When 3.2 g of ammonium chloride is dissolved in 75 g of water, the temperature of the solution decreases from 22.8°C to 20.1°C. What is the energy of dissolution of NH4Cl per mole? (The molecular mass of NH4Cl = 53.49 g/mol, and the specific heat of water = 4.18 J/g°C.)
A. 390 kJ/mol
• B. 125 kJ/mol
• C. 0.88 kJ/mol
• D. 14.8 kJ/mol

To solve for the energy of dissolution of \( \text{NH}_4\text{Cl} \) per mole, we'll follow these steps:

### Step 1: Calculate the heat absorbed by the solution
The formula to calculate the heat absorbed or released by the solution is:

\[
q = m \cdot c \cdot \Delta T
\]

where:
- \( q \) is the heat absorbed or released (in Joules),
- \( m \) is the mass of the water (in grams),
- \( c \) is the specific heat capacity of water (in J/g°C),
- \( \Delta T \) is the change in temperature (in °C).

Given:
- \( m = 75 \, \text{g} \)
- \( c = 4.18 \, \text{J/g°C} \)
- \( \Delta T = 20.1°C - 22.8°C = -2.7°C \) (the temperature decreases, so \( \Delta T \) is negative)

Substitute the values:

\[
q = 75 \, \text{g} \times 4.18 \, \text{J/g°C} \times (-2.7°C)
\]

\[
q = -846.15 \, \text{J}
\]

The negative sign indicates that the process is endothermic (heat is absorbed by the system).

### Step 2: Calculate the moles of \( \text{NH}_4\text{Cl} \) dissolved
The number of moles of \( \text{NH}_4\text{Cl} \) can be calculated using:

\[
\text{moles of } \text{NH}_4\text{Cl} = \frac{\text{mass of } \text{NH}_4\text{Cl}}{\text{molar mass of } \text{NH}_4\text{Cl}}
\]

Given:
- Mass of \( \text{NH}_4\text{Cl} = 3.2 \, \text{g} \)
- Molar mass of \( \text{NH}_4\text{Cl} = 53.49 \, \text{g/mol} \)

Substitute the values:

\[
\text{moles of } \text{NH}_4\text{Cl} = \frac{3.2 \, \text{g}}{53.49 \, \text{g/mol}} = 0.0598 \, \text{mol}
\]

### Step 3: Calculate the energy of dissolution per mole
The energy of dissolution per mole is given by:

\[
\text{Energy per mole} = \frac{q}{\text{moles of } \text{NH}_4\text{Cl}}
\]

Substitute the values:

\[
\text{Energy per mole} = \frac{-846.15 \, \text{J}}{0.0598 \, \text{mol}} = -14152.5 \, \text{J/mol} = -14.15 \, \text{kJ/mol}
\]

Since energy per mole is typically reported as a positive value (indicating energy absorbed in an endothermic process):

\[
\text{Energy of dissolution per mole} = 14.15 \, \text{kJ/mol}
\]

### Conclusion:
The closest answer is:

**D. 14.8 kJ/mol**

Would you like further details or have any questions?

Here are some related questions:
1. What is the significance of the sign of \( \Delta T \) in thermodynamics?
2. How does the specific heat capacity of a substance affect the amount of heat absorbed or released?
3. What would happen if a different amount of water was used in the dissolution?
4. How would the energy of dissolution change if the temperature drop was greater?
5. What is the difference between exothermic and endothermic processes in terms of energy changes?

**Tip:** Always pay attention to the sign of \( \Delta T \) when calculating heat transfer, as it indicates whether heat is absorbed or released.

Learn how to calculate the energy of dissolution of NH4Cl per mole with a step-by-step solution. Given specific conditions, including the mass of NH4Cl, the change in temperature, and the specific heat of water. Suitable for undergraduate studies in thermodynamics and chemical reactions.

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