\( \left|\begin{array}{l}\text { Constant-Volume Calorimetry } \\ \begin{array}{l}\text { A quantity of } 1.435 \mathrm{~g} \text { of naphthalene }\left(\mathrm{C}_{10} \mathrm{H}_{8}\right) \text { was burned in } \\ \text { a constant-volume bomb calorimeter. The temperature of } \\ \text { the water rose from } 20.28^{\circ} \mathrm{C} \text { to } 25.95^{\circ} \mathrm{C} \text {. If the heat } \\ \text { capacity of the bomb plus water was } 10.17 \mathrm{~kJ} /{ }^{\circ} \mathrm{C} \text {, calculate } \\ \text { the heat of combustion of naphthalene on a molar basis. } \\ \text { Find the molar heat of combustion. }\end{array} \\ \end{array}\right| \)

The heat absorbed by the calorimeter can be calculated using the formula \( q = C \Delta T \), where \( C \) is the heat capacity (10.17 kJ/°C) and \( \Delta T \) is the temperature change (25.95 °C - 20.28 °C = 5.67 °C). Thus, \( q = 10.17 \, \text{kJ/°C} \times 5.67 \, \text{°C} = 57.71 \, \text{kJ} \). Then, to find the molar heat of combustion, determine the number of moles of naphthalene burned: \( \text{moles} = \frac{1.435 \, \text{g}}{128.17 \, \text{g/mol}} \approx 0.0112 \, \text{mol} \). Therefore, the molar heat of combustion is \( \frac{57.71 \, \text{kJ}}{0.0112 \, \text{mol}} \approx -5140 \, \text{kJ/mol} \). Did you know that naphthalene was once used as an insect repellent and in mothballs? This organic compound, with its distinct aroma, has a historical significance beyond just fuel! It was a key player in the development of organic chemistry and has even been studied for its potential in environmental applications, highlighting its long-standing relevance in both science and culture. If you're diving into calorimetry, one common mistake is neglecting to account for all components in the heat capacity calculation. Always ensure that you've included everything from the calorimeter to the surrounding water. Additionally, make sure to convert your temperature changes accurately—it's easy to get mixed up. Lastly, remember that the heat of combustion is typically reported as a negative value since it represents an exothermic reaction. Happy experimenting!