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 per gram of quinone is approximately 25.47 kJ/g, and the heat of combustion per mole of quinone is approximately 2751.01 kJ/mol.

Step-by-step solution

1. Calculate the heat produced during the combustion.

To find the heat produced during the combustion, we will use the formula: q = C * ΔT where q is the heat produced, C is the heat capacity of the calorimeter, and ΔT is the temperature change. We have: C = 7.854 kJ/°C ΔT = 30.57°C - 23.44°C = 7.13°C Now we can calculate the heat produced: q = 7.854 kJ/°C * 7.13°C ≈ 56.04 kJ

2. Calculate the heat of combustion per gram of quinone.

To find the heat of combustion per gram of quinone, we will divide the total heat produced by the mass of quinone: q_per_gram = q / mass where mass = 2.2 g Now we can calculate the heat of combustion per gram of quinone: q_per_gram = 56.04 kJ / 2.2 g ≈ 25.47 kJ/g

3. Calculate the molar mass of quinone.

The molecular formula of quinone is C6H4O2, and we need to find its molar mass. We can use the periodic table to find the molar masses of each element present in quinone: C: 12.01 g/mol H: 1.008 g/mol O: 16.00 g/mol The molecular formula C6H4O2 has 6 carbon atoms, 4 hydrogen atoms, and 2 oxygen atoms. So the molar mass of quinone is: Molar_mass = 6 * 12.01 g/mol + 4 * 1.008 g/mol + 2 * 16.00 g/mol ≈ 108.10 g/mol

4. Calculate the heat of combustion per mole of quinone.

Finally, we can find the heat of combustion per mole of quinone by multiplying the heat of combustion per gram with the molar mass: q_per_mol = q_per_gram * Molar_mass q_per_mol = 25.47 kJ/g * 108.10 g/mol ≈ 2751.01 kJ/mol So, the heat of combustion per gram of quinone is approximately 25.47 kJ/g, and the heat of combustion per mole of quinone is approximately 2751.01 kJ/mol.

Key concepts

Heat Capacity

Heat capacity is a crucial concept in thermochemistry and calorimetry. It refers to the amount of heat required to raise the temperature of a substance by one degree Celsius. In the context of a bomb calorimeter, the heat capacity is essential for understanding how much energy is absorbed by the surroundings during a chemical reaction. The higher the heat capacity, the more heat is needed to change the temperature.

In our example, the calorimeter's heat capacity was given as 7.854 kJ/°C. This means, for every degree the temperature of the calorimeter increases, 7.854 kJ of energy is absorbed. To find the total energy absorbed (or the total heat produced during the combustion reaction) using the heat capacity, we multiply it by the temperature change observed. This simple but powerful use of heat capacity helps determine the energy released in the reaction.

Combustion Reaction

A combustion reaction is a high-temperature chemical reaction between a fuel and an oxidant, often oxygen, that produces heat and light. In our exercise, quinone is the fuel, undergoing combustion within the calorimeter. When substances combust, they typically release a significant amount of energy.

The combustion of quinone in the calorimeter causes the surrounding temperature to rise, which we measure to quantify the reaction's energy output. Combustion reactions are vital in understanding how various fuels, like hydrocarbons or quinone in this case, convert stored chemical energy into a usable form of heat energy. These reactions power everything from internal combustion engines to industrial processes, making them crucial for energy conversion studies.

Molar Mass Calculation

Calculating the molar mass of a compound is fundamental in chemistry. It helps convert between grams and moles, which is critical for making stoichiometric calculations in reactions. For quinone (C6H4O2), we add the atomic masses of each atom in the molecular formula to find its molar mass.

To find the molar mass:

• Carbon (C) has an atomic mass of 12.01 g/mol, and there are 6 atoms, so we have 6 * 12.01 g/mol.
• Hydrogen (H) has an atomic mass of 1.008 g/mol, with 4 atoms present, resulting in 4 * 1.008 g/mol.
• Oxygen (O) has an atomic mass of 16.00 g/mol; with 2 atoms, that's 2 * 16.00 g/mol.

Adding these values gives us a molar mass of 108.10 g/mol for quinone. This calculation is vital for determining the heat of combustion per mole of quinone, linking mass to energy transformations.

Calorimetry

Calorimetry involves measuring the heat of chemical reactions or physical changes and is a central technique in thermochemistry. In a bomb calorimeter, a sample is combusted in a sealed container, and the heat produced changes the temperature of the surrounding water or calorimeter material.

In the presented exercise, calorimetry allows us to determine the heat of combustion by noting the temperature change in the calorimeter, while accounting for its heat capacity. This technique helps scientists and engineers quantify energy changes, which is vital for studies in nutrition, material science, and energy production. Essentially, calorimetry acts as a gateway to understanding the energetic profile of different substances during various reactions.

Energy Conversion

Energy conversion is the process of transforming energy from one form to another. In thermochemistry, this often involves converting chemical energy into thermal energy, as seen in combustion reactions. Energy conversion is fundamental to countless applications, from power generation to everyday appliances.

In our example, the chemical energy in quinone was converted to thermal energy through combustion. This thermal energy then raised the temperature of the calorimeter. Understanding energy conversion is critical not only for assessing the efficiency of reactions but also for optimizing energy usage in various systems. It highlights how stored potential energy can be harnessed and utilized effectively, emphasizing its importance in scientific and industrial contexts.