When 1.022 g of anthracene, C14H10, is combusted in a bomb calorimeter that has a water jacket containing 500.0g of water, the temperature of the water increases by 25.65°C. Assuming that the specific heat of water is 4.18 J/(g "C), and that the heat absorption by the calorimeter is negligible, estimate the enthalpy of combustion per mole of anthracene (kJ/mol).
Thermochemistry
Thermochemistry can be considered as a branch of thermodynamics that deals with the connections between warmth, work, and various types of energy, formed because of different synthetic and actual cycles. Thermochemistry describes the energy changes that occur as a result of reactions or chemical changes in a substance.
Exergonic Reaction
The term exergonic is derived from the Greek word in which ‘ergon’ means work and exergonic means ‘work outside’. Exergonic reactions releases work energy. Exergonic reactions are different from exothermic reactions, the one that releases only heat energy during the course of the reaction. So, exothermic reaction is one type of exergonic reaction. Exergonic reaction releases work energy in different forms like heat, light or sound. For example, a glow stick releases light making that an exergonic reaction and not an exothermic reaction since no heat is released. Even endothermic reactions at very high temperature are exergonic.
![### Estimation of the Enthalpy of Combustion of Anthracene
**Problem Statement:**
When 1.022 g of anthracene, \( \text{C}_{14}\text{H}_{10} \), is combusted in a bomb calorimeter that has a water jacket containing 500.0 g of water, the temperature of the water increases by 25.65°C. Assuming that the specific heat of water is 4.18 J/(g·°C), and that the heat absorption by the calorimeter is negligible, estimate the enthalpy of combustion per mole of anthracene (kJ/mol).
**Calculations:**
1. **Determine the heat absorbed by the water (\( q \)):**
\[ q = m \cdot c \cdot \Delta T \]
Where:
- \( m \) = mass of water (500.0 g)
- \( c \) = specific heat of water (4.18 J/(g·°C))
- \( \Delta T \) = temperature change (25.65°C)
\[ q = 500.0 \, \text{g} \cdot 4.18 \, \frac{\text{J}}{\text{g·°C}} \cdot 25.65 \, \text{°C} \]
2. **Convert the heat absorbed by the water to kilojoules (kJ):**
\[ q \text{(in kJ)} = q \text{(in J)} \times \frac{1 \, \text{kJ}}{1000 \, \text{J}} \]
3. **Determine moles of anthracene combusted:**
\[ \text{Moles of anthracene} = \frac{1.022 \, \text{g}}{\text{Molecular weight of } \text{C}_{14}\text{H}_{10}} \]
The molecular weight of anthracene (\( \text{C}_{14}\text{H}_{10} \)):
\[ 14 \times 12.01 \, \text{g/mol} + 10 \times 1.008 \, \text{g/mol} = 178.23 \, \text{g/mol} \]
4. **Convert the heat absorbed by the water to per mole of anthracene:**
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