cold. Without doing any calculations, deduce the signs of \(\Delta G,{\rm{ }}\Delta H\), and \(\Delta S\) for this process, and justify your choices.

Short answer

Option B is correct answer \({\rm{HCl}}(g) + {\rm{N}}{{\rm{H}}_3}(g) \to {\rm{N}}{{\rm{H}}_4}{\rm{Cl}}(s)\)

Step-by-step solution

Define entropy of reaction

The relation of gibbs energy, enthalpy and entropy of reaction is follows:

\({\rm{dG}} = {\rm{dH}} - {\rm{TdS}}\)

Where, dG is change in gibbs energy

\({\rm{dH}}\)is change in enthalpy

\({\rm{d}}S\) is change in entropy

Reason for correct option.

The reaction of ammonium chloride with water is follows:

\({\rm{N}}{{\rm{H}}_4}{\rm{Cl}} + {{\rm{H}}_2}{\rm{O}} \to {\rm{N}}{{\rm{H}}_4}{\rm{OH}} + {\rm{HCl}}\)

As the reaction is spontaneous, the sign of dG is negative.

The resulting solution is cold which means the heat is not released and the reaction is endothermic. Thus, sign of \(d{\rm{H}}\) is positive.

\(\Delta G < 0,\Delta S > 0,\Delta H > 0\)

The formula of gibbs energy, enthalpy and entropy of reaction is:

\(\begin{array}{l}{\rm{dG}} = {\rm{dH}} - {\rm{TdS}}\\( - ) = ( + ) - {\rm{TdS}}\\{\rm{TdS}} = ( + ) + ( + ) = + \end{array}\)

Reason for incorrect option.

The given reaction for the production of ammonia is exothermic reaction with value \( - 46.28\;{\rm{kJ}}/{\rm{mol}}\). The reaction continuously releases the heat for the yielding of product. On increasing the temperature, the reaction goes in reverse direction toward the reactant. Thus, the reaction become non spontaneous and makes the Gibbs value more positive.

The given reaction for the production of alumina chromium is exothermic reaction with value \( - 272.8\;{\rm{kJ}}/{\rm{mol}}\). The reaction continuously releases the heat for the yielding of product. On increasing the temperature, the reaction goes in reverse direction toward the reactant. Thus, the reaction become non spontaneous and makes the Gibbs value more positive.

The given reaction for the production of Iron oxide is exothermic reaction with value \( - 850.72\;{\rm{kJ}}/{\rm{mol}}\). The reaction continuously releases the heat for the yielding of product. On increasing the temperature, the reaction goes in reverse direction toward the reactant. Thus, the reaction become non spontaneous and makes the Gibbs value more positive.

Hence, option (a), (c), (d) are incorrect.