Calculate the percentage of water of crystalline in Blue vitrial `CuSO_4 .5H_2O` (Atomic masses are given as` Cu = 63.5`,` S = 32`,` O = 16`,` H = 1`

Options

A. 0.072
B. 0.36
C. 0.5642
D. 0.64

Answer

To calculate the percentage of water of crystallization in Blue Vitriol, \( CuSO_4 \cdot 5H_2O \), we will follow these steps:

### Step 1: Calculate the molar mass of \( CuSO_4 \cdot 5H_2O \)

1. **Calculate the molar mass of \( CuSO_4 \)**:
- Copper (Cu): \( 63.5 \, g/mol \)
- Sulfur (S): \( 32 \, g/mol \)
- Oxygen (O): \( 16 \, g/mol \) (there are 4 oxygen atoms in \( CuSO_4 \))

\[ \text{Molar mass of } CuSO_4 = 63.5 + 32 + (16 \times 4) = 63.5 + 32 + 64 = 159.5 \, g/mol \]

2. **Calculate the molar mass of \( 5H_2O \)**:
- Hydrogen (H): \( 1 \, g/mol \) (there are 2 hydrogen atoms in \( H_2O \))
- Oxygen (O): \( 16 \, g/mol \)

\[ \text{Molar mass of } H_2O = (1 \times 2) + 16 = 2 + 16 = 18 \, g/mol \]
\[ \text{Molar mass of } 5H_2O = 5 \times 18 = 90 \, g/mol \]

3. **Total molar mass of \( CuSO_4 \cdot 5H_2O \)**:
\[ \text{Total molar mass} = \text{Molar mass of } CuSO_4 + \text{Molar mass of } 5H_2O = 159.5 + 90 = 249.5 \, g/mol \]

### Step 2: Calculate the percentage of water in \( CuSO_4 \cdot 5H_2O \)

1. **Use the formula for percentage**:
\[ \text{Percentage of water} = \left( \frac{\text{Mass of water}}{\text{Total mass}} \right) \times 100 \]
\[ \text{Percentage of water} = \left( \frac{90}{249.5} \right) \times 100 \]

2. **Calculate the percentage**:
\[ \text{Percentage of water} = \left( 0.3603 \right) \times 100 \approx 36.03\% \]

### Final Answer:
The percentage of water of crystallization in Blue Vitriol \( CuSO_4 \cdot 5H_2O \) is approximately **36.03%**.

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