This question involves understanding the reactivity of hydrogen halides with silver nitrate and the solubility of their precipitates in sodium thiosulfate solution. Let's break it down step by step.

Step 1: Reaction with AgNO₃

Hydrogen halides (HX) react with AgNO₃ to form silver halide precipitates (AgX):

$\mathrm{HX}+\mathrm{AgNO}{}_3\to \mathrm{AgX}\downarrow +\mathrm{HNO}{}_3$

AgCl, AgBr, and AgI are insoluble and form precipitates, while AgF is soluble and does not precipitate.

Step 2: Solubility in Na₂S₂O₃

Sodium thiosulfate (Na₂S₂O₃) dissolves certain silver halides by forming soluble complexes:

$\mathrm{AgX}+2{\mathrm{Na}}_2{S}_2{O}_3\to \mathrm{Na}{}_3\left[\mathrm{Ag}\right(S_2{O}_3\left){}_2\right]+\mathrm{NaX}$

AgBr and AgI dissolve in Na₂S₂O₃, but AgCl does not; it dissolves in ammonia instead.

Step 3: Analyze Each Halide

• HF: AgF is soluble, so no precipitate forms with AgNO₃.
• HCl: Forms AgCl precipitate, but it dissolves in NH₃, not in Na₂S₂O₃.
• HBr: Forms AgBr precipitate, which dissolves in Na₂S₂O₃.
• HI: Forms AgI precipitate, which also dissolves in Na₂S₂O₃.

Final Answer

HBr and HI react with AgNO₃(aq) to give precipitates that dissolve in Na₂S₂O₃(aq).

Related Topics & Formulae

Solubility Rules: AgCl, AgBr, AgI are insoluble; AgF is soluble.

Complex Formation: AgBr and AgI form soluble complexes with thiosulfate: $\mathrm{AgX}+2S_2{O}_3{}^2-\to \left[\mathrm{Ag}\right(S_2{O}_3\left){}_2\right]{}^3-$

Key Concept: The ability of silver halides to dissolve in complexing agents like thiosulfate or ammonia depends on the stability of the complex formed, which varies with the halide ion.