Question

A \(2.200-g\) sample of quinone \(\left(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}\right)\) is burned in a bomb calorimeter whose total heat capacity is \(7.854 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\). The temperature of the calorimeter increases from \(23.44^{\circ} \mathrm{C}\) to \(30.57^{\circ} \mathrm{C}\). What is the heat of combustion per gram of quinone? Per mole of quinone?

Short answer

The heat of combustion for quinone is approximately 25.46 kJ/g and 2750 kJ/mol.

Step-by-step solution

Calculate the total heat generated

Using the data provided, we can calculate the total heat (q) generated during the combustion process. We know that the total heat capacity (C) of the calorimeter is 7.854 kJ/°C and the temperature change (ΔT) is the final temperature minus the initial temperature, which is 30.57 °C - 23.44 °C = 7.13 °C The total heat generated can be calculated using the formula: q = C × ΔT q = 7.854 kJ/°C × 7.13 °C q = 56.005 kJ (approximately 56.01 kJ)

Calculate the heat of combustion per gram

Once we have the total heat generated (56.01 kJ), we can now find the heat of combustion per gram of quinone. We know that the sample mass is 2.2 g, so we can divide the heat generated by the sample mass to obtain the heat of combustion per gram: Heat of combustion per gram = q / sample mass Heat of combustion per gram = 56.01 kJ / 2.2 g = 25.46 kJ/g

Calculate the molar mass of quinone

To find the heat of combustion per mole of quinone, we first need to determine the molar mass. The molecular formula of quinone is C_6H_4O_2, so we need to add up the molar masses of all the elements in the formula: Molar mass of quinone = (6 × Molar mass of Carbon) + (4 × Molar mass of Hydrogen) + (2 × Molar mass of Oxygen) Molar mass of quinone = (6 × 12.01 g/mol) + (4 × 1.01 g/mol) + (2 × 16.00 g/mol) Molar mass of quinone = 108.06 g/mol

Calculate the heat of combustion per mole

Now that we know the molar mass of quinone (108.06 g/mol), we can calculate the heat of combustion per mole by multiplying the heat of combustion per gram (25.46 kJ/g) by the molar mass of quinone: Heat of combustion per mole = Heat of combustion per gram × Molar mass of quinone Heat of combustion per mole = 25.46 kJ/g × 108.06 g/mol = 2749.59 kJ/mol (approximately 2750 kJ/mol) In conclusion, the heat of combustion for quinone is approximately 25.46 kJ/g and 2750 kJ/mol.