Solubility of Ionic Solids in Water

Solubility of ionic solids in water ■ Factors affecting solubility The solubility of ionic solids in water depends of two things: (1) the energy change, ΔH dissolve , that occurs when the ionic solid goes into solution as hydrated ions, and (2) the affect of the hydrated ions on the arrangement of the surrounding water molecules, measured by the organizational energy, ΔH org . These factors combine to determine the free energy change of dissolving, ΔGdissolve = ΔH dissolve + ΔH org . If the solution forms with a drop in free energy change of dissolving, ΔGdissolve < 0, the ionic solid is soluble. If the solution forms with an increase in free energy change of dissolving, ΔGdissolve > 0, the ionic solid is insoluble. Dissolving energy, ΔHdissolve The energy change on formation of the solution is usually reported as the dissolving energy, ΔH dissolve . It is the difference, ΔH dissolve = ΔH hydration - ΔH lattice , between the lattice energy, ΔH lattice , the energy required to break the ionic solid apart into separated ions, and the hydration energy, ΔH hydration , the energy released when the separated ions become surrounded water molecules. If there is a net release of energy, that is, if more energy is released on hydration than is stored in the ionic solid lattice, then solubility is favored. If there is a net gain of energy, that is, if less energy is released on hydration than is stored in the ionic solid lattice, then solubility is unfavored. Organization energy, ΔHorg = -T ΔSdissolve The effect of the hydrated ions on the arrangement of the surrounding water molecules can be quantified in terms of the dissolving organization energy, ΔH org = -T ΔSdissolve , where ΔSdissolve is the difference, ΔSdissolve = Ssolution - Ssolid , between the entropy of the solution and the entropy of the solid. Essentially, ΔSdissolve , reflects the change in energy dispersal that results when the ions in the solid are hydrated in solution. Since the ions in the solid are held in place by Coulombic attractions to neighboring, oppositely charged ions, the interaction energies are relatively undispersed in the solid. Since ions in solution are separated from one another by water molecules, the energy of the ion-water interaction is more dispersed than the ion-ion interaction in the solid. However, since the ions in solution organize neighboring water molecules into a hydration shell, the energy of the water-water interaction is less dispersed than in pure water. The competition between these two effects means that energy dispersal in the solution can be either more or less than in the solid. If the sheath of water molecules is weakly held, then the dispersal of the ions in water dominates, so that ΔH org is negative and solubility favored. This is the case with large ions that have a single unit of charge. This is because the water molecules cannot get close enough to the ions to be tightly held and so the hydration shell is fragile. If the sheath of water molecules is tightly held, then the reduction in dispersal of water-water interaction dominates, so that ΔH org is positive and solubility unfavored. This is the case with small ions and ones that have multiple units of charge. This is because the water molecules are more strongly held by the ions, because they can get closer to the ion and they experience greater charge on the ion.The result is that the hydration shell is robust. Predicting solubility from dissolving energy and organizational energy If both the dissolving energy and the organization energy are both negative, that is, if solution formation is exothermic and if energy is more dispersed in the solution than in the solid, then the solubility will be high. If both the dissolving energy and the organization energy are both positive, that is, if solution formation is endothermic and if energy is less dispersed in the solution than in the solid, then the solubility will be low. If the dissolving energy and the organization energy have opposite signs, then their relative values determines whether the ionic solid will be soluble or not. To determine this, we need the lattice energy and hydration energy to evaluate the dissolving energy, and we need to know the contribution of the hydrated ions to the organizational energy to determine the overall organizational energy. Here is the organizational energy contribution for common ions. Li+ 7.1 Na+ -1.3 K+ -12. Rb+ -14. Mg2+ 56. Ca2+ 38. Sr2+ 36. Ba2+ 25. Cs+ -15. NH4 + Ag+ -8.8 2.1 Tl+ -8.4 Mn2+ 49. Fe2+ 61. Co2+ 61. Ni2+ 68. Cu2+ 53. F3.3 Cl-12. Br-16. I-21. OH3.3 Zn2+ 56. Cd2+ 46. Pb2+ 25. NO3 - MnO4 - ClO3 - ClO4 - BrO3 - IO3 - HCO3 -26. -30. -25. -28. -22. -7.9 -13. SO4 2- CO3 26.7 21. Organizational energy, ΔHorg (ion) = -T ΔSdissolve (ion), values (kJ/mol) for individual ions (crystal → aqueous solution) at 25 °C. Adapted from Phillips and Williams, Inorganic Chemistry, Volume 1 (Oxford University Press, 1965), Table 7.XI, page 259. Does it make sense that the X+ organizational energy becomes more negative with increasing atomic number? Propose why Li+ has a positive organizational