The formula of sodium dicyanoaurate(I) complex can be determined as follows:
1. **Identify the Central Metal and Its Oxidation State:**
- The central metal in this complex is gold (Au).
- The "(I)" in the name indicates that gold is in the +1 oxidation state.
2. **Identify the Ligands:**
- The ligands are "dicyano," which means there are two cyanide (CN⁻) groups coordinated to the gold.
3. **Determine the Overall Charge of the Complex:**
- Each cyanide ligand carries a -1 charge.
- Since there are two cyanide ligands, the total negative charge from the ligands is -2.
- To balance this negative charge, the gold ion (Au⁺) must have a +1 charge.
- Sodium (Na⁺) is used to balance the charge of the entire complex ion. Since the complex ion itself has a -1 charge, one sodium ion (Na⁺) will balance this charge.
4. **Combine Everything:**
- The complex ion is \([Au(CN)_2]^- \).
- The sodium ion (Na⁺) balances this charge, so the formula of the complex is \( \text{Na[Au(CN)_2]} \).
So, the formula of sodium dicyanoaurate(I) complex is **Na[Au(CN)₂]**.