The reaction involved in the refining of silver recovery from a nitrate solution using copper metal is a classic example of a single displacement reaction. Here's the balanced chemical equation:

2AgNO₃(aq) + Cu(s) → Cu(NO₃)₂(aq) + 2Ag(s)

Explanation:

* AgNO₃(aq) represents silver nitrate dissolved in water (aqueous solution).

* Cu(s) represents solid copper metal.

* Cu(NO₃)₂(aq) represents copper(II) nitrate dissolved in water.

* 2Ag(s) represents solid silver metal.

How it works:

1. Displacement: The more reactive copper metal displaces the less reactive silver ions (Ag⁺) from the silver nitrate solution.

2. Redox reaction: This is a redox reaction where copper is oxidized (loses electrons) and silver is reduced (gains electrons).

3. Formation of copper nitrate: The copper ions (Cu²⁺) formed then combine with the nitrate ions (NO₃⁻) to create copper(II) nitrate.

4. Solid silver: The displaced silver ions gain electrons and become solid silver metal, which can be collected and refined further.

Key points:

* Copper is a better reducing agent than silver.

* The reaction is exothermic, meaning it releases heat.

* This method is a relatively simple and cost-effective way to extract silver from solutions.