A : For `H_2CO_3 K_(a_1) lt K_(a_2)`.
R : `H_2CO_3` is weaker acid than `HCO_3^-`

Options

A. If both Assertion & Reason are true and the reason in the corret explanation of the assertion, then mark
B. If both assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark
C. If Assertion is true statement but Reason is false then mark
D. If both Assertion and Reason are false statements , then mark

Answer

To solve the question, we need to analyze the assertion (A) and the reason (R) provided:

### Assertion (A): For \( H_2CO_3 \), \( K_{a_1} < K_{a_2} \).
### Reason (R): \( H_2CO_3 \) is a weaker acid than \( HCO_3^- \).

### Step-by-step Solution:

1. **Understanding the Dissociation of Carbonic Acid (\( H_2CO_3 \))**:
- Carbonic acid (\( H_2CO_3 \)) is a diprotic acid, meaning it can donate two protons (H⁺).
- The first dissociation can be represented as:
\[ H_2CO_3 \rightleftharpoons H^+ + HCO_3^- \]
This dissociation constant is denoted as \( K_{a_1} \).

2. **Second Dissociation of Bicarbonate (\( HCO_3^- \))**:
- The second dissociation of bicarbonate is:
\[ HCO_3^- \rightleftharpoons H^+ + CO_3^{2-} \]
This dissociation constant is denoted as \( K_{a_2} \).

3. **Comparing \( K_{a_1} \) and \( K_{a_2} \)**:
- For diprotic acids, the first dissociation constant (\( K_{a_1} \)) is usually greater than the second dissociation constant (\( K_{a_2} \)) because the first proton is generally more easily lost than the second.
- Therefore, we can conclude that:
\[ K_{a_1} > K_{a_2} \]
- This contradicts the assertion \( K_{a_1} < K_{a_2} \).

4. **Analyzing the Acidity**:
- The strength of an acid is determined by its ability to donate protons.
- \( H_2CO_3 \) can donate two protons, while \( HCO_3^- \) can only donate one.
- Thus, \( H_2CO_3 \) is a stronger acid than \( HCO_3^- \).

5. **Conclusion**:
- Both the assertion (A) and the reason (R) are false.
- Therefore, the correct answer is that both the assertion and reason are false.

### Final Answer:
Both assertion and reason are false.