What quantity of Cu, in moles, can these electrons produce?
Cu deposited: 0.3952 g
6.219 × 10-3 mol Cu
Charge passed: 1200 C
1.2 × 10-2 mol e- passed
The correct answer and explanation is :
To determine the quantity of Cu in moles that can be produced from the charge passed, we need to use the relationship between the amount of charge and the number of moles of electrons involved in the process. This relationship is governed by the Faraday constant and stoichiometry of the reaction.
Step 1: Identify the known values
- Cu deposited: 0.3952 g
- Moles of Cu deposited: 6.219 × 10^-3 mol
- Charge passed: 1200 C
- Moles of electrons passed: 1.2 × 10^-2 mol e-
We can use this information to calculate how many moles of copper (Cu) can be deposited based on the charge passed and the moles of electrons involved.
Step 2: Relationship between moles of Cu and moles of electrons
In the electrochemical reaction where copper is deposited, the half-reaction is:
[
\text{Cu}^{2+} + 2e^- \rightarrow \text{Cu (s)}
]
This indicates that for every mole of Cu deposited, 2 moles of electrons are required.
Step 3: Calculate the moles of Cu that can be produced
From the problem, we are told that 1.2 × 10^-2 mol of electrons were passed. Since 2 moles of electrons are required to deposit 1 mole of Cu, we can set up the following proportion:
[
\frac{\text{moles of Cu}}{\text{moles of electrons}} = \frac{1 \text{ mol Cu}}{2 \text{ mol e}^-}
]
Using the moles of electrons passed (1.2 × 10^-2 mol e^-), we can calculate the moles of Cu:
[
\text{moles of Cu} = \frac{1.2 \times 10^{-2} \, \text{mol e}^-}{2} = 6.0 \times 10^{-3} \, \text{mol Cu}
]
Thus, the quantity of Cu that can be produced from the 1.2 × 10^-2 mol of electrons is 6.0 × 10^-3 mol of Cu.
Step 4: Confirm the result with the given data
We are given that 6.219 × 10^-3 mol of Cu were deposited for a certain amount of charge, and 1.2 × 10^-2 mol of electrons were passed. Our calculation aligns closely with this, confirming that the deposition of 6.0 × 10^-3 mol of Cu is correct, given the moles of electrons passed.
Hence, 6.0 × 10^-3 mol of Cu is the amount that can be produced from the charge passed.