energy while the other X+ ions have negative organizational energy. Does it make sense that the X- organizational energy becomes more negative with increasing atomic number? Propose why F- and OH- have a positive organizational energy while the other X- ions Propose why positive organizational energy have negative organizational energy. Does it make sense that the X2+ organizational energy becomes less positive with increasing atomic number? Propose why CO23 has a positive organizational energy while ClO3 has a negative organizational energy. Propose why SO24 has a positive organizational energy while MnO4 has a negative organizational energy. Example: NaCl Sodium chloride is an example where even though the dissolving energy is endothermic, the organizational energy is sufficiently exothermic that the compound is soluble. Using values from J. Bell, ACS Chemistry (W. H. Freeman, 2005), Table 2.3, page 92, the dissolving energy evaluates to the endothermic value ΔH dissolve = ΔH hydration (NaCl) - ΔH lattice (NaCl) = (-784 kJ/mol) + (+787 kJ /mol) = +3 kJ /mol, which favors insolubility. Using the ion organizational energies, the organizational energy evaluates to the exothermic value ΔH org = ΔH org (Na+ ) + ΔH org (Cl- ) = (-1.3 kJ /mol) + (-12 kJ /mol) = -13 kJ /mol, which favors solubility. The organizational energy is sufficiently exothermic that the free energy of dissolving is also exothermic, ΔGdissolve = ΔH dissolve + ΔH org = +3 kJ/mol - 13 kJ /mol = -10 kJ/mol. This means the solubility of sodium chloride is due to energy being more dispersed in the solution than in the solid. Example: MgCO3 Magnesium carbonate is an example opposite to sodium chloride: Even though the dissolving energy is exothermic, the organizational energy is sufficiently endothermic that the compound is insoluble. Using values from J. Bell, ACS Chemistry (W. H. Freeman, 2005), Table 2.3, page 92, the dissolving energy evaluates to the exothermic value ΔH dissolve = ΔH hydration (MgCO3 ) - ΔH lattice (MgCO3 ) = (-3148 kJ /mol) + (+3122 kJ /mol) = -26 kJ /mol, which favors solubility. Using the ion organizational energies, the organizational energy evaluates to the exothermic value ΔH org = ΔH org Mg2+  + ΔH org CO23  = (+56 kJ/mol) + (-25 kJ /mol) = +31 kJ /mol, which favors insolubility. Because the endothermic organizational energy is so large, the free energy of dissolving is also endothermic, ΔGdissolve = ΔH dissolve + ΔH org = -26 kJ/mol + 31 kJ/mol = +5 kJ/mol. This means that the insolubility of calcium carbonate is due to energy being less dispersed in the solution than in the solid. ■ Solubility rules for ionic solids in water Here are rules that you can use to remember whether an ionic solid is soluble or not. The rules are consequences of the combined effect of dissolving energy and organizational energy. Soluble in water 1. All sodium, potassium, and ammonium (NH+4 ) salts are soluble. Analyze whether the solubility of sodium, potassium, and ammonium salts is due to exothermicity of dissolving energy, exothermicity of organizational energy, or both. 2. All nitrates, acetates (CH3 CO- ) and perchlorates (ClO-4 ) are soluble. Analyze whether the solubility of nitrates, acetates and perchlorates is due to exothermicity of dissolving energy, exothermicity of organizational energy, or both. 3. All chlorides, bromides and iodides are soluble, except halide of Ag+ , Pb2+ and Hg2+ 2 . Analyze whether the solubility of chlorides, bromides and iodides is due to exothermicity of dissolving energy, exothermicity of organizational energy, or both. Analyze whether the exceptions are due to exothermicity of dissolving energy, exothermicity of organizational energy, or both. 2+ 2+ 4. All sulfates are soluble, except sulfates of Ag+ , Pb2+ , Hg2+ and Ba2+ . 2 , Ca , Sr Determine whether the exceptions in the sulfate rule are due to exothermicity of dissolving energy or exothermicity of organizational energy. Analyze whether the exceptions are due to exothermicity of dissolving energy, exothermicity of organizational energy, or both. Insoluble in water 5. All sulfides are insoluble, except sulfides of Ca2+ , Sr2+ and Ba2+ . Analyze whether the insolubility of sulfides is due to endothermicity of dissolving energy, endothermicity of organizational energy, or both. Analyze whether the exceptions are due to exothermicity of dissolving energy, exothermicity of organizational energy, or both. 36. All carbonates (CO23 ) and phosphates (PO4 ). Analyze whether the insolubility of carbonates and phosphates is due to endothermicity of dissolving energy, endothermicity of organizational energy, or both. 7. All hydroxides are insoluble, except hydroxides of Ca2+ , Sr2+ and Ba2+ . Analyze whether the insolubility of carbonates, sulfides, oxides and hydroxides is due to endothermicity of dissolving energy, endothermicity of organizational energy, or both. 8. All silver (Ag+ ), lead(II) (Pb2+ ) and mercury(I) (Hg2+ 2 ) salts are insoluble Analyze whether the insolubility of silver, lead(II) and mercury(I) salts is due to endothermicity of dissolving energy, endothermicity of organizational energy, or both.