Comparison of enthalpy change for the dissolution of alkaline earth metal oxides

Compare the heat liberated per mole for the following reactions:


$\ce{MgO + H2O -> Mg(OH)2}$


$\ce{CaO + H2O -> Ca(OH)2}$


$\ce{SrO + H2O -> Sr(OH)2}$


$\ce{BaO + H2O -> Ba(OH)2}$


**Data for lattice enthalpy; $\ce{MO (s)->M^2+ (g) + O^2- (g)}$**





| $^1$Metal Oxide | Lattice Enthalpy (kJ/mol) |
| --- | --- |
| $\ce{MgO}$ | +3923 |
| $\ce{CaO}$ | +3517 |
| $\ce{SrO}$ | +3312 |
| $\ce{BaO}$ | +3120 |



**Data for hydration enthalpy; $\ce{M^2+ (g)->M^2+ (aq)}$**





| $^1$Metal Ion | Hydration Enthalpy (kJ/mol) |
| --- | --- |
| $\ce{Mg^2+}$ | -1921 |
| $\ce{Ca^2+}$ | -1577 |
| $\ce{Sr^2+}$ | -1443 |
| $\ce{Ba^2+}$ | -1305 |



**Data for enthalpy of formation; $\ce{M (s) + O2 (g) + H2 (g)->M(OH)2 (s)}$**





| $^2$Metal Hydroxide | Formation Enthalpy (kJ/mol) |
| --- | --- |
| $\ce{Mg(OH)2}$ | -925 |
| $\ce{Ca(OH)2}$ | -985 |
| $\ce{Sr(OH)2}$ | -959 |
| $\ce{Ba(OH)2}$ | -945 |



Energy required to break the lattice is positive, enthalpy of hydration is negative and enthalpy of formation is also negative. Hence, the net energy will sum up to a positive value. But these reactions are highly exothermic. Thus, there must be other energies to be considered.


Apart from lattice enthalpy, hydration enthalpy and enthalpy of formation what other factors to be considered?


P.S.: The highest value is for $\ce{Ca(OH)2}$.


**References:**


1. Concise Inorganic Chemistry- 4E by J. D. Lee & Sudarshan Guha (ISBN 9788126566495)
2. Table 6.3, Lange's Handbook of Chemistry- 15E




Some of the information pertains to the solid hydroxide and some pertains to the hydroxide in solution. As magnesium and calcium hydroxide actually have only limited solubility, I will assume the former applies.


You have enthalpies of formation for the solid hydroxides. From the Wikipedia articles for the respective compounds we can also get these enthalpies of formation, all in kilohoules per mole at 25°C:


$\ce{H2O}: -285$ (liquid)


$\ce{MgO}: -602$


$\ce{CaO}: -635$


$\ce{SrO}: -592$


$\ce{BaO}: -582$\*


\*There is surprising disagreeement over the heat of firmation of barium oxide, for instance [NIST](https://webbook.nist.gov/cgi/cbook.cgi?ID=C17194002&Units=SI&Mask=2) gives $-548$ kJ/mol.


From these values we may render all the hydroxide formations exothermic:


$\ce{MO + H2O -> M(OH)2(s)}$


$\ce{Mg}: \Delta H = -38$ kJ/mol


$\ce{Ca}: \Delta H = -65$ kJ/mol


$\ce{Sr}: \Delta H = -82$ kJ/mol


$\ce{Ba}: \Delta H = -78$ kJ/mol ($-112$ using NIST value for $\ce{BaO}$)


We see that on a molar basis, strontium or barium evolves the most heat, depending on which source is used for the barium data. But if we divide each of these results by the molecular weight of the product, we find that because of its lighter weight and still relatively high heat release calcium has the strongest heat effect per unit mass.


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