The problem given involves the electrolysis of a molten mixture containing sodium chloride (NaCl) and calcium chloride (CaCl_2). To understand why this specific composition is used, let's consider the role of each component and the properties they impart to the mixture.
1. **Properties of NaCl and CaCl2:**
- Sodium chloride (NaCl) has a melting point of approximately 801°C.
- Calcium chloride (CaCl_2) has a melting point of around 772°C.
- A mixture of these salts lowers the overall melting point compared to pure NaCl. This phenomenon is known as freezing point depression, which occurs when a solute is added to a solvent, causing the melting point of the mixture to be lower than that of the pure components.
2. **Electrolysis Considerations:**
- A lower melting point is beneficial for the electrolysis process because it reduces energy consumption, making the process more economical.
- Lower temperature also minimizes corrosion and other high-temperature-related issues.
- The mixture’s lower melting point allows for a more manageable and efficient electrolysis setup.
3. **Role of Other Options:**
- The options stating Ca^{2+} can reduce or displace Na from NaCl are not valid in this context, since reduction and displacement reactions that produce elemental sodium are not thermodynamically favorable with Ca^{2+}.
- The role of CaCl_2 in assisting the conduction of electricity is secondary compared to its ability to lower the melting point.
4. **Conclusion:**
Therefore, the correct answer is: this mixture has a lower melting point than NaCl. This property is crucial for efficient and cost-effective electrolysis of sodium.