Magnesium is extracted electrolysing fused magnesium chloride containing `NaC1`and `CaC1_(2)`using:

Options

A. a nickel cathode and a graphite anode
B. the iron container as anode and a nickel cathode
C. the iron container as cathode and a graphite anode
D. the nickel container as cathode and iron anode

Answer

To solve the question regarding the extraction of magnesium through the electrolysis of fused magnesium chloride containing NaCl and CaCl2, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Electrolysis Process**:
- Electrolysis involves the decomposition of a compound by passing an electric current through it. In this case, we are focusing on magnesium chloride (MgCl2) mixed with sodium chloride (NaCl) and calcium chloride (CaCl2).

2. **Identifying the Electrolytic Cell Setup**:
- The electrolytic cell consists of two electrodes: a cathode (negative electrode) and an anode (positive electrode). The materials used for these electrodes can affect the efficiency of the process.

3. **Analyzing the Given Options**:
- The options provided are:
1. Nickel cathode and graphite anode
2. Iron container as anode and nickel as cathode
3. Iron container as cathode and graphite as anode
4. Nickel container as cathode and iron as anode

4. **Selecting the Appropriate Electrode Materials**:
- The extraction of magnesium typically requires a stable and conductive cathode and an anode that can withstand the corrosive environment.
- In this case, the iron container is suitable as a cathode because it can handle the electrolysis of molten salts and is more economical.

5. **Reactions at the Electrodes**:
- At the **cathode** (iron container), magnesium ions (Mg²⁺) are reduced to magnesium metal (Mg) by gaining electrons:
\[ \text{Mg}^{2+} + 2e^- \rightarrow \text{Mg} \]
- At the **anode** (graphite), chloride ions (Cl⁻) are oxidized to chlorine gas (Cl₂) by losing electrons:
\[ 2\text{Cl}^- \rightarrow \text{Cl}_2 + 2e^- \]

6. **Overall Reaction**:
- The overall reaction for the electrolysis of magnesium chloride can be summarized as:
\[ \text{MgCl}_2 \rightarrow \text{Mg} + \text{Cl}_2 \]

7. **Conclusion**:
- Based on the analysis, the most suitable setup for the electrolysis of fused magnesium chloride containing NaCl and CaCl2 is **option 3: iron container as cathode and graphite as anode**.

### Final Answer:
The correct option is **option 3: Iron container as cathode and graphite as anode**.