The heats evolved and absorbed when 100 g each of `CuSO_(4)andCuSO_(4)*5H_(2)O` are dissolved in water are 41.7 and 4.7 kJ/mole respectively. The heat of hydration of `CuSo_(4)` is (in kJ/mole)

Options

A. `-66.59`
B. `+11.72`
C. `-78.2`
D. `+78.2`

Answer

To find the heat of hydration of CuSO4, we can follow these steps:

### Step 1: Write the dissolution reactions
- For CuSO4:
\[ \text{CuSO}_4 (s) \rightarrow \text{CuSO}_4 (aq) \quad \Delta H = -41.7 \text{ kJ/mol} \]
- For CuSO4·5H2O:
\[ \text{CuSO}_4 \cdot 5\text{H}_2\text{O} (s) \rightarrow \text{CuSO}_4 (aq) + 5\text{H}_2\text{O} (l) \quad \Delta H = +4.7 \text{ kJ/mol} \]

### Step 2: Calculate moles of CuSO4 and CuSO4·5H2O
- Molar mass of CuSO4 = 159.5 g/mol
- Moles of CuSO4:
\[ \text{Moles of CuSO}_4 = \frac{100 \text{ g}}{159.5 \text{ g/mol}} \approx 0.626 \text{ mol} \]

- Molar mass of CuSO4·5H2O = 249.5 g/mol
- Moles of CuSO4·5H2O:
\[ \text{Moles of CuSO}_4 \cdot 5\text{H}_2\text{O} = \frac{100 \text{ g}}{249.5 \text{ g/mol}} \approx 0.401 \text{ mol} \]

### Step 3: Calculate heat of solution per mole
- For CuSO4:
\[ \text{Heat of solution per mole} = \frac{-41.7 \text{ kJ}}{0.626 \text{ mol}} \approx -66.51 \text{ kJ/mol} \]

- For CuSO4·5H2O:
\[ \text{Heat of solution per mole} = \frac{4.7 \text{ kJ}}{0.401 \text{ mol}} \approx 11.72 \text{ kJ/mol} \]

### Step 4: Calculate the heat of hydration of CuSO4
- The heat of hydration of CuSO4 can be calculated using the following relationship:
\[ \text{Heat of hydration of CuSO}_4 = \text{Heat of solution of CuSO}_4 \cdot 5\text{H}_2\text{O} - \text{Heat of solution of CuSO}_4 \]
\[ = -66.51 \text{ kJ/mol} + 11.72 \text{ kJ/mol} = -54.79 \text{ kJ/mol} \]

### Final Answer
The heat of hydration of CuSO4 is approximately \(-54.79 \text{ kJ/mol}\).

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