'A' Level Chemistry Problem Analysis: Chemical Energetics

QN: In which of the following processes are both the enthalpy change △H and entropy change △S positive?

Thought process:

Entropy - Compare LHS vs RHS. Gases have highest degree of disorderliness, followed by aqueous, lastly solid. When both sides have the same state, compare no. of moles.

Enthalpy - For some reactions, reference bond enthalpies/energies data in the Data Booklet to determine whether process is exothermic or endothermic. For others, such as (B) which involves a change of state, things should be pretty obvious. For others, like (D), you should know that by Hess Law, Solution enthaply = (endothermic) Lattice Dissociation enthalpy + (exothermic) Hydration enthalpy (which is the ion-dipole interactions between polar water molecule and the cations & anions).

Addendum regarding option (D), ie dissolving or solution of ammonium nitrate into water:

This is a well known endothermic reaction (ie. your hand feels cold when holding the test tube containing the reaction mixture).

What about entropy change? This is trickier than at first glance.

Entropy would both increase and decrease (there will be of course either a net increase or decrease, overall) for the following reasons :

1) Entropy would be expected to increase because solid state to aqueous state involves an obvious increase in disorderliness.

2) Entropy would be expected to decrease because of ion-dipole interactions between water molecules and cations & anions (charge density and hence ion-dipole interactions is always higher & stronger for cations than anions, do you know why?). Disorderly water molecules now arrange themselves in an orderly fashion around the ions, particularly those of high charge density (eg. Al3+, Fe3+). For the NH4+ ion, each H atom is capable of forming extra strong (since the positive formal charge on N is strongly electron withdrawing by induction) hydrogen bonds with the solvent water molecules, decreasing entropy.

3) Entropy would also be expected to decrease slightly because of a lowered temperature (due to the reaction being endothermic), and hence less kinetic energy results in less disorderliness of all species present, ions and molecules.

Overall, entropy entropy change would have to take into consideration both the simultaneous increase and decrease in entropy (as discussed above).

But because we know all nitrate (V) compounds and all ammonium compounds are soluble (which means of course, ammonium nitrate is certainly soluble!), meaning that the solution (dissolving) is a feasible & spontaneous process, so by Gibbs Free Energy formula (△G = △H - T△S), we surmise that the entropy change must be positive (ie. favourable) and large enough to overcome the unfavourable (endothermic) enthalpy change.

Hence, both options B and D are correct.


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