The electrolytes usually used in the electroplating of gold and silver, respectively, are

Options

A. `[Au(OH)_4]^(-) and [Ag(OH)_2]^(-)`
B. `[Au(CN)_2]^(-) and [AgCl_2]^(-)`
C. `[Au(NH_3)_2]^+ and [Ag(CN)_2]^_`
D. `[Au(CN)_2]^(-) and [Ag(CN)_2]^(-)`

Answer

To determine the electrolytes used in the electroplating of gold and silver, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Electroplating**: Electroplating is a process that uses electrical current to reduce dissolved metal cations so that they form a coherent metal coating on an electrode.

2. **Electrolyte for Silver Electroplating**:
- The anode used in silver electroplating is typically a bar of silver.
- The electrolyte solution used for silver electroplating is silver cyanide, which can be represented as \( \text{Ag(CN)}_2^- \). This compound is soluble in water and provides the necessary silver ions for the plating process.

3. **Electrolyte for Gold Electroplating**:
- Similarly, for gold electroplating, a gold anode is used.
- The electrolyte solution for gold electroplating is gold cyanide, represented as \( \text{Au(CN)}_2^- \). This also provides the necessary gold ions for the plating.

4. **Conclusion**:
- Therefore, the electrolytes used in the electroplating of silver and gold are \( \text{Ag(CN)}_2^- \) and \( \text{Au(CN)}_2^- \), respectively.

5. **Final Answer**: The correct answer is option D: \( \text{Ag(CN)}_2^- \) for silver and \( \text{Au(CN)}_2^- \) for gold.