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'A' Level Chemistry Problem Analysis: Solubility of Magnesium Chloride And Gibbs Free Energy
QN: Given that experimental evidence has shown magnesium chloride to be soluble at all temperatures, explain this in terms of Gibbs Free Energy. Thought process and remarks: This question was included in a top JC prelim paper, in which the mark scheme solution given was erroneous in its overgeneralized sweeping statement, "change in entropy of solution/dissolving is (*always) positive as there is a change from a more ordered state to a more disordered state for the ionic compound (*and water), from solid (*and liquid) to aqueous states." (*implied) If this were true, then magnesium carbonate would be soluble (since it has a favourably exothermic solution enthalpy), but it is not! (ie. it's insoluble). While the erroneous aspect of the mark scheme does not invalidate the question, or change the fact that magnesium chloride is soluble at all temperatures, the sentence is still erroneous and misleading, and I would encourage students to want to seek to understand the truth better for themselves, rather than blindly accept and memorize things. Let's consider magnesium carbonate, which is known to be (almost) insoluble at all temperatures, even though the solution enthalpy (ie. lattice dissociation enthalpy + hydration enthalpy) is overall exothermic (-25.3kJ/mol), which means the solution/dissolving process should be favourable, based on enthalpy argument. But the fact that magensium carbonate is insoluble, means that the overall solution entropy change (from solid to aqueous) must be negative, or unfavourable, and that it outweighs the favourable solution enthalpy. Why does this happen? Many students have the misconception that solution entropy change is always positive or favourable, when a solid dissolves in a solvent (eg. water), into the aqueous state. The increase in disorderliness or entropy is obvious when you consider the orderly solid lattice ionic structure being broken apart into the more disorderly aqueous state, as far as the ions are concerned. However, do not forget that the water molecules now become more ordered or orderly (cations attracting partial -ve oxygens of water, anions attracting partial +ve hydrogens of water), due to ion-dipole interactions with the ions. Mg2+ is dipositive while CO3 2- is dinegative, and as such, both ions have strong ordering power over surrounding water molecules in aqueous state. Hence, overall entropy is negative (ie. decrease in entropy of solvent water molecules, outweighs increase in entropy of this particular ionic compound from solid to aqueous). And the fact that magnesium carbonate is (almost) insoluble at all temperatures, demonstrates or proves that the unfavourable decrease in entropy for magnesium carbonate must outweigh the favourable exothermic enthalpy for the solution/dissolving process. If entropy change (for a solid to aqueous state) was always positive for all ionic compounds (as implied by the errorneous mark scheme), then magnesium carbonate would be soluble (since it has a favourably exothermic solution enthalpy), but it is not! (ie. it's insoluble). Now, back to magnesium chloride. By Hess Law, the overall solution enthalpy is the sum of the (endothermic) lattice dissociation enthalpy and the (exothermic) hydration enthalpy. Experimental evidence has shown that the (exothermic) hydration enthalpy outweighs the (endothermic) lattice dissociation enthalpy, to give a overall favourable (exothermic) solution enthalpy of approximately -150kJ/mol. The overall entropy change of Mg(s) to Mg(g) to Mg2+(g) to Mg2+(aq), is unfavourably negative (ie. more orderly), due to the high charge density of the dipositive Mg2+ ion, resulting in a high ordering power over water molecules in (stronger) ion-dipole interactions. The overall entropy change of Cl2(g) to 2Cl(g) to 2Cl-(g) to 2Cl-(aq), is favourably positive (ie. more disorderly), due to the (relatively) lower charge density of the uninegative Cl- ion, resulting in a lower ordering power over water molecules in (weaker) ion-dipole interactions. Because (the question specifies that) experimental evidence has shown magnesium chloride to be soluble at all temperatures, hence the student / exam candidate is expected to be able to deduce that the increase in entropy for the solution of the chloride ion outweighs the decrease in entropy for the solution of the magnesium ion, such that overall entropy change is favourably positive. And furthermore, because solution enthalpy is also favourably exothermic, hence magnesium chloride is soluble at all temperatures, based on the Gibbs Free Energy concept and formula. Again, the point of this article, is that if you come across something that does not feel right to you, don't blindly accept it (eg. just because it came from a top JC's prelim paper mark scheme), but (hopefully you would want to) seek to learn the (**relative leading edge) truth for yourself. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The above content is contributed by Mr Heng, owner and 'A' Level Chemistry tutor at Bedok Funland JC. He also goes by the handle UltimaOnline on various online popular homework forums.
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