The percentage by mass of water of crystallisation in hydrated copper sulphate is [Given: Atomic mass of Cu = 63.5 u, H = 1 u, O = 16 u and S = 32 u]

Options

A. `42%`
B. `32%`
C. `63%`
D. `24%`

Answer

To find the percentage by mass of water of crystallization in hydrated copper sulfate (CuSO₄·5H₂O), we will follow these steps:

### Step 1: Calculate the molar mass of CuSO₄
- Atomic mass of Copper (Cu) = 63.5 u
- Atomic mass of Sulfur (S) = 32 u
- Atomic mass of Oxygen (O) = 16 u

The formula for copper sulfate is CuSO₄, which consists of:
- 1 Copper (Cu)
- 1 Sulfur (S)
- 4 Oxygens (O)

Calculating the molar mass:
\[ \text{Molar mass of CuSO₄} = 63.5 + 32 + (4 \times 16) \]
\[ = 63.5 + 32 + 64 \]
\[ = 159.5 \, \text{u} \]

### Step 2: Calculate the molar mass of water (H₂O)
- Atomic mass of Hydrogen (H) = 1 u
- Atomic mass of Oxygen (O) = 16 u

The formula for water is H₂O, which consists of:
- 2 Hydrogens (H)
- 1 Oxygen (O)

Calculating the molar mass:
\[ \text{Molar mass of H₂O} = (2 \times 1) + 16 \]
\[ = 2 + 16 \]
\[ = 18 \, \text{u} \]

### Step 3: Calculate the total mass of water in CuSO₄·5H₂O
Since there are 5 water molecules in hydrated copper sulfate:
\[ \text{Total mass of water} = 5 \times \text{Molar mass of H₂O} \]
\[ = 5 \times 18 \]
\[ = 90 \, \text{u} \]

### Step 4: Calculate the molar mass of hydrated copper sulfate (CuSO₄·5H₂O)
\[ \text{Molar mass of CuSO₄·5H₂O} = \text{Molar mass of CuSO₄} + \text{Total mass of water} \]
\[ = 159.5 + 90 \]
\[ = 249.5 \, \text{u} \]

### Step 5: Calculate the percentage by mass of water of crystallization
\[ \text{Percentage of water} = \left( \frac{\text{Total mass of water}}{\text{Molar mass of CuSO₄·5H₂O}} \right) \times 100 \]
\[ = \left( \frac{90}{249.5} \right) \times 100 \]
\[ \approx 36.1\% \]

### Final Answer:
The percentage by mass of water of crystallization in hydrated copper sulfate (CuSO₄·5H₂O) is approximately **36.1%**.

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