The quantity of electricity required to deposit 180g of Ag from a molten silver trioxonitrate(V) is [Ag = 108]

1. Analyze the question

We are asked to calculate the quantity of electricity (in Faradays) needed to deposit a specific mass of silver (Ag) from a solution of silver trioxonitrate(V) ($AgNO_3$).

2. Explain the concept

To solve this, we use Faraday’s First Law of Electrolysis, which states that the mass of a substance deposited during electrolysis is proportional to the quantity of electricity passed through the electrolyte.

The reaction for the deposition of silver is: $Ag^+_{(aq)} + e^- \rightarrow Ag_{(s)}$

From this equation, we see that 1 mole of electrons (which is equal to 1 Faraday) is required to deposit 1 mole of silver.

3. Show the solution

Step 1: Determine the molar mass of Silver (Ag) Given in the question: $Ag = 108\text{ g/mol}$.

Step 2: Calculate the number of moles of Ag to be deposited $\text{Number of moles} = \frac{\text{mass}}{\text{molar mass}}$ $\text{Moles of Ag} = \frac{180\text{ g}}{108\text{ g/mol}}$ $\text{Moles of Ag} = 1.666... \approx 1.67\text{ moles}$

Step 3: Relate moles to Faraday Since the reaction $Ag^+ + e^- \rightarrow Ag$ shows that 1 mole of Ag requires 1 Faraday (1F) of electricity: $1.67\text{ moles of Ag}$ will require $1.67\text{ Faradays}$ of electricity.

4. Identify the answer

Comparing our result to the given options: A. 1.08F B. 3.30F C. 1.67F D. 1.80F

The calculated value matches option C.

5. Tip

Always remember the "1 mole = 1 Faraday" rule for monovalent ions like $Ag^+$, $Na^+$, or $K^+$. If the metal were divalent (like $Cu^{2+}$ or $Zn^{2+}$), you would need 2 Faradays per mole. Always check the valency of the metal from its position in the periodic table or the chemical formula provided!