Hydrolysis constants of two salts `K_(A) and K_(B)` of weak acids HA and are `10^(-8) and 10^(-6)` . If the dissociation constant of third acid HC is `10^(-2)`. The order of acidic strength of three acids will be

Options

A. `HA gt HB gt HC`
B. ` HB gt HA gt HC`
C. `HC gt HA gt HB`
D. `HA = HB = HC`

Answer

To determine the order of acidic strength of the three acids (HA, HB, and HC) based on their hydrolysis constants and dissociation constants, we can follow these steps:

### Step 1: Understand the relationship between hydrolysis constants and dissociation constants
The hydrolysis constant (K) of a salt is related to the dissociation constant (Ka) of the weak acid from which the salt is derived. The relationship is given by:

\[ K = \frac{K_w}{K_a} \]

where \( K_w \) is the ion product of water, which is \( 10^{-14} \) at 25°C.

### Step 2: Calculate the dissociation constants of acids HA and HB
Given:
- \( K_A = 10^{-8} \) for HA
- \( K_B = 10^{-6} \) for HB

Using the relationship:

1. For HA:
\[ K_{aA} = \frac{K_w}{K_A} = \frac{10^{-14}}{10^{-8}} = 10^{-6} \]

2. For HB:
\[ K_{aB} = \frac{K_w}{K_B} = \frac{10^{-14}}{10^{-6}} = 10^{-8} \]

### Step 3: Identify the dissociation constant of acid HC
Given:
- \( K_C = 10^{-2} \) for HC

### Step 4: Compare the dissociation constants
Now we have the following dissociation constants:
- \( K_{aA} = 10^{-6} \)
- \( K_{aB} = 10^{-8} \)
- \( K_{aC} = 10^{-2} \)

### Step 5: Determine the order of acidic strength
The strength of an acid increases with an increase in its dissociation constant. Therefore, we can arrange the acids in order of increasing strength:
- HC has the highest dissociation constant \( (10^{-2}) \), making it the strongest acid.
- HA has the next highest dissociation constant \( (10^{-6}) \).
- HB has the lowest dissociation constant \( (10^{-8}) \).

### Conclusion
The order of acidic strength of the three acids is:
\[ HC > HA > HB \]