The stepwise and overall stability constants are related as

Options

A. `beta_n=K_1+K_2+K_3+K_4+…+K_n`
B. `beta_n=K_1-K_2-K_3_k_4….K_n`
C. `beta_n=K_1+K_2-k_3-K_4+…..-K_n`
D. `beta_n=K_1xx K_2xxK_3xxK_4xx…….K_n`

Answer

To relate the stepwise stability constants to the overall stability constant for a coordination compound, we can follow these steps:

### Step 1: Define Stepwise Stability Constants
The stepwise stability constant (K) for the formation of a complex can be defined for each step in the formation of the complex. For example, if we have a metal ion (M) and a ligand (L), the formation of the complex can be represented as follows:

1. Formation of the first complex:
\[ M + L \rightleftharpoons ML \quad (K_1) \]

2. Formation of the second complex:
\[ ML + L \rightleftharpoons ML_2 \quad (K_2) \]

3. Formation of the third complex:
\[ ML_2 + L \rightleftharpoons ML_3 \quad (K_3) \]

And so on, until we reach the n-th complex:
\[ ML_{n-1} + L \rightleftharpoons ML_n \quad (K_n) \]

### Step 2: Define Overall Stability Constant
The overall stability constant (β) for the formation of the n-th complex (ML_n) can be defined as the equilibrium constant for the overall reaction from the free metal ion and ligands to the fully formed complex:

\[ M + nL \rightleftharpoons ML_n \quad (\beta) \]

### Step 3: Relate Stepwise and Overall Stability Constants
The overall stability constant (β) can be expressed as the product of the stepwise stability constants:

\[ \beta = K_1 \times K_2 \times K_3 \times \ldots \times K_n \]

This relationship shows that the overall stability constant is the product of all the stepwise stability constants for each step in the formation of the complex.

### Conclusion
Thus, the relationship between stepwise stability constants and the overall stability constant can be summarized as:
\[ \beta = K_1 \cdot K_2 \cdot K_3 \cdots K_n \]