Question

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?

Short answer

The heat capacity of the calorimeter is \(1.647 \,\mathrm{kJ/^\circ C}\), the energy of combustion per gram of vanillin is \(25.13\,\mathrm{kJ/g}\), and the energy per mole of vanillin is \(3822.53 \,\mathrm{kJ/mol}\).

Step-by-step solution

Calculate the energy released by benzoic acid

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

Calculate the heat capacity of the calorimeter

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

Calculate the energy released by vanillin combustion

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

Calculate the energy of combustion per gram and per mole of vanillin

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.

Key concepts

Heat Capacity

When discussing bomb calorimetry, heat capacity is a key concept. Heat capacity is the amount of energy needed to raise the temperature of a system by one degree Celsius. This measure is crucial as it allows us to determine how much energy is absorbed or released during a reaction.
For instance, during the combustion of benzoic acid in the calorimeter, a known quantity of energy causes a specific temperature change. By dividing the energy release by the temperature change, we obtain the heat capacity of the calorimeter.
With a calculated heat capacity of 1.647 kJ/°C, any further reactions in the calorimeter can help determine the energy changes by simply measuring the temperature shifts. Understanding this concept is vital for accurate energy measurements in chemical reactions within calorimeters.

Combustion Reaction

A combustion reaction is a chemical process where a substance combines with oxygen, releasing energy in the form of heat and light. This type of reaction is common in everyday life, from burning wood to the functioning of internal combustion engines.
In our context, benzoic acid and vanillin undergo combustion inside a bomb calorimeter. The calorimeter acts as an isolated system where all energy changes can be accurately measured.
Benzoic acid, known for releasing a significant amount of energy upon combustion, serves as a calibration standard. When vanillin is combusted, the energy change observed is due to the breakdown of its chemical bonds and formation of new products, primarily carbon dioxide and water. These reactions illustrate the fundamental principles of thermochemistry as they demonstrate energy conversion from chemical potential energy to thermal energy.

Energy Calculation

Energy calculation in bomb calorimetry involves measuring the heat released or absorbed during a chemical reaction. This is typically expressed in kilojoules (kJ).
Initially, the energy released by the combustion of benzoic acid is calculated using its known energy content per gram. By burning 0.1584 g of benzoic acid and observing the temperature rise, we calculate the total energy release.
Subsequently, understanding the calorimeter's heat capacity allows for the calculation of energy changes in other reactions. Thus, when vanillin is burned, the increase in temperature reflects the energy released. This approach enables the determination of energy per gram and per mole of a substance, aiding in comprehensive energy evaluations of different chemical processes.

Vanillin

Vanillin is not only a flavoring agent in food but also a subject of chemical analysis. It has the molecular formula C\(_8\)H\(_8\)O\(_3\).
In the context of calorimetry, vanillin serves as a sample whose combustion energy needs to be determined. By combusting a known quantity in a calorimeter, we can assess how much energy is released. This information is crucial for various applications, such as flavor manufacturing or pharmaceutical development.
For vanillin, the energy released per gram and per mole through combustion has been calculated. This highlights the profound nature of chemical energy transformations and the utility of bomb calorimetry in quantifying such energy changes for diverse substances.