A sample of a hydrate of barium chloride weighing 61 g was heated until all the water of hydration is removed. The dried sample weighed 52 g. The formula of the hydrated salt is : (atomic mass, Ba = 137 amu, Cl = 35.5 amu)

Options

A. `BaCl_(2). H_(2)O`
B. `BaCl_(2).3H_(2)O`
C. `Bacl_(2).4H_(2)O`
D. `BaCl_(2).2H_(2)O`

Answer

To determine the formula of the hydrated salt of barium chloride, we can follow these steps:

### Step 1: Determine the mass of water lost
We start with the total mass of the hydrated salt and the mass of the anhydrous salt after heating.

- Mass of hydrated barium chloride = 61 g
- Mass of anhydrous barium chloride = 52 g

To find the mass of water lost during heating, we subtract the mass of the anhydrous salt from the mass of the hydrated salt:

\[ \text{Mass of water} = \text{Mass of hydrated salt} - \text{Mass of anhydrous salt} = 61 \, \text{g} - 52 \, \text{g} = 9 \, \text{g} \]

### Step 2: Calculate the molar mass of barium chloride
Next, we need to calculate the molar mass of barium chloride (BaCl₂).

- Atomic mass of Ba = 137 g/mol
- Atomic mass of Cl = 35.5 g/mol

The molar mass of BaCl₂ is calculated as follows:

\[ \text{Molar mass of BaCl}_2 = 137 \, \text{g/mol} + 2 \times 35.5 \, \text{g/mol} = 137 + 71 = 208 \, \text{g/mol} \]

### Step 3: Calculate the number of moles of anhydrous barium chloride
Now, we can calculate the number of moles of anhydrous barium chloride using its mass and molar mass:

\[ \text{Number of moles of BaCl}_2 = \frac{\text{Mass of BaCl}_2}{\text{Molar mass of BaCl}_2} = \frac{52 \, \text{g}}{208 \, \text{g/mol}} = 0.25 \, \text{mol} \]

### Step 4: Calculate the number of moles of water
Next, we calculate the number of moles of water lost. The molar mass of water (H₂O) is 18 g/mol.

\[ \text{Number of moles of H}_2\text{O} = \frac{\text{Mass of water}}{\text{Molar mass of H}_2\text{O}} = \frac{9 \, \text{g}}{18 \, \text{g/mol}} = 0.5 \, \text{mol} \]

### Step 5: Determine the ratio of moles of water to moles of barium chloride
Now, we find the ratio of the moles of water to the moles of barium chloride:

\[ \text{Ratio} = \frac{\text{Number of moles of H}_2\text{O}}{\text{Number of moles of BaCl}_2} = \frac{0.5 \, \text{mol}}{0.25 \, \text{mol}} = 2 \]

### Step 6: Write the formula of the hydrated salt
Since the ratio of moles of water to moles of barium chloride is 2, we can write the formula of the hydrated salt as:

\[ \text{BaCl}_2 \cdot 2\text{H}_2\text{O} \]

### Final Answer
The formula of the hydrated salt is **BaCl₂ · 2H₂O**.

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