What mass of Cu would be produced by the cathodic reduction of Cu ^ 2+ when 1.60A of current passes through a…

1. Analyze the question

We are asked to calculate the mass of Copper (Cu) deposited during electrolysis.

• Current ($I$): 1.60 A
• Time ($t$): 1 hour
• Faraday's Constant ($F$): 96,500 C/mol
• Molar mass of Copper ($M$): 64 g/mol
• Reaction: $\text{Cu}^{2+} + 2e^- \rightarrow \text{Cu}$ (This tells us the number of moles of electrons, $n$, is 2).

2. Explain the concept

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

Where:

• $m$ = mass in grams
• $M$ = molar mass
• $I$ = current in Amperes
• $t$ = time in seconds
• $n$ = number of electrons transferred
• $F$ = Faraday's constant

3. Show the solution

Step 1: Convert time to seconds. Since the formula requires time in seconds: $t = 1 \text{ hour} = 60 \times 60 = 3600 \text{ seconds}$

Step 2: Calculate the quantity of electricity ($Q$). $Q = I \times t$ $Q = 1.60 \text{ A} \times 3600 \text{ s} = 5760 \text{ Coulombs}$

Step 3: Calculate the mass ($m$) using the formula. $m = \frac{64 \times 5760}{2 \times 96500}$ $m = \frac{368640}{193000}$ $m \approx 1.91 \text{ g}$

4. Identify the answer

Comparing our result to the given options, the correct value is 1.91g.

Correct Option: C

5. Tip

Always remember to convert time from hours or minutes to seconds before plugging it into the Faraday formula. Also, check the valency of the metal ion (the charge) to determine the value of $n$; for $\text{Cu}^{2+}$, $n=2$, but for $\text{Ag}^+$, $n=1$. This is a common place where students lose marks!