What number of moles of Cu 2+ will be deposited by 360 coulombs of electricity? [f = 96500 C mol -1]

1. Analyze the Question

We are asked to calculate the number of moles of Copper ions ($Cu^{2+}$) deposited when a specific quantity of electricity (360 Coulombs) is passed through an electrolytic cell. We are given the Faraday constant ($F = 96500 \text{ C mol}^{-1}$).

2. Explain the Concept

To solve this, we use Faraday’s First Law of Electrolysis, which relates the quantity of electricity ($Q$) to the amount of substance deposited.

The reaction for the deposition of copper is:

From this equation, we see that 2 moles of electrons are required to deposit 1 mole of copper. The quantity of electricity ($Q$) is related to the number of moles of electrons ($n_e$) by the formula:

Where:

• $Q$ = Quantity of electricity in Coulombs (C)
• $n_e$ = Number of moles of electrons
• $F$ = Faraday's constant ($96500 \text{ C mol}^{-1}$)

3. Show the Solution

Step 1: Calculate the number of moles of electrons ($n_e$) used.

Step 2: Relate moles of electrons to moles of Copper. From the half-equation $Cu^{2+} + 2e^- \rightarrow Cu$, we know that:

Therefore, the moles of $Cu$ deposited is half the moles of electrons:

Step 3: Convert to standard form.

Rounding to three significant figures, we get $1.87 \times 10^{-3} \text{ mole}$.

4. Identify the Answer

Comparing our result with the given options, it matches Option B. (Note: The text in your prompt had a slight typo "10 10 -3", but it clearly refers to $10^{-3}$).

5. Exam Tip

Always check the valency of the metal ion! If the question asked for $Ag^+$ (Silver), you would divide by 1 because it only needs 1 mole of electrons. For $Cu^{2+}$, always remember to divide by 2. A quick way to remember: Moles of substance = $\frac{Q}{n \times F}$, where $n$ is the charge on the ion.