Question

Quinone is an important type of molecule that is involved in photosynthesis. The transport of electrons mediated by quinone in certain enzymes allows plants to take water, carbon dioxide, and the energy of sunlight to create glucose. A \(0.1964-\mathrm{g}\) sample of quinone \(\left(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}\right)\) is burned in a bomb calorimeter with a heat capacity of \(1.56 \mathrm{kJ} / \mathrm{C}\). The temperature of the calorimeter increases by \(3.2^{\circ} \mathrm{C}\). Calculate the energy of combustion of quinone per gram and per mole.

Short answer

The energy of combustion of quinone is approximately 25.42 kJ/g and 2738.26 kJ/mol.

Step-by-step solution

1. Calculate the energy released (q)

The energy released (q) in the reaction can be calculated using the equation: \[q = C \times \Delta T\] Where: q = energy released in kJ C = heat capacity of the bomb calorimeter (1.56 kJ/℃) ΔT = change in temperature (3.2℃) Now, we can plug the given values into the equation: \[q = 1.56 \ \frac{\mathrm{kJ}}{^\circ\mathrm{C}} \times 3.2^{\circ}\mathrm{C}\]

2. Calculate the energy of combustion per gram

First, let's find the energy released (q) from the calculation done in step 1: \[q = 1.56 \ \frac{\mathrm{kJ}}{^\circ\mathrm{C}} \times 3.2^{\circ}\mathrm{C} = 4.992 \ \mathrm{kJ}\] Now, we can find the energy of combustion per gram by dividing the energy released (q) by the mass of the quinone sample: \[\frac{4.992 \ \mathrm{kJ}}{0.1964 \ \mathrm{g}}\]

3. Determine the molar mass of quinone

The molar mass of quinone (C6H4O2) can be determined by using the atomic masses of carbon, hydrogen, and oxygen: Carbon: 12.01 g/mol (6 atoms) Hydrogen: 1.01 g/mol (4 atoms) Oxygen: 16.00 g/mol (2 atoms) Molar mass of quinone: \[M = 6 \times 12.01 \ \mathrm{g/mol} + 4 \times 1.01 \ \mathrm{g/mol} + 2 \times 16.00 \ \mathrm{g/mol}\]

4. Calculate the energy of combustion per mole

First, let's find the molar mass (M) of quinone from the calculation in step 3: \[M = 6 \times 12.01 \ \mathrm{g/mol} + 4 \times 1.01 \ \mathrm{g/mol} + 2 \times 16.00 \ \mathrm{g/mol} = 108.06 \ \mathrm{g/mol}\] Now, let's calculate the moles of quinone in the 0.1964 g sample: \[\mathrm{Moles} = \frac{0.1964 \ \mathrm{g}}{108.06 \ \mathrm{g/mol}}\] Then, calculate the energy of combustion per mole by dividing the energy released (q) by the moles of quinone: \[\frac{4.992 \ \mathrm{kJ}}{\mathrm{Moles}}\] Now, we can plug in the given and calculated values for energy of combustion per gram and per mole: Energy of combustion per gram: \[\frac{4.992 \ \mathrm{kJ}}{0.1964 \ \mathrm{g}} = 25.42 \ \frac{\mathrm{kJ}}{\mathrm{g}}\] Energy of combustion per mole: \[\frac{4.992 \ \mathrm{kJ}}{\frac{0.1964 \ \mathrm{g}}{108.06 \ \mathrm{g/mol}}} = 2738.26 \ \frac{\mathrm{kJ}}{\mathrm{mol}}\] So, the energy of combustion of quinone is approximately 25.42 kJ/g and 2738.26 kJ/mol.

Key concepts

Bomb Calorimeter

A bomb calorimeter is an essential tool in thermochemistry, designed to measure the heat of combustion of a substance. It consists of a strong, sealed container known as the bomb, which is submerged in water and contained within the calorimeter itself. When a sample is burned in the bomb, the heat released causes an increase in temperature of the water, which can be measured to determine the amount of energy released during the combustion.

The process is highly controlled and allows for accurate measurements, making it an invaluable device for scientists and students alike in understanding the energetic transformations during chemical reactions. If you're dealing with a bomb calorimeter in your experiments, remembering its precision is crucial for determining the heat capacity of the calorimeter and ultimately, to calculate the energy of combustion accurately.

Thermochemistry

Thermochemistry is the study of the heat involved in chemical processes and physical transformations. It bases its principles on the law of conservation of energy, which states that energy cannot be created or destroyed, only converted from one form to another. Therefore, in the context of combustion, thermochemistry analyzes the energy transfer that occurs when a substance reacts with oxygen to produce heat.

Understanding thermochemistry is essential for applications ranging from designing energy-efficient processes to predicting the impact of chemical reactions on the environment. The calculation of the energy of combustion, for instance, utilizes principles of thermochemistry to quantify the energy released by substances like quinone during reactions, giving insight into the energy that can be converted to do work or the amount that may be released into the surrounding environment.

Molar Mass Calculation

The molar mass calculation is a fundamental concept in chemistry that involves determining the mass of one mole of a substance. It is calculated by summing the mass of all the atoms in a molecule based on the atomic mass of each element, typically expressed in grams per mole (g/mol). For example, in the case of quinone (C6H4O2), the molar mass is calculated by adding up the atomic masses of six carbon atoms, four hydrogen atoms, and two oxygen atoms.

Knowing the molar mass is crucial, especially when converting between the mass of a substance and the number of moles, which is vital for chemical stoichiometry and in calculations like those involving bomb calorimeters. Ultimately, this allows for the determination of the energy of combustion per mole, a key step to relating experimental data to theoretical principles and making sense of the amount of energy a substance can release.