Problem 63 - Chemistry: An Atoms-Focused Approach

Question

The complete combustion of \(1.200 \mathrm{g}\) of cinnamaldehyde \((\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O},\) one of the compounds in cinnamon) in a bomb. calorimeter \(\left(C_{\text {calorimeter }}=3.640 \mathrm{kJ} /^{\circ} \mathrm{C}\right)\) produced an increase in temperature of \(12.79^{\circ} \mathrm{C} .\) How much thermal energy is produced during the complete combustion of one mole of cinnamaldehyde?

Step-by-Step Solution

Answer

Solution: Follow these steps: 1. Calculate the energy change during the combustion using the given temperature change (12.79°C) and heat capacity of the calorimeter (3.640 kJ/°C). 2. Calculate the moles of cinnamaldehyde in the 1.200g sample using its molar mass. 3. Divide the energy change during combustion by the moles of cinnamaldehyde to find the energy per mole of cinnamaldehyde.

Step 1: (Step 1: Calculate the energy change during the combustion)

(As given, the temperature change of the calorimeter is \(12.79^{\circ} \mathrm{C}\) and its heat capacity is \(3.640 \mathrm{kJ}/^{\circ} \mathrm{C}\). We can calculate the energy change during the combustion using the formula: \(\Delta E = C_\text{calorimeter} \cdot \Delta T\). \[\Delta E = 3.640 \mathrm{kJ}/^{\circ} \mathrm{C} \times 12.79^{\circ} \mathrm{C}\])

Step 2: (Step 2: Calculate the moles of cinnamaldehyde in the sample)

(Calculate the moles of cinnamaldehyde using its molar mass (\(M\)) and the given mass (1.200g). The molar mass of cinnamaldehyde is \(9 \times (12.01 \mathrm{g/mol}) + 8 \times(1.008 \mathrm{g/mol}) + 1 \times (16.00 \mathrm{g/mol})\). \[n = \frac{1.200\mathrm{g}}{M}\])

Step 3: (Step 3: Calculate the energy per mole of cinnamaldehyde)

(To calculate the energy per mole of cinnamaldehyde, we divide the energy change during the combustion (\(\Delta E\)) by the moles (n) of cinnamaldehyde. \[E_\text{per mole} = \frac{\Delta E}{n}\]) Putting it all together, the thermal energy produced during the complete combustion of one mole of cinnamaldehyde can be found using these steps.

Key Concepts

Calorimetry

Calorimetry is the science of measuring heat changes during chemical reactions or physical changes. Here, it plays a vital role in understanding the energy changes in reactions, such as combustion. When a substance burns, heat is transferred, and calorimetry helps in quantifying this heat.

To measure the thermal energy or enthalpy change during a reaction, a bomb calorimeter is often used. It is an insulated device where the reaction takes place, capturing the heat released. The temperature change within the calorimeter indicates how much energy has been either absorbed or released.

In our given exercise, we use the formula:

\[\Delta E = C_\text{calorimeter} \times \Delta T\]

Where:

• \(C_\text{calorimeter}\) is the heat capacity of the calorimeter.
• \(\Delta T\) is the change in temperature.

Practical calorimetry calculations are critical for understanding energy changes in both chemistry and physical science contexts.

Combustion Reactions

Combustion reactions are chemical processes where a substance reacts with oxygen to release energy in the form of heat and often light. These reactions are typically exothermic, meaning they release energy.

Cinnamaldehyde, when undergoing complete combustion, reacts with oxygen to produce carbon dioxide, water, and energy. The general form of a combustion reaction is:

\[\text{Fuel} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} + \text{Energy}\]

In the provided exercise, the combustion of cinnamaldehyde results in a notable temperature increase captured by the calorimeter, indicating significant energy release. Understanding combustion reactions is crucial in fields ranging from energy production to understanding organic compound behaviors in various environments.

Molar Mass Calculation

Calculating the molar mass of a compound is a fundamental skill in chemistry, necessary for determining the number of moles in a given sample. Molar mass is calculated by adding the atomic masses of each element in a compound, multiplied by their respective quantities in a molecule.

For cinnamaldehyde (\(\text{C}_9\text{H}_8\text{O}\)), its molar mass can be calculated as follows:

• Carbon (C): \(9 \times 12.01 \text{ g/mol}\)
• Hydrogen (H): \(8 \times 1.008 \text{ g/mol}\)
• Oxygen (O): \(1 \times 16.00 \text{ g/mol}\)

Adding these values gives the total molar mass of cinnamaldehyde. Once you have the molar mass, you can find the number of moles \(n\) by using the formula:

\[n = \frac{\text{mass of sample}}{\text{molar mass}}\]

This calculation is key when converting a mass measurement into moles, allowing for further thermodynamic calculations in exercises involving calorimetry and combustion reactions.