Stability constant is more for the complex:

Options

A. (a) `[Ag(NH_3)_2]^(+)`
B. (b) `[Cu(NH_3)_4]^(2+)`
C. (c) `[Ag(CN)_2]^(-1)`
D. (d) `[Co(NH_3)_6]^(3+)`

Explanation

To determine which complex has the highest stability constant, we need to analyze the given complexes based on the factors affecting stability constants. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the oxidation states of the central metal ions in each complex.
- **A:** Ag (Silver) in Ag(NH3)2+ has an oxidation state of +1.
- **B:** Cu (Copper) in Cu(NH3)4^2+ has an oxidation state of +2.
- **C:** Ag (Silver) in Ag(CN)2^- has an oxidation state of +1.
- **D:** Co (Cobalt) in Co(NH3)6^3+ has an oxidation state of +3.

**Hint:** Higher oxidation states of the central metal ion generally lead to greater stability of the complex.

### Step 2: Determine the coordination numbers of each complex.
- **A:** Coordination number = 2 (from 2 NH3).
- **B:** Coordination number = 4 (from 4 NH3).
- **C:** Coordination number = 2 (from 2 CN^-).
- **D:** Coordination number = 6 (from 6 NH3).

**Hint:** A higher coordination number can contribute to greater stability of the complex.

### Step 3: Analyze the basicity of the ligands.
- **A:** NH3 is a neutral ligand and has moderate basicity.
- **B:** NH3 is a neutral ligand and has moderate basicity.
- **C:** CN^- is a stronger field ligand compared to NH3 and has higher basicity.
- **D:** NH3 is a neutral ligand and has moderate basicity.

**Hint:** The basicity of ligands affects the stability of the complex; stronger basic ligands can stabilize the complex better.

### Step 4: Compare the factors for stability.
1. **Oxidation State:**
- D (Co^3+) has the highest oxidation state (+3).

2. **Coordination Number:**
- D (Co(NH3)6^3+) has the highest coordination number (6).

3. **Basicity of Ligands:**
- NH3 is less basic than CN^-, but since D has the highest coordination number and oxidation state, it outweighs the basicity factor.

### Conclusion:
Considering all three factors (oxidation state, coordination number, and basicity of ligands), complex D (Co(NH3)6^3+) is the most stable due to its high oxidation state and coordination number.

**Final Answer:** The stability constant is more for the complex D (Co(NH3)6^3+).

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