Ions in Solution & Precipitation Reactions

Dissolving an ionic solid is a tug-of-war. The ions in the crystal attract each other strongly; water molecules pull the ions out by surrounding them (hydration). If the attraction of water for the ions wins, the compound dissolves. If the ions attract each other more strongly than water can pull them apart, the compound stays solid. Ions carrying charges of 2 or 3 (such as ${\text{Ca}}^{2+}$ with ${\text{CO}}_3^{2-}$, or ${\text{Fe}}^{3+}$ with ${\text{PO}}_4^{3-}$) hold each other very tightly, which is why most carbonates, phosphates and hydroxides of metals other than Group 1 are insoluble. Singly charged ions like ${\text{Na}}^{+}$, ${\text{K}}^{+}$ and ${\text{NO}}_3^{-}$ are held loosely, so their compounds nearly always dissolve. You don't need to calculate this — the solubility table summarises the results of experiments — but it explains why the rules look the way they do. 'Insoluble' in these rules really means very slightly soluble: less than about 0.1 g dissolves per 100 mL, so the vast majority of the ions come out as a solid. A solubility table tells you which combinations of ions form soluble (stays dissolved, stays aqueous) vs. insoluble (forms a solid precipitate) compounds. Read it by checking the anion first, then looking for exceptions involving the cation. A few high-yield rules:

• Soluble: all Group 1 (alkali metal, e.g. ${\text{Na}}^{+}$, ${\text{K}}^{+}$) and ${\text{NH}}_4^{+}$ compounds — no exceptions.
• Soluble: all nitrates (${\text{NO}}_3^{-}$) and acetates (${\text{C}}_2{\text{H}}_3{\text{O}}_2^{-}$) — no exceptions.
• Soluble (with exceptions): most chlorides, bromides, and iodides — EXCEPT those of ${\text{Ag}}^{+}$, ${\text{Pb}}^{2+}$, and ${\text{Hg}}_2^{2+}$, which are insoluble.
• Soluble (with exceptions): most sulfates — EXCEPT ${\text{BaSO}}_4$, ${\text{PbSO}}_4$, ${\text{SrSO}}_4$ (insoluble) and ${\text{CaSO}}_4$ (only slightly soluble).
• Generally INSOLUBLE (unless paired with Group 1 or ${\text{NH}}_4^{+}$): carbonates (${\text{CO}}_3^{2-}$), phosphates (${\text{PO}}_4^{3-}$), hydroxides (${\text{OH}}^{-}$), and sulfides (${\text{S}}^{2-}$). Exception: ${\text{Ca(OH)}}_2$ is slightly soluble; ${\text{Ba(OH)}}_2$ and ${\text{Sr(OH)}}_2$ are soluble.

Take mixing lead(II) nitrate solution with potassium iodide solution — a classic demonstration that produces a bright yellow precipitate of lead(II) iodide. The same reaction can be written at three levels of detail. Use a four-step method every time: (1) write the ions present in each solution; (2) swap partners to find the two possible new compounds, writing each formula so its charges balance; (3) check each new compound against the solubility table and mark it (aq) or (s); (4) balance the formula equation, split every (aq) compound into ions, and cancel what appears unchanged on both sides. If both possible products are (aq), write 'no reaction' — all four ions simply stay mixed in solution.

• Formula equation — shows complete, neutral formulas, exactly as you'd write any balanced equation.
• Total ionic equation — rewrites every soluble (aqueous) compound as its separate ions; only the insoluble precipitate is written as a whole formula, since it doesn't dissociate.
• Net ionic equation — cancels out any ion that appears unchanged on both sides (these are called spectator ions, since they don't participate in forming the precipitate), leaving only the ions that actually react.

Why bother with the net ionic equation? Because it shows the chemistry that actually happens, stripped of bystanders. Any soluble lead(II) salt mixed with any soluble iodide gives exactly the same net reaction, ${\text{Pb}}^{2+}+2{\text{I}}^{-}\to {\text{PbI}}_2$, whether the spectators are ${\text{K}}^{+}$ and ${\text{NO}}_3^{-}$ or ${\text{Na}}^{+}$ and ${\text{C}}_2{\text{H}}_3{\text{O}}_2^{-}$. The net ionic equation is also what you use for stoichiometry: it tells you the mole ratio of the ions that form the solid. A good check: a correct net ionic equation is balanced for BOTH atoms and total charge (here, $2+$ and $2\times 1-$ add to zero on the left, matching the neutral solid).

Precipitation reactions are the everyday tools of water chemistry. Hard water contains dissolved ${\text{Ca}}^{2+}$ and ${\text{Mg}}^{2+}$; when it is heated, carbonate ions form and ${\text{CaCO}}_3$ precipitates as the scale that coats kettles and hot-water pipes. Municipal treatment plants add aluminum sulfate (alum) or iron(III) salts, which form gelatinous hydroxide precipitates such as ${\text{Al(OH)}}_3$ that trap suspended clay and bacteria as they settle. Wastewater plants remove phosphate — which would otherwise feed algae blooms in lakes — by precipitating it as insoluble iron(III) or aluminum phosphate. And in the lab, adding ${\text{AgNO}}_3$ to a water sample and weighing the white $\text{AgCl}$ that forms is a classic way to measure chloride content. In each case the chemist chooses an added ion that forms an insoluble compound with the unwanted ion, while its partner ion is a harmless spectator.