Precipitate Reaction of Hydrogen Halides with Silver Nitrate and Sodium Thiosulfate

To determine which hydrogen halides react with aqueous silver nitrate ($\text{AgNO}_3$) to give a precipitate that dissolves in aqueous sodium thiosulfate ($\text{Na}_2\text{S}_2\text{O}_3$), we analyze the behavior of each hydrogen halide ($\text{HX}$):

1. Reaction with Aqueous $\text{AgNO}_3$:

   • $\text{HF}$ (Option B): $\text{HF}(\text{aq}) + \text{AgNO}_3(\text{aq}) \rightarrow \text{AgF}(\text{aq}) + \text{HNO}_3(\text{aq})$ Silver fluoride ($\text{AgF}$) is highly soluble in water due to the high hydration energy of the fluoride ion ($\text{F}^-$). Therefore, no precipitate is formed.

   • $\text{HCl}$ (Option A): $\text{HCl}(\text{aq}) + \text{AgNO}_3(\text{aq}) \rightarrow \text{AgCl}(\text{s})\downarrow + \text{HNO}_3(\text{aq})$ A white precipitate of silver chloride ($\text{AgCl}$) is formed.

   • $\text{HBr}$ (Option C): $\text{HBr}(\text{aq}) + \text{AgNO}_3(\text{aq}) \rightarrow \text{AgBr}(\text{s})\downarrow + \text{HNO}_3(\text{aq})$ A pale yellow precipitate of silver bromide ($\text{AgBr}$) is formed.

   • $\text{HI}$ (Option D): $\text{HI}(\text{aq}) + \text{AgNO}_3(\text{aq}) \rightarrow \text{AgI}(\text{s})\downarrow + \text{HNO}_3(\text{aq})$ A yellow precipitate of silver iodide ($\text{AgI}$) is formed.

2. Dissolution of Precipitates in Aqueous $\text{Na}_2\text{S}_2\text{O}_3$: The silver halide precipitates ($\text{AgCl}$, $\text{AgBr}$, and $\text{AgI}$) react with sodium thiosulfate to form a soluble complex, sodium dithiosulphatoargentate(I):

   $\text{AgX}(\text{s}) + 2\text{Na}_2\text{S}_2\text{O}_3(\text{aq}) \rightarrow \text{Na}_3[\text{Ag}(\text{S}_2\text{O}_3)_2](\text{aq}) + \text{NaX}(\text{aq}) \quad (\text{where } \text{X} = \text{Cl}, \text{Br}, \text{I})$

   Because the formation constant ($K_f$) of the complex $[\text{Ag}(\text{S}_2\text{O}_3)_2]^{3-}$ is extremely high, even the least soluble silver halide, $\text{AgI}$, dissolves in aqueous $\text{Na}_2\text{S}_2\text{O}_3$.

Thus, $\text{HCl}$, $\text{HBr}$, and $\text{HI}$ form precipitates with $\text{AgNO}_3(\text{aq})$ that subsequently dissolve in $\text{Na}_2\text{S}_2\text{O}_3(\text{aq})$.

Correct Options: (A), (C), and (D)