Introduction: The complex potassium dicyanodioxalatonickelate (II) is a coordination compound that contains nickel as the central atom. When this complex is dissolved in solution, it undergoes dissociation, releasing ions into the solution.

Dissociation of the complex: The complex potassium dicyanodioxalatonickelate (II) dissociates in solution to give the following ions:

1. Potassium ions (K+): These are positively charged ions that are released from the complex. Each complex unit contains one potassium ion.

2. Nickel ions (Ni2+): These are positively charged ions that are released from the complex. Each complex unit contains one nickel ion.

3. Dicyanodioxalato ligands (C2O4CN2-): These are negatively charged ligands that remain attached to the nickel ion. Each complex unit contains two dicyanodioxalato ligands.

4. Cyanide ions (CN-): These are negatively charged ions that are released from the complex. Each complex unit contains two cyanide ions.

5. Oxalate ions (C2O4^2-): These are negatively charged ions that are released from the complex. Each complex unit contains two oxalate ions.

Total number of ions: Based on the dissociation of the complex, the total number of ions released into the solution is 5, which includes one potassium ion, one nickel ion, two dicyanodioxalato ligands, two cyanide ions, and two oxalate ions.

Conclusion: In summary, the complex potassium dicyanodioxalatonickelate (II) dissociates in solution to release five different ions, including potassium ions, nickel ions, dicyanodioxalato ligands, cyanide ions, and oxalate ions.