`Na_(2)SO_(4).xH_(2)O` has `50% H_(2)O`. Henxe, `x` is :

Options

A. `4`
B. `5`
C. `6`
D. `8`

Explanation

To find the value of \( x \) in the compound \( \text{Na}_2\text{SO}_4 \cdot x\text{H}_2\text{O} \) given that it contains 50% water, we can follow these steps:

### Step 1: Calculate the molar mass of sodium sulfate (\( \text{Na}_2\text{SO}_4 \))
The molar mass of sodium sulfate is calculated as follows:
- Sodium (Na): \( 22.99 \, \text{g/mol} \times 2 = 45.98 \, \text{g/mol} \)
- Sulfur (S): \( 32.07 \, \text{g/mol} \)
- Oxygen (O): \( 16.00 \, \text{g/mol} \times 4 = 64.00 \, \text{g/mol} \)

Adding these together:
\[ \text{Molar mass of } \text{Na}_2\text{SO}_4 = 45.98 + 32.07 + 64.00 = 142.05 \, \text{g/mol} \approx 142 \, \text{g/mol} \]

### Step 2: Write the expression for the molar mass of \( \text{Na}_2\text{SO}_4 \cdot x\text{H}_2\text{O} \)
The molar mass of the hydrated salt can be expressed as:
\[ \text{Molar mass of } \text{Na}_2\text{SO}_4 \cdot x\text{H}_2\text{O} = 142 + 18x \]
where \( 18 \, \text{g/mol} \) is the molar mass of water (\( \text{H}_2\text{O} \)).

### Step 3: Set up the equation based on the percentage of water
Given that the compound is 50% water, we can set up the equation:
\[ \frac{18x}{142 + 18x} = 0.5 \]

### Step 4: Solve the equation
Cross-multiplying gives:
\[ 18x = 0.5(142 + 18x) \]
Expanding the right side:
\[ 18x = 71 + 9x \]
Now, isolate \( x \):
\[ 18x - 9x = 71 \]
\[ 9x = 71 \]
\[ x = \frac{71}{9} \approx 7.89 \approx 8 \]

### Conclusion
Thus, the value of \( x \) is approximately 8.