The first and second dissociation constant of an acid `H_2A ` are ` 1.0 xx 10 ^(-5) and 5.0 xx 10^(-10) ` respectively . The overall dissociation constant of the acid will be :
` 5.0 xx 10^(-5)`
` 5.0 xx 10 ^(-15)`
` 5.0 xx 10 ^(-15)`
` 0.2 xx 10 ^(5)`

Options

A. ` 5.0 xx 10^(-5)`
B. ` 5.0 xx 10 ^(-15)`
C. ` 5.0 xx 10 ^(-15)`
D. ` 0.2 xx 10 ^(5)`

Explanation

To find the overall dissociation constant of the acid \( H_2A \), we can follow these steps:

### Step 1: Understand the Dissociation Process
The acid \( H_2A \) dissociates in two steps:
1. \( H_2A \rightleftharpoons HA^- + H^+ \) (First dissociation)
2. \( HA^- \rightleftharpoons A^{2-} + H^+ \) (Second dissociation)

### Step 2: Write the Dissociation Constants
The dissociation constants for these reactions are given as:
- \( K_1 \) for the first dissociation:
\[ K_1 = 1.0 \times 10^{-5} \]
- \( K_2 \) for the second dissociation:
\[ K_2 = 5.0 \times 10^{-10} \]

### Step 3: Calculate the Overall Dissociation Constant
The overall dissociation constant \( K \) for the complete dissociation of \( H_2A \) can be calculated by multiplying the two dissociation constants:
\[ K = K_1 \times K_2 \]
Substituting the values:
\[ K = (1.0 \times 10^{-5}) \times (5.0 \times 10^{-10}) \]

### Step 4: Perform the Calculation
Now, we perform the multiplication:
\[ K = 1.0 \times 5.0 \times 10^{-5} \times 10^{-10} = 5.0 \times 10^{-15} \]

### Step 5: Conclusion
The overall dissociation constant of the acid \( H_2A \) is:
\[ K = 5.0 \times 10^{-15} \]

### Final Answer
The correct option is:
\[ 5.0 \times 10^{-15} \]

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