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 am u, Cl = 35.5 am u)

Options

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

Explanation

To solve the problem of determining the formula of the hydrated salt of barium chloride, we will follow these steps:

### Step 1: Calculate the mass of water lost during heating
The initial mass of the hydrate is given as 61 g, and the mass of the dried sample (barium chloride) is 52 g.

**Calculation:**
\[ \text{Mass of water lost} = \text{Initial mass} - \text{Final mass} = 61 \, \text{g} - 52 \, \text{g} = 9 \, \text{g} \]

### Step 2: Determine the molar mass of barium chloride (BaCl₂)
We know the atomic masses:
- Barium (Ba) = 137 amu
- Chlorine (Cl) = 35.5 amu

**Calculation:**
\[ \text{Molar mass of BaCl}_2 = \text{Mass of Ba} + 2 \times \text{Mass of Cl} = 137 \, \text{g/mol} + 2 \times 35.5 \, \text{g/mol} = 137 + 71 = 208 \, \text{g/mol} \]

### Step 3: Calculate the number of moles of BaCl₂
Using the mass of the dried sample (52 g) and the molar mass (208 g/mol), we can find the number of moles of BaCl₂.

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

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

**Calculation:**
\[ \text{Number of moles of H}_2O = \frac{\text{Mass}}{\text{Molar mass}} = \frac{9 \, \text{g}}{18 \, \text{g/mol}} = 0.5 \, \text{mol} \]

### Step 5: Determine the ratio of moles of BaCl₂ to moles of water
Now we can find the ratio of moles of BaCl₂ to moles of water to determine the value of X in BaCl₂·XH₂O.

**Calculation:**
\[ \text{Ratio} = \frac{\text{Moles of H}_2O}{\text{Moles of BaCl}_2} = \frac{0.5 \, \text{mol}}{0.25 \, \text{mol}} = 2 \]

### Conclusion: Write the formula of the hydrated salt
Since the ratio is 2, we can conclude that the formula of the hydrated salt is:
\[ \text{BaCl}_2 \cdot 2\text{H}_2O \]

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

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