In 100ml , 0.1N `Na_2CO_3.xH_2O` solution. Mass of solute is 1.43g, then value of X is:

Answer

To find the value of \( x \) in the compound \( Na_2CO_3 \cdot xH_2O \), we will follow these steps:

### Step 1: Calculate the number of equivalents
The number of equivalents can be calculated using the formula:
\[ \text{Number of equivalents} = \text{Normality} \times \text{Volume in liters} \]
Given:
- Normality (N) = 0.1 N
- Volume = 100 ml = 0.1 L (since 1000 ml = 1 L)

So,
\[ \text{Number of equivalents} = 0.1 \, \text{N} \times 0.1 \, \text{L} = 0.01 \, \text{equivalents} \]

### Step 2: Relate equivalents to moles
The number of equivalents is also related to the number of moles and the valency factor. For \( Na_2CO_3 \), the valency factor is 2 (as it dissociates into 2 sodium ions and 1 carbonate ion).

Using the formula:
\[ \text{Number of equivalents} = \text{Number of moles} \times \text{Valency factor} \]
Let \( n \) be the number of moles:
\[ 0.01 = n \times 2 \]
Thus,
\[ n = \frac{0.01}{2} = 0.005 \, \text{moles} \]

### Step 3: Use the number of moles to find the molecular weight
We know that:
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molecular weight}} \]
Given mass of solute = 1.43 g, we can write:
\[ 0.005 = \frac{1.43}{\text{Molecular weight}} \]
Rearranging gives:
\[ \text{Molecular weight} = \frac{1.43}{0.005} = 286 \, \text{g/mol} \]

### Step 4: Calculate the molecular weight of \( Na_2CO_3 \cdot xH_2O \)
The molecular weight of \( Na_2CO_3 \) is calculated as follows:
- Sodium (Na) = 23 g/mol, so \( 2 \times 23 = 46 \) g/mol
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol, so \( 3 \times 16 = 48 \) g/mol

Thus, the molecular weight of \( Na_2CO_3 \) is:
\[ 46 + 12 + 48 = 106 \, \text{g/mol} \]
Now, including the water of hydration:
\[ \text{Molecular weight of } Na_2CO_3 \cdot xH_2O = 106 + 18x \]

### Step 5: Set up the equation
Now we can set up the equation:
\[ 106 + 18x = 286 \]

### Step 6: Solve for \( x \)
Rearranging gives:
\[ 18x = 286 - 106 \]
\[ 18x = 180 \]
\[ x = \frac{180}{18} = 10 \]

### Conclusion
Thus, the value of \( x \) is:
\[ \boxed{10} \]