Hydrolysis constants of two salts `K_(hA) and K_(hB)` 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), we will analyze the given hydrolysis constants and the dissociation constant of the third acid. Here’s a step-by-step solution:

### Step 1: Understand the relationship between hydrolysis constant and dissociation constant
The hydrolysis constant \( K_h \) of a salt is inversely proportional to the dissociation constant \( K_a \) of the corresponding weak acid. The relationship can be expressed as:
\[ K_h \times K_a = K_w \]
where \( K_w \) is the dissociation constant of water, which is \( 10^{-14} \) at room temperature.

### Step 2: Calculate the dissociation constants for acids HA and HB
1. For acid HA:
\[ K_{hA} = 10^{-8} \]
Using the relationship:
\[ K_{hA} \times K_{aA} = K_w \]
Substituting the values:
\[ 10^{-8} \times K_{aA} = 10^{-14} \]
Solving for \( K_{aA} \):
\[ K_{aA} = \frac{10^{-14}}{10^{-8}} = 10^{-6} \]

2. For acid HB:
\[ K_{hB} = 10^{-6} \]
Using the same relationship:
\[ K_{hB} \times K_{aB} = K_w \]
Substituting the values:
\[ 10^{-6} \times K_{aB} = 10^{-14} \]
Solving for \( K_{aB} \):
\[ K_{aB} = \frac{10^{-14}}{10^{-6}} = 10^{-8} \]

### Step 3: Identify the dissociation constant for acid HC
The dissociation constant for acid HC is given as:
\[ K_{aC} = 10^{-2} \]

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

### Step 5: Determine the order of acidic strength
The strength of an acid is directly proportional to its dissociation constant. Therefore, we can rank the acids based on their dissociation constants:
- \( K_{aC} > K_{aA} > K_{aB} \)

Thus, the order of acidic strength is:
\[ HC > HA > HB \]

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