The complex that dissolves in water is:

🧠 Soluble vs Insoluble Coordination Compounds

Simple ionic salts of complex anions/cations with alkali metal counter-ions ($\mathrm{K^+}$, $\mathrm{Na^+}$) are typically water-soluble. Heavy heteropoly anions, mixed-valence pigments, and large neutral cluster complexes tend to be insoluble.

🗺️ Evaluate Each

| Complex | Water-soluble? | Reason | |---|---|---| | $(\mathrm{NH_4})_3[\mathrm{As(Mo_3O_{10})_4}]$ | No | Heteropoly anion analog of ammonium phosphomolybdate — yellow precipitate | | $\mathrm{Fe_4[Fe(CN)_6]_3}$ | No | Insoluble Prussian blue (mixed-valence Fe(II)/Fe(III)) | | $\mathrm{K_3[Co(NO_2)_6]}$ | Yes | Sodium cobaltinitrite analogue; potassium salt is soluble (contrast: Na₃ is also a yellow ppt for K⁺ analytical test) | | $[\mathrm{Fe_3(OH)_2(OAc)_6}]\mathrm{Cl}$ | No | Basic iron acetate cluster — insoluble in water |

⚡ Salt-Solubility Heuristic

For coordination salts, ask: is the counter-ion small + alkali ($\mathrm{K^+}$, $\mathrm{Na^+}$, $\mathrm{NH_4^+}$) and does the complex ion itself lack a precipitation-driving structure (mixed-valence, polyoxometallate, basic cluster)? If both, soluble.

⚠️ Watch the Direction of Tests

$\mathrm{Na_3[Co(NO_2)_6]}$ is soluble; mixing with K⁺ gives yellow $\mathrm{K_3[Co(NO_2)_6]}$ ppt — but only at high K⁺ concentrations. At low concentrations, $\mathrm{K_3[Co(NO_2)_6]}$ is itself soluble enough for solution chemistry.

$\boxed{\text{Answer: (3) } \mathrm{K_3[Co(NO_2)_6]}}$