The enthalpy of solution is a balance between lattice energy and the sum of the hydration energies of the ions: ΔH solution = -ΔH lattice + ΔHhyd (X+) + ΔHhyd (Y-)
In any group of the periodic table:
· The lattice energies become less exothermic as the group is descended
· The hydration energies of the cations become less exothermic down the group as well
Therefore, the change in ΔH solution down the group is determined by which quantity (ΔH lattice or hydration enthalpies of the ions) shows the greater decrease.
Remember that:
· The lattice energy of ionic compounds depends on: the product of the charges on the ions divided by the sum of the ionic radii of both ions.
· The hydration enthalpies of the ions depend on their charge density: charge of the ion divided by its ionic radius.
| Ionic compound | Lattice energy/ kJmol-1 | Hydration enthalpy of cation/kJmol-1 | ΔHsolution/ kJmol-1 | ΔS° (surroundings)/ JK-1mol-1 | Hydrated ion | Relative* entropy value of hydrated ion/ JK-1mol-1 |
| Mg(OH)2 (s) | -2842 | -1920 | +3 | -10 | Mg2+(aq) | -138 |
| Ca(OH)2 (s) | -2553 | -1650 | -16 | +54 | Ca2+ (aq) | -53 |
| Sr(OH)2 (s) | -2354 | -1480 | -46 | +154 | Sr2+(aq) | -33 |
| Ba(OH)2 (s) | -2228 | -1360 | -52 | +174 | Ba2+(aq) | +10 |
| Change down the group | 614 | 560 | More exothermic | -184, so more likely to dissolve | | -148, so more likely to dissolve |
| MgSO4(s) | -2874 | -1920 | -91 | +305 | Mg2+(aq) | -138 |
| CaSO4(s) | -2677 | -1650 | -18 | +60 | Ca2+ (aq) | -53 |
| SrSO4(s) | -2516 | -1480 | -9 | +30 | Sr2+(aq) | -33 |
| BaSO4(s) | -2424 | -1360 | +19 | -63 | Ba2+(aq) | +10 |
| Change down the group | 450 | 560 | Less exothermic | -368 , so less likely to dissolve | | -148, so more likely to dissolve |
Group 2 hydroxides:
As seen in the table above, for the hydroxides of group 2, there’s a greater change in lattice energy than there is in hydration enthalpy of the cation. This results in the enthalpy of solution becoming more exothermic down the group.
Explanation:
ΔH solution = -ΔH lattice + ΔHhyd (X+) + ΔHhyd (OH-) . (The value of ΔHhyd (OH-) is constant for all compounds, so it is not included in the calculations below).
ΔH solution of Mg(OH)2 = 2842 – 1920 = 922 kJmol-1
ΔH solution of Ba(OH)2 = 2228 – 1360 = 868 kJmol-1
The values above are not the true values for ΔHsolution as we haven’t subtracted the value of the hydration enthalpy of the anion. However, these values show you that as you go down the group the ΔH solution becomes more negative, i.e. more exothermic.
However, solubility does not depend only on ΔH solution, it depends on ΔS° (system) as well. It’s difficult to determine the ΔS° (system) for ionic solids. ΔS° (total) = ΔS° (system) + (-ΔH solution/T)
Therefore, the relative entropy for the hydrated ion is used instead. | The entropy of the hydrated ion increases as the ionic radius increases. |
Also, the change in the entropy of the cation becomes more +ve down the group which favors solubility as well. As both factors favor an increase of solubility down the group; Ba(OH)2 is more soluble than Mg(OH)2. I.e. Solubility of group 2 hydroxides increases down the group.
Note that: an ionic solid dissolves when ΔS° (total) is +ve. There’re two factors that determine the value of ΔS° (total): ΔH solution or ΔS° (surroundings) and ΔS° (system) or entropy of the hydrated ion.
If the change in one of these factors is greater down the group than that of the other factor, then the greater change is the main factor determining the solubility down the group.There’s a greater change in the hydration enthalpies of the cations than that of the lattice energy. Therefore, the ΔH solution becomes less exothermic down the group.
Explanation:
ΔH solution = -ΔH lattice + ΔHhyd (X+) + ΔHhyd (SO42-) . (The value of ΔHhyd (SO42-) is constant for all compounds, so it is not included in the calculations below).
ΔH solution of MgSO4 = 2874 – 1920 = 954 kJmol-1
ΔH solution of BaSO4 = 2424 – 1360 = 1064 kJmol-1The values above are not the true values for ΔHsolution as we haven’t subtracted the value of the hydration enthalpy of the anion. However, these values show you that as you go down the group the ΔH solution becomes less negative, i.e. less exothermic.
Note that: The OH- ion is similar in size to the group 2 cations. The sum of the ionic radii of both cations and the OH- increases considerably down the group as the value of the radius of the cation increases down the group. ∴ Change in ΔH lattice is greater than that of the group 2 sulfates.
In addition, the sulfate ion is much larger than any of the group 2 cations. So, the sum of the ionic radii changes only by a small amount. ∴ the change in the hydration enthalpies is greater than the change in ΔH lattice of the group 2 sulfates. Also note that: ΔH lattice of the group 2 sulfates is more exothermic than that of group 2 hydroxides. Even though the sum of the ionic radii of group 2 sulfates is larger than that of group 2 hydroxides, the product of the charges of the group 2 sulfates is larger than that of group 2 hydroxides. Therefore ΔH lattice is more exothermic.
As enthalpy of solution becomes less exothermic down the group, the ΔS° (surroundings) becomes less positive which favors insolubility.
The change in the entropy of the cation becomes more +ve down the group which favors solubility. But the change in ΔS° (surroundings) is much greater than the change of the entropy of the hydrated ion. Hence, the solubility of group 2 sulfates decreases down the group. | Substance | ΔHsolution/kJmol-1 | ΔS° (surroundings)/ JK-1mol-1 | Hydrated ion | Relative entropy value of hydrated ion/ JK-1mol-1 |
| AgF | -20 | +67 | F-(aq) | -14 |
| AgCl | +66 | -221 | Cl-(aq) | +57 |
| AgBr | +85 | -285 | Br-(aq) | +82 |
| AgI | +113 | -379 | I-(aq) | +111 |
| Change down the group from F to I | More endothermic | -446, so less likely to dissolve | | -125, so more likely to dissolve |
∴ ΔS° (surroundings) becomes more negative down the group which favors insolubility.
The entropy of the hydrated ion increases down the group which favors solubility. However, the change in ΔS° (surroundings) is much greater than the change in the entropy of the hydrated ions. Therefore, solubility of the silver halides decreases down the group.
*AgCl, AgBr & AgI are insoluble and form colored ppt.
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