Given the following `K_(a)` values, determine which species is the strongest base ?
`HSO_(4)^(-)=1.2xx10^(-2),H_(2)PO_(4)^(-)=6.3xx10^(-8),HCO_(3)^(-)=4.7xx10^(-11)`
(a)`CO_(3)^(2-)`
(b)`H_(2)SO_(4)`
(c)`SO_(4)^(2-)`
(d)`HPO_(4)^(2-)`

Options

A. `CO_(3)^(2-)`
B. `H_(2)SO_(4)`
C. `SO_(4)^(2-)`
D. `HPO_(4)^(2-)`

Answer

To determine which species is the strongest base among the given options based on the provided \( K_a \) values, we can follow these steps:

### Step 1: Understand the relationship between \( K_a \) and strength of acids
The strength of an acid is directly related to its \( K_a \) value. A larger \( K_a \) value indicates a stronger acid, which means it dissociates more in solution, producing more \( H^+ \) ions.

### Step 2: Identify the \( K_a \) values provided
The given \( K_a \) values are:
- \( HSO_4^- = 1.2 \times 10^{-2} \)
- \( H_2PO_4^- = 6.3 \times 10^{-8} \)
- \( HCO_3^- = 4.7 \times 10^{-11} \)

### Step 3: Determine the order of acid strength
From the \( K_a \) values, we can rank the acids in terms of their strength:
1. \( HSO_4^- \) (strongest acid)
2. \( H_2PO_4^- \)
3. \( HCO_3^- \) (weakest acid)

### Step 4: Identify the conjugate bases
The conjugate bases of these acids are:
- The conjugate base of \( HSO_4^- \) is \( SO_4^{2-} \)
- The conjugate base of \( H_2PO_4^- \) is \( HPO_4^{2-} \)
- The conjugate base of \( HCO_3^- \) is \( CO_3^{2-} \)

### Step 5: Determine the strength of the conjugate bases
The strength of a base is inversely related to the strength of its conjugate acid. Therefore:
- The conjugate base of the strongest acid \( HSO_4^- \) (which is \( SO_4^{2-} \)) will be the weakest base.
- The conjugate base of the medium strength acid \( H_2PO_4^- \) (which is \( HPO_4^{2-} \)) will be stronger than \( SO_4^{2-} \).
- The conjugate base of the weakest acid \( HCO_3^- \) (which is \( CO_3^{2-} \)) will be the strongest base.

### Step 6: Compare the bases
Based on the above analysis, we can rank the bases:
1. \( CO_3^{2-} \) (strongest base)
2. \( HPO_4^{2-} \)
3. \( SO_4^{2-} \) (weakest base)

### Conclusion
Thus, the strongest base among the given options is:
**(a) \( CO_3^{2-} \)**

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