From the stability constant (hypothetical vlues ) , given below, predict which is the most stable complex ?

Options

A. `Cu^(2+)+4NH_(3) to [Cu(NH_(3))_(4)]^(2+), " " K=4.5xx10^(11)`
B. `Cu^(2+)4CN^(-) to [Cu(CN)_(4)]^(3-)," " K=2.0xx10^(27)`
C. `Cu^(2+)+2en to [Cu(en)_(2)]^(2+)," " K=3.0xx10^(15)`
D. `Cu^(2+)+4H_(2)O to [Cu(H_(2)O)_(4)]^(2+)," : K=9.5xx10^(8)`

Explanation

To determine which complex is the most stable based on the provided stability constants, we will follow these steps:

### Step 1: Understand Stability Constant
The stability constant (K) is an equilibrium constant that indicates the stability of a complex formed in solution. A higher value of K signifies a more stable complex.

### Step 2: Analyze Given Stability Constants
We have the following hypothetical stability constants for different complexes:
- Option 1: \( K_1 = 10^{11} \)
- Option 2: \( K_2 = 2 \times 10^{27} \)
- Option 3: \( K_3 = 2^{15} \)
- Option 4: \( K_4 = 10^{8} \)

### Step 3: Compare the Values
To find the most stable complex, we need to compare the numerical values of the stability constants:
- \( K_1 = 10^{11} \)
- \( K_2 = 2 \times 10^{27} \) (This is the largest)
- \( K_3 = 2^{15} \) which is approximately \( 32768 \) (or \( 3.2768 \times 10^4 \))
- \( K_4 = 10^{8} \)

### Step 4: Identify the Highest Value
From the comparison:
- \( K_2 = 2 \times 10^{27} \) is significantly larger than the other values.

### Conclusion
Thus, the complex corresponding to Option 2, which has the stability constant \( K_2 = 2 \times 10^{27} \), is the most stable complex among all the given options.