The combustion of 0.1584 g benzoic acid increases the temperature of a bomb calorimeter by \(2.54^{\circ} \mathrm{C}\). Calculate the heat capacity of this calorimeter. (The energy released by combustion of benzoic acid is \(26.42 \mathrm{kJ} / \mathrm{g} .\) A 0.2130 -g sample of vanillin \(\left(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\right)\) is then burned in the same calorimeter, and the temperature increases by \(3.25^{\circ} \mathrm{C}\). What is the energy of combustion per gram of vanillin? Per mole of vanillin?

To find the energy released by the combustion of benzoic acid, we can use the given energy per gram, and multiply it by the mass of benzoic acid combusted. Energy released = Mass of benzoic acid × Energy per gram of benzoic acid Energy released = 0.1584 g × 26.42 kJ/g = 4.183168 kJ

We can determine the heat capacity of the calorimeter with the energy released in the combustion of benzoic acid, and the temperature change. Heat capacity = Energy released / Change in temperature Heat capacity = 4.183168 kJ / 2.54 °C = 1.647 kJ/°C

Now that we have the heat capacity of the calorimeter, we can find the total energy released by the combustion of vanillin using its temperature change. Energy released (vanillin) = Heat capacity × Change in temperature Energy released (vanillin) = 1.647 kJ/°C × 3.25 °C = 5.35275 kJ

We now have the total energy released by combustion of vanillin. To find the energy per gram, we can divide the total energy released by the mass of vanillin combusted. Energy per gram (vanillin) = Energy released (vanillin) / Mass of vanillin Energy per gram (vanillin) = 5.35275 kJ / 0.2130 g = 25.13 kJ/g To find the energy per mole, we first need to find the molar mass of vanillin (C8H8O3), which is: Molar mass (vanillin) = 8(12.01) + 8(1.008) + 3(16.00) = 152.15 g/mol Now, we can calculate the energy per mole by multiplying the energy per gram by the molar mass of vanillin. Energy per mole (vanillin) = Energy per gram (vanillin) × Molar mass (vanillin) Energy per mole (vanillin) = 25.13 kJ/g × 152.15 g/mol = 3822.53 kJ/mol Therefore, the heat capacity of the calorimeter is 1.647 kJ/°C, the energy of combustion per gram of vanillin is 25.13 kJ/g, and the energy per mole of vanillin is 3822.53 kJ/mol.