Correct relation between dissociation constants of a di-basic acid

Options

A. `K_(a_1)=K_(a_2)`
B. `K_(a_1) gt K_(a_2)`
C. `K_(a_1) lt K_(a_2)`
D. `K_(a_1) =1/(K_(a_2))`

Answer

To determine the correct relation between the dissociation constants of a dibasic acid, we need to analyze the dissociation process of the acid step by step.

### Step 1: Understanding Dibasic Acids
A dibasic acid is an acid that can donate two protons (H⁺ ions) to a solution. This means it has two dissociation steps.

### Step 2: First Dissociation
The first dissociation of a dibasic acid (let's denote it as H₂A) can be represented as:
\[ \text{H}_2\text{A} \rightleftharpoons \text{H}^+ + \text{HA}^- \]
The dissociation constant for this reaction is called \( K_{a1} \).

### Step 3: Second Dissociation
The second dissociation occurs when the conjugate base (HA⁻) loses another proton:
\[ \text{HA}^- \rightleftharpoons \text{H}^+ + \text{A}^{2-} \]
The dissociation constant for this reaction is called \( K_{a2} \).

### Step 4: Analyzing the Equilibrium
In the first dissociation, the acid (H₂A) loses its first proton to form HA⁻. In the second dissociation, HA⁻ loses its proton to form A²⁻.

### Step 5: Comparing the Constants
When the second proton is lost, the resulting species (A²⁻) is negatively charged. This negatively charged species will have a stronger attraction to the positively charged proton (H⁺). As a result, the equilibrium for the second dissociation will favor the reverse reaction, meaning that it is less likely to occur compared to the first dissociation.

### Conclusion
Thus, the relation between the dissociation constants is:
\[ K_{a1} > K_{a2} \]
This indicates that the first dissociation constant is greater than the second dissociation constant.

### Final Answer
The correct relation between the dissociation constants of a dibasic acid is:
\[ K_{a1} > K_{a2} \]

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