Question

What is the quantity of electricity (in coulombs) required to deposit all the silver from \(250 \mathrm{~mL}\) of \(1 \mathrm{M}\) \(\mathrm{AgNO}_{3}\) solution? \((\mathrm{Ag}=108)\) (a) \(2412.5\) (b) 24125 (c) \(4825.0\) (d) 48250

Short answer

The correct answer is (b) 24125 coulombs.

Step-by-step solution

Determine the Moles of Silver Nitrate

Since the solution is 1 M (1 mol/L), we can calculate the moles of \(\mathrm{AgNO}_3\) in 250 mL of solution by converting the volume to liters and multiplying by the molarity:\[\text{Moles of } \mathrm{AgNO}_3 = 1 \text{ M} \times 0.250 \text{ L} = 0.25 \text{ moles}\]

Determine the Moles of Silver Ion

The dissociation of \(\mathrm{AgNO}_3\) in water is represented by the equation:\[\mathrm{AgNO}_3 \rightarrow \mathrm{Ag}^+ + \mathrm{NO}_3^-\]Since 1 mole of \(\mathrm{AgNO}_3\) produces 1 mole of \(\mathrm{Ag}^+\), there are 0.25 moles of \(\mathrm{Ag}^+\) available in the solution.

Use Faraday's Law to Calculate Charge

Faraday's law of electrolysis states that the amount of substance deposited at an electrode is proportional to the quantity of electricity that passes through the circuit. To discharge 1 mole of \(\mathrm{Ag}^+\), 1 mole of electrons (or 1 Faraday which is \(96500\) coulombs) is required:\[\text{Electricity required} = 0.25 \text{ moles } \times 96500 \text{ C/mol} = 24125 \text{ C}\]

Key concepts

Faraday's Law

Faraday's Law of Electrolysis is a fundamental principle in electrochemistry. It helps us understand the relationship between electric charges and chemical changes. This law states that the amount of substance altered at an electrode during electrolysis is proportional to the amount of electric charge passed through the circuit.

A key part of Faraday's Law involves a constant known as Faraday's constant, symbolized as \( F \). This constant signifies the charge of one mole of electrons, which is 96500 coulombs. In simple terms, if you pass 96500 coulombs of electric charge, you electrically deposit or dissolve one mole of a substance at the electrode.

Consider these key points:

• Faraday's constant, \( F \), is 96500 C/mol.
• The more charge you pass, the more material is deposited or dissolved.
• The process is directly proportional to the amount of charge.

Understanding this principle is crucial for calculating how much electricity we would need in processes like metal plating or extraction, as shown in the silver deposition task.

Electrolysis

Electrolysis is a chemical process used to drive a non-spontaneous chemical reaction using electricity. It's like reverse battery functionality, where instead of getting electricity from a chemical reaction, you apply electricity to create a chemical reaction. In electrolysis, electrical energy is converted into chemical energy.

During electrolysis, an electric current is passed through a substance causing a chemical change. This traditionally occurs in an electrolyte solution, such as our example with silver nitrate \( \mathrm{AgNO}_3 \). This substance breaks down, forming positive and negative ions.
Key aspects of electrolysis:

• Involves an electrolyte, usually a liquid containing ions.
• Ions move towards electrodes, where deposition of the substance occurs.
• Requires an external source of electricity to proceed.

So, in the case of silver deposition, the electrolyte is silver nitrate. When a certain amount of electricity passes through, silver ions move towards the electrode resulting in the deposition of metallic silver.

Moles Calculation

Calculating moles is foundational in chemistry to relate the amount of a substance to a measurable quantity, like mass or volume. In our case with silver nitrate \( \mathrm{AgNO}_3 \), calculating moles helps establish how much of a component participates in reactions. The concept of molarity, a measure of the concentration of a solution, is used
The process for determining moles:

• Identify the molarity of the solution. For this solution, it's 1 mol/L.
• Convert the solution volume from milliliters to liters for calculation. Here, 250 mL equals 0.25 L.
• Multiply the molarity by the volume in liters to find moles.

Thus, for 250 mL of a 1 M solution of \( \mathrm{AgNO}_3 \), this gives us 0.25 moles. This calculation forms the basis for deciding how much electricity will be needed to deposit silver by electrolysis.

Silver Deposition

Silver deposition is an example of using electrolysis to obtain a pure metal. By applying electricity, silver ions \( \mathrm{Ag}^+ \) from the solution are drawn to the negatively charged electrode. They gain electrons and arrange as metallic silver on the electrode. This process also exemplifies the reduction process in redox reactions.

Considerations in silver deposition:

• Silver ions in the solution are freed through dissociation of \( \mathrm{AgNO}_3 \).
• As the electric current flows, \( \mathrm{Ag}^+ \) ions gain electrons, converting them into atomic silver.
• The practical amount of electricity needed for this conversion is governed by Faraday's Law.

The quantity of electricity required depends on the number of moles of silver ions and is calculated as shown in previous sections. For our example, 96500 C charge deposits one mole of silver, and thus 24125 C deposits 0.25 moles as provided in the exercise result.