Problem 64 - Chemistry: An Atoms-Focused Approach

Question

Spices The aromatic hydrocarbon cymene \(\left(\mathrm{C}_{10} \mathrm{H}_{14}\right)\) is found in nearly 100 spices and fragrances, including coriander, anise, and thyme. The complete combustion of \(1.608 \mathrm{g}\) of cymene in a bomb calorimeter \(\left(C_{\text {calorimeter }}=3.640 \mathrm{kJ} /^{\circ} \mathrm{C}\right)\) produced an increase in temperature of \(19.35^{\circ} \mathrm{C} .\) How much thermal energy is produced during the complete combustion of one mole of cymene?

Step-by-Step Solution

Answer

Answer: The thermal energy produced during the complete combustion of one mole of cymene is approximately 5876 kJ/mol.

Step 1: (Step 1: Calculate the thermal energy released for the given mass of cymene)

To determine the thermal energy released during the complete combustion of \(1.608 \ \text{g}\) of cymene, we will use the equation: \(\displaystyle \textrm{Thermal energy released} = C_{\textrm{calorimeter}} \times \Delta T\) where \(C_{\textrm{calorimeter}}= 3.640 \ \mathrm{kJ/}^{\circ} \mathrm{C}\) and \(\Delta T = 19.35^{\circ} \mathrm{C}\). Thermal energy released = \((3.640 \ \mathrm{kJ/}^{\circ} \mathrm{C}) (19.35^{\circ} \mathrm{C}) = 70.427 \ \mathrm{kJ}\)

Step 2: (Step 2: Calculate the moles of the given mass of cymene)

We will now determine the number of moles of \(1.608 \ \text{g}\) of cymene. The molar mass of cymene (\(\mathrm{C}_{10} \mathrm{H}_{14}\) ) is: \(10\times 12.01 \ \mathrm{g/mol} + 14\times 1.008 \ \mathrm{g/mol} = 134.22 \ \mathrm{g/mol}\) Number of moles = \(\displaystyle \frac{\text{mass}}{\text{molar mass}}\) Number of moles = \(\displaystyle \frac{1.608 \ \text{g}}{134.22 \ \text{g/mol}} \approx 0.01198 \ \text{mol}\)

Step 3: (Step 3: Calculate the thermal energy produced during the complete combustion of one mole of cymene)

Finally, we will find the thermal energy produced during the complete combustion of one mole of cymene. To do this, we will use the equation: \(\displaystyle \textrm{Thermal energy per mole} = \frac{\textrm{Total thermal energy released}}{\textrm{Number of moles}}\) Thermal energy per mole = \(\displaystyle \frac{70.427 \ \mathrm{kJ}}{0.01198 \ \text{mol}} \approx 5876 \ \mathrm{kJ/mol}\) The thermal energy produced during the complete combustion of one mole of cymene is approximately \(5876 \ \mathrm{kJ/mol}\).

Key Concepts

Combustion Reactions

Combustion reactions are chemical processes where a substance combines with oxygen and releases energy. This energy typically comes in the form of heat and light.
In a combustion reaction, hydrocarbons like cymene, a component found in many spices, combine with oxygen to produce carbon dioxide and water. Essentially, it's a burning process, and it's why things like wood, gasoline, and other fuels can produce energy.

Key features of combustion reactions include:

• **Reactants**: Usually a hydrocarbon and oxygen.
• **Products**: Carbon dioxide and water.
• **Exothermic**: Produces heat and sometimes light.

This exothermic characteristic is what makes combustion reactions useful for producing energy, as seen in the complete combustion of cymene producing substantial thermal energy.

Calorimetry

Calorimetry is the science of measuring the amount of heat involved in a chemical or physical process. It's a crucial process for understanding how much energy is generated or consumed. In our example of cymene's combustion, a bomb calorimeter was used.

A bomb calorimeter is a sealed container that ensures all heat produced by the reaction is absorbed by the surrounding water and calorimeter itself, thereby allowing precise measurements of temperature change.

When using a bomb calorimeter, the following steps are generally observed:

• **Calorimeter Constant**: The known heat capacity of the calorimeter, in this case, 3.640 kJ/°C.
• **Temperature Change**: The difference in temperature before and after the reaction, which was 19.35°C.
• **Calculation**: The heat produced is calculated by multiplying the calorimeter constant by the temperature change.

For cymene, this multiplication revealed that 70.427 kJ of energy was released during its combustion, showcasing the effectiveness of calorimetry in measuring thermal energy changes.

Molar Mass Calculation

Molar mass is a vital concept in chemistry that denotes the mass of one mole of a substance. It's essential for converting between grams and moles, two units often used in chemical calculations.

To calculate the molar mass, consider the atomic masses of elements in a compound. For cymene, \text{C}_{10}\text{H}_{14}, the molar mass was calculated step-by-step:

• Carbon (C): Has an atomic mass of 12.01 g/mol. For 10 carbon atoms, it’s \( 10 \times 12.01 \ \text{g/mol} \).
• Hydrogen (H): Each hydrogen atom has a mass of 1.008 g/mol. For 14 hydrogen atoms, it’s \( 14 \times 1.008 \ \text{g/mol} \).

Adding these together, cymene’s molar mass is 134.22 g/mol.

Understanding molar mass is essential; it enables us to convert the mass of cymene (1.608 g) into moles (approximately 0.01198 mol). These conversions are crucial in determining how much energy is produced per mole in chemical reactions such as combustion.