The hydrolysis constants of two salts `M_(1)X` and `M_(2)X` formed from strong acid and weak base are `10^(-6)` and `10^(-3)` respectively. If the dissociation constant of third Base is `10^(-3)` , then the order of basic strengths is:

Options

A. `M_(1) OH lt M_(2) OH lt M_(3)OH`
B. `M_(1) OH gt M_(2)OH gt M_(3)OH`
C. `M_(2)OH gt M_(1)OH gt M_(2)OH`
D. None of these

Answer

To determine the order of basic strengths of the bases derived from the salts \( M_1X \), \( M_2X \), and the third base \( M_3 \), we will use the relationship between hydrolysis constant (\( K_h \)), dissociation constant of water (\( K_w \)), and the dissociation constant of the base (\( K_b \)).

### Step-by-Step Solution:

1. **Understand the relationship**:
The dissociation constant for a base can be calculated using the formula:
\[ K_b = \frac{K_w}{K_h} \]
where \( K_w \) is the dissociation constant of water (approximately \( 10^{-14} \) at 25°C) and \( K_h \) is the hydrolysis constant of the salt.

2. **Calculate \( K_b \) for \( M_1OH \)**:
Given \( K_h \) for \( M_1X \) is \( 10^{-6} \):
\[ K_{b1} = \frac{K_w}{K_h1} = \frac{10^{-14}}{10^{-6}} = 10^{-8} \]

3. **Calculate \( K_b \) for \( M_2OH \)**:
Given \( K_h \) for \( M_2X \) is \( 10^{-3} \):
\[ K_{b2} = \frac{K_w}{K_h2} = \frac{10^{-14}}{10^{-3}} = 10^{-11} \]

4. **Identify \( K_b \) for \( M_3OH \)**:
The dissociation constant for the third base \( M_3 \) is given directly as \( 10^{-3} \):
\[ K_{b3} = 10^{-3} \]

5. **Compare the \( K_b \) values**:
Now we have:
- \( K_{b1} = 10^{-8} \)
- \( K_{b2} = 10^{-11} \)
- \( K_{b3} = 10^{-3} \)

To compare the basic strengths, we note that a higher \( K_b \) indicates a stronger base. Therefore:
\[ K_{b3} > K_{b1} > K_{b2} \]

6. **Order of basic strengths**:
Thus, the order of basic strengths is:
\[ M_3OH > M_1OH > M_2OH \]

### Final Answer:
The order of basic strengths is:
\[ M_3OH > M_1OH > M_2OH \]