Problem 66 - Chemistry: An Atoms-Focused Approach

Question

The flavor of anise is due to anethole, a compound with the molecular formula \(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}\) Combustion of one mole of anethole produces \(5541 \mathrm{kJ}\) of thermal energy. If \(0.950 \mathrm{g}\) of anethole is combusted in a bomb calorimeter whose heat capacity ( \(C_{\text {calorimeter }}\) ) is \(7.854 \mathrm{kJ} /^{\circ} \mathrm{C},\) what is the change in temperature of the calorimeter?

Step-by-Step Solution

Answer

Answer: The change in temperature of the calorimeter is 4.52°C.

Step 1: Calculate the molar mass of anethole

In order to find the energy released by the combustion of the given mass of anethole, we first need to determine the molar mass of anethole. The molecular formula of anethole is \(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}\). Using the atomic masses of carbon, hydrogen, and oxygen, we can calculate the molar mass: Molar mass of anethole = (10 × 12.01) (Carbon) + (12 × 1.01) (Hydrogen) + (1 × 16.00) (Oxygen) Molar mass of anethole = \(120.1 + 12.12 + 16.00 = 148.22 \mathrm{g/mol}\)

Step 2: Calculate moles of anethole in given mass

We are given that the mass of anethole combusted is 0.950 g. Using the molar mass of anethole, we can calculate the moles of anethole: Moles of anethole = \(\frac{\text{mass}}{\text{molar mass}} = \frac{0.950 \mathrm{g}}{148.22 \mathrm{g/mol}} = 0.00641 \mathrm{mol}\)

Step 3: Calculate energy produced by combustion of given mass of anethole

We are given that combustion of one mole of anethole produces 5541 kJ of thermal energy. Therefore, the total energy produced by the combustion of 0.00641 mol of anethole will be: Energy produced = (Energy per mole) × (moles of anethole) Energy produced = \(5541 \mathrm{kJ/mol} \times 0.00641 \mathrm{mol} = 35.51 \mathrm{kJ}\)

Step 4: Calculate the change in temperature of the calorimeter

We are given the heat capacity of the calorimeter, \(C_{\text{calorimeter}} = 7.854 \mathrm{kJ} /^{\circ} \mathrm{C}\). We can use this information to calculate the change in temperature of the calorimeter: Change in temperature = \(\frac{\text{Energy produced}}{\text{Heat capacity of calorimeter}} = \frac{35.51 \mathrm{kJ}}{7.854 \mathrm{kJ/^{\circ} \mathrm{C}}} = 4.52 ^{\circ} \mathrm{C}\) Hence, the change in temperature of the calorimeter is \(4.52 ^{\circ} \mathrm{C}\).

Key Concepts

Molar Mass Calculation

When embarking on the journey of calculating chemical reactions, understanding molar mass is a fundamental step. Molar mass is the weight of one mole of a substance, often denoted in grams per mole (g/mol). To calculate the molar mass of a compound like anethole, you need to sum the atomic masses of all the atoms in its molecular formula, which is \(\text{C}_{10}\text{H}_{12}\text{O}\) for anethole.
Here's how the calculation was performed:

• Carbon (C) has an atomic mass of 12.01 g/mol, and there are 10 carbon atoms in anethole, giving us \(10 \times 12.01 = 120.1 \text{ g/mol}\).
• Hydrogen (H) weighs 1.01 g/mol and there are 12 hydrogen atoms, hence \(12 \times 1.01 = 12.12 \text{ g/mol}\).
• Oxygen (O) has a singular presence with an atomic mass of 16.00 g/mol.

By adding these together, \(120.1 + 12.12 + 16.00\), the molar mass of anethole is determined to be 148.22 g/mol. Knowing this value is essential for converting between mass and moles in chemical equations.

Combustion Energy

The energy released during combustion is crucial to understand various chemical processes. Combustion energy is the amount of energy released as heat when a compound undergoes complete burning in the presence of oxygen. For anethole, we are aware that the combustion of one mole produces \(5541 \text{kJ}\) of thermal energy.
To use this information in practical scenarios, such as our exercise, you often need to convert the mass of the substance you're using into moles using the previously calculated molar mass. With anethole, knowing that \(0.950 \text{ g}\) combusted corresponds to \(0.00641 \text{ mol}\) due to its molar mass of 148.22 g/mol helps you determine smaller scales of combustion energy.

• First, calculate the moles: \(\text{moles of anethole} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.950 \text{ g}}{148.22 \text{ g/mol}} = 0.00641 \text{ mol}\).
• Then find the energy released: \(\text{Energy produced} = 5541 \text{kJ/mol} \times 0.00641 \text{ mol} = 35.51 \text{kJ}\).

This calculated energy shows the thermal energy generated during the combustion of the specific amount of anethole used in the experiment.

Heat Capacity of Calorimeter

Understanding the heat capacity of a calorimeter is vital when measuring heat changes in chemical reactions. A bomb calorimeter is a robust device used to determine the heat of combustion reactions, and its heat capacity represents how much heat the calorimeter can absorb per degree Celsius (°C) of temperature increase.
In the given problem, the calorimeter has a heat capacity \(C_{\text{calorimeter}}\) of \(7.854 \text{kJ/°C}\). This measure allows us to find out how much the temperature changes when the calorimeter absorbs a certain amount of thermal energy during a reaction.

• Using the formula \(\text{Change in temperature} = \frac{\text{Energy produced}}{\text{Heat capacity of calorimeter}}\), we determine how much heat causes a temperature change.
• Here, \(\text{Change in temperature} = \frac{35.51 \text{kJ}}{7.854 \text{kJ/°C}} = 4.52 \text{°C}\).

Thus, the converted energy from the combustion of anethole results in an increased temperature of \(4.52 \text{°C}\) in the calorimeter. This understanding helps in designing and conducting precise experimental setups in chemistry.