If the percentage of water of crystallization in `MgSO_(4) .x H_(2)O` is `13%`. What is the value of `x` :

Options

A. `1`
B. `4`
C. `5`
D. `7`

Explanation

To find the value of \( x \) in the compound \( MgSO_4 \cdot x H_2O \) where the percentage of water of crystallization is given as 13%, we can follow these steps:

### Step 1: Determine the molar mass of \( MgSO_4 \)
The molar mass of \( MgSO_4 \) (magnesium sulfate) is given as 120.4 g/mol.

### Step 2: Calculate the molar mass of water
The molar mass of water \( H_2O \) is 18 g/mol.

### Step 3: Write the total molar mass of the hydrated compound
The total molar mass of \( MgSO_4 \cdot x H_2O \) can be expressed as:
\[ \text{Total Molar Mass} = \text{Molar Mass of } MgSO_4 + x \times \text{Molar Mass of } H_2O \]
\[ = 120.4 + 18x \text{ g/mol} \]

### Step 4: Set up the equation for the percentage of water
The mass of water in the compound is \( 18x \) g. The percentage of water in the compound is given as 13%. Therefore, we can set up the equation:
\[ \frac{18x}{120.4 + 18x} \times 100 = 13 \]

### Step 5: Simplify the equation
We can simplify the equation:
\[ 18x = 0.13(120.4 + 18x) \]
Expanding the right side:
\[ 18x = 15.652 + 2.34x \]

### Step 6: Rearranging the equation
Now, we can rearrange the equation to isolate \( x \):
\[ 18x - 2.34x = 15.652 \]
\[ 15.66x = 15.652 \]

### Step 7: Solve for \( x \)
Now, divide both sides by 15.66:
\[ x = \frac{15.652}{15.66} \approx 1 \]

Thus, the value of \( x \) is approximately 1.

### Final Answer
\[ x = 1 \]

---