a Coffee cup calorimeter initially contains 125 g of water , at a temperature of `24.2^(@)`C ,8 of ammonium nitrate `(NH_(4)NO_(3))` also at `24.2^(@)C`is added to the Water and the final temperature is `18.2^(@)c` What is the heat of solution of ammonium nitrate in KJ /mol? (The specific heat capacity of the solution is `4.2J//^(@)c`.)

Options

A. 33.51kJ /mol
B. 39.5kJ/mol
C. 32.2kJ/mol
D. 37.3kJ/mol

Answer

To solve the problem of finding the heat of solution of ammonium nitrate (NH₄NO₃) in a coffee cup calorimeter, we can follow these steps:

### Step 1: Calculate the moles of ammonium nitrate (NH₄NO₃)
1. **Molecular weight of NH₄NO₃**:
- N: 14 g/mol (2 Nitrogen atoms) = 14 * 2 = 28 g/mol
- H: 1 g/mol (4 Hydrogen atoms) = 1 * 4 = 4 g/mol
- O: 16 g/mol (3 Oxygen atoms) = 16 * 3 = 48 g/mol
- Total = 28 + 4 + 48 = 80 g/mol

2. **Calculate moles of NH₄NO₃**:
- Given mass = 8 g
- Moles = mass / molar mass = 8 g / 80 g/mol = 0.1 mol

### Step 2: Calculate the heat change (ΔH)
1. **Use the formula for heat change**:
\[ q = m \cdot C_p \cdot \Delta T \]
where:
- \(m\) = total mass of the solution (water + ammonium nitrate)
- \(C_p\) = specific heat capacity of the solution (4.2 J/°C)
- \(\Delta T\) = change in temperature

2. **Calculate total mass**:
- Mass of water = 125 g
- Mass of NH₄NO₃ = 8 g
- Total mass = 125 g + 8 g = 133 g

3. **Calculate the change in temperature (ΔT)**:
- Initial temperature = 24.2 °C
- Final temperature = 18.2 °C
- \(\Delta T = 24.2 °C - 18.2 °C = 6 °C\)

4. **Substitute values into the heat change formula**:
\[ q = 133 \, \text{g} \cdot 4.2 \, \text{J/°C} \cdot 6 \, \text{°C} \]
\[ q = 133 \cdot 4.2 \cdot 6 = 3366.6 \, \text{J} \]

### Step 3: Convert heat change to kilojoules
1. **Convert J to kJ**:
\[ q = 3366.6 \, \text{J} \div 1000 = 3.3666 \, \text{kJ} \]

### Step 4: Calculate the heat of solution per mole
1. **Since the calculated heat change is for 0.1 moles, we need to find the heat of solution per mole**:
\[ \Delta H = \frac{q}{\text{moles}} = \frac{3.3666 \, \text{kJ}}{0.1 \, \text{mol}} = 33.666 \, \text{kJ/mol} \]

### Final Answer
The heat of solution of ammonium nitrate is approximately **33.67 kJ/mol**.

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