For poly basic acid , the dissociation constant have a different valves for each step.
`H_(3)AhArrH^(+)+A,Keq=Ka_(1)`
`H_(2)AhArrH^(+)+A^(-2),Keq=Ka_(2)`
`HA^(2)hArrH^(+)+A^(3-),Keq=Ka_(3)`
What is the observed trend of dissociation constant im successive stages ?

Options

A. `K_(a_(1))gtK_(a_(2))gtK_(a_(3))`
B. `K_(a_(1))=K_(a_(2))=K_(a_(3))`
C. `K_(a_(1))ltK_(a_(2))ltK_(a_(3))`
D. `K_(a_(1))=K_(a_(2))+K_(a_(3))`

Explanation

To analyze the trend of dissociation constants (Ka) for a polybasic acid during successive stages of dissociation, we can follow these steps:

### Step 1: Understand the Dissociation Process
A polybasic acid can donate more than one proton (H⁺). Each step of dissociation has its own equilibrium constant (Ka). For the given acid, we have:
1. \( H_3A \rightleftharpoons H^+ + H_2A^- \) with \( K_{a1} \)
2. \( H_2A^- \rightleftharpoons H^+ + HA^{2-} \) with \( K_{a2} \)
3. \( HA^{2-} \rightleftharpoons H^+ + A^{3-} \) with \( K_{a3} \)

### Step 2: Analyze the First Dissociation Constant \( K_{a1} \)
In the first dissociation, \( H_3A \) loses a proton to form \( H^+ \) and \( H_2A^- \). Since \( H_3A \) is a neutral molecule, it has a relatively higher tendency to lose a proton compared to the subsequent steps.

### Step 3: Analyze the Second Dissociation Constant \( K_{a2} \)
In the second dissociation, \( H_2A^- \) loses another proton to form \( H^+ \) and \( HA^{2-} \). Here, \( H_2A^- \) carries a negative charge, which makes it less favorable to lose another proton compared to the first dissociation. Therefore, we can conclude that:
\[ K_{a2} < K_{a1} \]

### Step 4: Analyze the Third Dissociation Constant \( K_{a3} \)
In the third dissociation, \( HA^{2-} \) loses a proton to form \( H^+ \) and \( A^{3-} \). The species \( HA^{2-} \) has an even greater negative charge, making it even less favorable to lose a proton. Thus, we can conclude that:
\[ K_{a3} < K_{a2} \]

### Step 5: Establish the Trend
From the analysis, we can summarize the trend of the dissociation constants:
\[ K_{a1} > K_{a2} > K_{a3} \]

This indicates that as we progress through the stages of dissociation, the tendency of the acid to lose protons decreases, leading to a decrease in the values of the dissociation constants.

### Final Answer
The observed trend of dissociation constants in successive stages is:
\[ K_{a1} > K_{a2} > K_{a3} \]

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