A `6.85g` sample of the hydrated`Sr(OH)_2.x H_2O` is dried in an oven to given `3.13g` of anhydrous `sr(OH)_2.` What is the value of `x?` (Atomic masses : `Sr=87.60.O=16.0,H=1.0)`

Options

A. 8
B. 12
C. 10
D. 6

Answer

To find the value of \( x \) in the hydrated compound \( Sr(OH)_2 \cdot x H_2O \), we can follow these steps:

### Step 1: Determine the mass of water lost
We start with the total mass of the hydrated compound and subtract the mass of the anhydrous compound to find the mass of water that was lost during drying.

\[ \text{Mass of water lost} = \text{Mass of hydrated compound} - \text{Mass of anhydrous compound} \]
\[ \text{Mass of water lost} = 6.85 \, g - 3.13 \, g = 3.72 \, g \]

### Step 2: Calculate the molar mass of \( Sr(OH)_2 \)
Next, we calculate the molar mass of the anhydrous \( Sr(OH)_2 \).

- Molar mass of \( Sr = 87.60 \, g/mol \)
- Molar mass of \( O = 16.00 \, g/mol \) (2 oxygen atoms contribute \( 2 \times 16.00 = 32.00 \, g/mol \))
- Molar mass of \( H = 1.00 \, g/mol \) (2 hydrogen atoms contribute \( 2 \times 1.00 = 2.00 \, g/mol \))

Calculating the total molar mass:
\[ \text{Molar mass of } Sr(OH)_2 = 87.60 + 32.00 + 2.00 = 121.60 \, g/mol \]

### Step 3: Set up the equation for moles
The moles of \( Sr(OH)_2 \) produced can be calculated using its mass and molar mass:
\[ \text{Moles of } Sr(OH)_2 = \frac{\text{Mass}}{\text{Molar mass}} = \frac{3.13 \, g}{121.60 \, g/mol} \approx 0.0257 \, mol \]

### Step 4: Relate moles of water to moles of \( Sr(OH)_2 \)
The number of moles of water lost can be calculated using the mass of water lost and the molar mass of water \( (H_2O) \):
- Molar mass of \( H_2O = 18.00 \, g/mol \)

Calculating the moles of water:
\[ \text{Moles of } H_2O = \frac{3.72 \, g}{18.00 \, g/mol} \approx 0.2067 \, mol \]

### Step 5: Find the value of \( x \)
Since each mole of \( Sr(OH)_2 \) is associated with \( x \) moles of water, we can set up the equation:
\[ \text{Moles of } H_2O = x \times \text{Moles of } Sr(OH)_2 \]
\[ 0.2067 = x \times 0.0257 \]
Solving for \( x \):
\[ x = \frac{0.2067}{0.0257} \approx 8.04 \]

Thus, rounding to the nearest whole number, we find:
\[ x \approx 8 \]

### Final Answer:
The value of \( x \) is **8**.

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