Reactions Feasible in Liquid Ammonia

Liquid ammonia (\( \text{NH}_3 \)) is a polar protic solvent with properties analogous to water, but it behaves differently regarding solubility and acid-base chemistry. It undergoes autoionization like water:

\( 2\text{NH}_3 \rightleftharpoons \text{NH}_4^+ + \text{NH}_2^- \)

In liquid ammonia, \( \text{NH}_4^+ \) is the acidic species and \( \text{NH}_2^- \) is the basic species. Many ionic salts dissolve well in liquid ammonia. Reactions that lead to precipitation of a less soluble compound or are favorable acid-base reactions or redox reactions can occur.

Analyzing Each Reaction

Let's examine each given reaction to determine its feasibility in liquid \( \text{NH}_3 \):

1. \( \text{(i) KNO}_3 + \text{AgCl} \rightarrow \text{KCl} + \text{AgNO}_3 \)

   This is a metathesis (double displacement) reaction. In liquid \( \text{NH}_3 \), many salts are soluble. \( \text{KNO}_3 \) and \( \text{KCl} \) are generally soluble alkali metal salts. \( \text{AgNO}_3 \) is also soluble. However, the solubility of salts in liquid \( \text{NH}_3 \) differs from water. Silver chloride (\( \text{AgCl} \)), which is sparingly soluble in water, reacts with liquid ammonia to form the soluble complex ion \( \text{[Ag(NH}_3\text{)}_2\text{]}^+ \). Both \( \text{KNO}_3 \) and \( \text{AgNO}_3 \) are soluble in liquid \( \text{NH}_3 \). While direct precipitation of \( \text{KCl} \) or \( \text{AgNO}_3 \) isn't the primary driving force as it might be in water, reactions that occur readily in water via precipitation can often occur in liquid ammonia if a suitable driving force exists, such as different solvation energies or complex formation. Given the other options and common reactions in liquid \( \text{NH}_3 \), this type of salt exchange is considered feasible, potentially driven by differences in lattice energies or solvation.

2. \( \text{(ii) NH}_4\text{Br} + \text{KNH}_2 \rightarrow \text{KBr} + 2\text{NH}_3 \)

   This is an acid-base reaction in the liquid ammonia solvent system. \( \text{NH}_4^+ \) (from \( \text{NH}_4\text{Br} \)) is the acid species in liquid ammonia, and \( \text{NH}_2^- \) (from \( \text{KNH}_2 \)) is the basic species. The reaction between an acid (\( \text{NH}_4^+ \)) and a base (\( \text{NH}_2^- \)) in this solvent system produces the solvent (\( \text{NH}_3 \)) and a salt (\( \text{KBr} \)). This is analogous to the neutralization reaction \( \text{H}^+ + \text{OH}^- \rightarrow \text{H}_2\text{O} \) in water. This reaction is highly feasible and goes to completion.

3. \( \text{(iii) Fe(CO)}_5 + 2\text{e}^- \rightarrow \text{[Fe(CO)}_4\text{]}^{2-} + \text{CO} \)

   This reaction involves the reduction of iron pentacarbonyl (\( \text{Fe(CO)}_5 \)). Liquid ammonia is a solvent commonly used for reduction reactions, particularly those involving alkali metals as reducing agents (e.g., Birch reduction). While the electron source is not explicitly shown (it would typically be dissolved alkali metal like Na or K), this type of reduction of metal carbonyls to form anionic carbonyl complexes is a well-known reaction that can be carried out in liquid ammonia. The reaction involves the gain of electrons by \( \text{Fe(CO)}_5 \) to form the dianion \( \text{[Fe(CO)}_4\text{]}^{2-} \) and release of \( \text{CO} \). This redox reaction is feasible in liquid \( \text{NH}_3 \).

Based on the analysis, all three reactions (i), (ii), and (iii) are considered feasible in liquid \( \text{NH}_3 \).