Problem 107 - General Chemistry

Question

A \(10.00-\mathrm{g}\) sample of acetic acid, \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), was burned in a bomb calorimeter in an excess of oxygen. $$ \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(l)+2 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ The temperature of the calorimeter rose from \(25.00^{\circ} \mathrm{C}\) to \(35.84^{\circ} \mathrm{C}\). If the heat capacity of the calorimeter and its contents is \(13.43 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\), what is the enthalpy change for the reaction?

Step-by-Step Solution

Answer

The enthalpy change for the reaction is \(-874.6 \, \text{kJ/mol}\).

Step 1: Identify Given Values

First, write down all known quantities from the problem statement. We have:- Mass of acetic acid, \(10.00\, \text{g}\).- Temperature change, \(\Delta T = 35.84^{\circ} \text{C} - 25.00^{\circ} \text{C}\).- Heat capacity of the calorimeter, \(13.43\, \text{kJ}/^{\circ} \text{C}\).

Step 2: Calculate Temperature Change

Calculate the temperature change using the given temperatures:\[\Delta T = 35.84^{\circ} \text{C} - 25.00^{\circ} \text{C} = 10.84^{\circ} \text{C}\]

Step 3: Calculate Heat Absorbed by Calorimeter

Using the heat capacity of the calorimeter, calculate the heat absorbed:\[ q = C_{\text{cal}} \times \Delta T = 13.43\, \text{kJ}/^{\circ} \text{C} \times 10.84^{\circ} \text{C} = 145.5952 \, \text{kJ} \]

Step 4: Calculate the Enthalpy Change per Gram

The heat absorbed by the calorimeter represents the enthalpy change for the amount of acetic acid combusted. Since the reaction is exothermic, the enthalpy change per gram of acetic acid is:\[ \Delta H = -q = -145.5952 \, \text{kJ} \]

Step 5: Convert Mass to Moles

Calculate the molar mass of acetic acid, \( \text{HC}_2\text{H}_3\text{O}_2\), which is \( (2\times12.01) + (4\times1.01) + (2\times16.00) = 60.05 \, \text{g/mol} \).Find the number of moles:\[ \text{moles of }\text{HC}_2\text{H}_3\text{O}_2 = \frac{10.00 \, \text{g}}{60.05 \, \text{g/mol}} = 0.1665 \, \text{mol} \]

Step 6: Calculate Enthalpy Change per Mole

Convert the total enthalpy change to a molar basis:\[ \Delta H_{\text{mol}} = \frac{-145.5952 \, \text{kJ}}{0.1665 \, \text{mol}} = -874.6 \, \text{kJ/mol} \]

Key Concepts

Enthalpy Change

Enthalpy change is a concept in thermodynamics that measures the amount of heat absorbed or released during a chemical reaction at constant pressure. In the context of a bomb calorimeter, the enthalpy change can be calculated by determining the heat absorbed or released by the system, often using a water bath or other medium to measure changes in temperature.
The formula to calculate enthalpy change (\( \Delta H \)) is:

• \( \Delta H = q \)
• Here, \( q \) is the heat absorbed or released.

In this exercise, enthalpy change was determined for the combustion of acetic acid in a bomb calorimeter. By measuring the temperature change of the calorimeter, we were able to calculate the heat energy change. The enthalpy change per mole was ultimately obtained by dividing the total energy change by the number of moles of acetic acid combusted. This provides insight into whether the reaction was exothermic or endothermic, and how energetically favorable the reaction might be in real-world conditions.

Heat Capacity

Heat capacity is an important property that determines how a substance or system responds to changes in heat energy. It quantifies the amount of heat required to raise the temperature of the system by one degree Celsius.
In the context of a calorimeter, the heat capacity informs us how much energy is required to change the temperature of the entire system, including the surrounding materials. Knowing the heat capacity allows us to calculate the total heat absorbed or released during a reaction. The formula for calculating the heat absorbed (\( q \)) is given by:

• \( q = C_{\text{cal}} \times \Delta T \)
• where \( C_{\text{cal}} \) is the heat capacity of the calorimeter and \( \Delta T \) is the change in temperature.

For this exercise, the heat capacity of the calorimeter was given as 13.43 kJ/°C. By multiplying this value by the temperature change measured during the combustion reaction, we were able to calculate the total heat energy change for the system.

Exothermic Reaction

An exothermic reaction is one that releases heat energy to the surroundings. This type of reaction is characterized by a decrease in the enthalpy of the system, resulting in the surroundings absorbing heat, thereby increasing in temperature.
In our problem, the combustion of acetic acid in the presence of oxygen is an exothermic reaction. This is evidenced by the rise in temperature of the calorimeter during the reaction, signifying heat being given off to the environment.
The final calculation showed a negative enthalpy change, \( \Delta H = -874.6 \, \text{kJ/mol} \), emphasizing that the reaction released a significant amount of energy. Observing and understanding such reactions can be vital in multiple fields, from power generation to the culinary arts, each seeking to harness the energy released for various applications.
Exothermic reactions are often preferred in industrial processes due to their energy-producing nature, making them cost-effective and efficient.

Calorimeter

A calorimeter is a device used to measure the amount of heat involved in a chemical or physical process. Bomb calorimeters, in particular, are designed to measure the heat of combustion of a sample within a sealed, robust container, which ensures that the reaction occurs in a controlled environment.
The basic principle of a calorimeter relies on the law of energy conservation. Heat absorbed or released is transferred to the surrounding water or medium, allowing for measurement of temperature changes. From these changes, the amount of heat exchanged in the reaction can be deduced.
Key aspects of a bomb calorimeter include:

• An insulated container to maintain an isolated system
• A known heat capacity to aid in calculations
• Accurate temperature measurement devices

In this exercise, the bomb calorimeter allowed us to determine the heat of combustion for acetic acid by carefully measuring the temperature rise in the contained medium, translating these changes into an enthalpy value for the reaction. Understanding how to use a calorimeter effectively is crucial in experiments where precise energy measurements are necessary.