When 96500 coulomb of electricity is passed through a copper sulphate solution, the amount of copper deposited will be:

Options

A. `0.25` mol
B. `0.50` mol
C. `1.00` mol
D. `2.00` mol

Answer

To determine the amount of copper deposited when 96500 coulombs of electricity is passed through a copper sulfate solution, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Faraday's Law of Electrolysis**:
Faraday's first law states that the amount of substance deposited at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.

2. **Identify the Reaction**:
At the cathode, copper ions (Cu²⁺) are reduced to copper metal (Cu):
\[ \text{Cu}^{2+} + 2e^- \rightarrow \text{Cu} \]
This reaction indicates that 2 moles of electrons are required to deposit 1 mole of copper.

3. **Use Faraday's Constant**:
Faraday's constant (F) is approximately 96500 coulombs per mole of electrons. This means that to deposit 1 mole of copper, we need 2 moles of electrons, which corresponds to:
\[ 2 \times 96500 \, \text{C} = 193000 \, \text{C} \]

4. **Calculate Moles of Copper Deposited**:
Given that we are passing 96500 coulombs of electricity, we can calculate the moles of copper deposited using the relationship:
\[ \text{Moles of Cu} = \frac{\text{Charge (C)}}{F \times \text{number of electrons required for 1 mole of Cu}} \]
Here, the number of electrons required for 1 mole of copper is 2. Therefore:
\[ \text{Moles of Cu} = \frac{96500 \, \text{C}}{96500 \, \text{C/mole} \times 2} = \frac{96500}{193000} = 0.5 \, \text{moles} \]

5. **Calculate the Mass of Copper Deposited**:
The molar mass of copper (Cu) is approximately 63.5 g/mol. Thus, the mass of copper deposited can be calculated as:
\[ \text{Mass of Cu} = \text{Moles of Cu} \times \text{Molar Mass of Cu} \]
\[ \text{Mass of Cu} = 0.5 \, \text{moles} \times 63.5 \, \text{g/mol} = 31.75 \, \text{g} \]

6. **Final Answer**:
Therefore, the amount of copper deposited when 96500 coulombs of electricity is passed through a copper sulfate solution is **31.75 grams**.