Problem 60 - Chemistry The Central Science

Question

Under constant-volume conditions, the heat of combustion of benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) is \(26.38 \mathrm{~kJ} / \mathrm{g}\). A 2.760 -g sample of benzoic acid is burned in a bomb calorimeter. The temperature of the calorimeter increases from \(21.60^{\circ} \mathrm{C}\) to \(29.93^{\circ} \mathrm{C}\). (a) What is the total heat capacity of the calorimeter? (b) \(\mathrm{A}\) 1.440-g sample of a new organic substance is combusted in the same calorimeter. The temperature of the calorimeter increases from \(22.14^{\circ} \mathrm{C}\) to \(27.09^{\circ} \mathrm{C}\). What is the heat of combustion per gram of the new substance? (c) Suppose that in changing samples, a portion of the water in the calorimeter were lost. In what way, if any, would this change the heat capacity of the calorimeter?

Step-by-Step Solution

Answer

In summary: (a) The total heat capacity of the calorimeter is 8.74 kJ/°C. (b) The heat of combustion per gram of the new substance is 30.04 kJ/g. (c) Losing a portion of water in the calorimeter could decrease its overall heat capacity; however, the effect might not be significant if the change is small. In case of substantial water loss, recalibration of the calorimeter would be necessary to determine the new heat capacity.

Step 1: Part (a): Heat Capacity of the Calorimeter

First, we need to calculate the total heat released by the combustion of benzoic acid (ΔH_benzoic). We know that the heat of combustion of benzoic acid is: ΔH_benzoic = 26.38 kJ/g Given that we have 2.760 g of benzoic acid, the total heat released during its combustion is: ΔH_total = ΔH_benzoic × mass ΔH_total = 26.38 kJ/g × 2.760 g = 72.8072 kJ Now, we know the temperature change of the calorimeter during the combustion of benzoic acid: ΔT_calorimeter = T_final - T_initial ΔT_calorimeter = 29.93°C - 21.60°C = 8.33°C We can now find the total heat capacity (C_calorimeter) of the calorimeter: C_calorimeter = ΔH_total / ΔT_calorimeter C_calorimeter = 72.8072 kJ / 8.33°C ≈ 8.74 kJ/°C

Step 2: Part (b): Heat of Combustion of the New Substance

To determine the heat of combustion per gram of the new substance, we first need to calculate the total heat released during its combustion: The temperature change of the calorimeter during the combustion of the new substance is: ΔT_calorimeter_new = T_final - T_initial ΔT_calorimeter_new = 27.09°C - 22.14°C = 4.95°C Now, we can use the heat capacity of the calorimeter to find the total heat released by the new substance: ΔH_total_new = C_calorimeter × ΔT_calorimeter_new ΔH_total_new = 8.74 kJ/°C × 4.95°C ≈ 43.26 kJ We are also given that the mass of the new substance is 1.440 g. We can now calculate the heat of combustion per gram of the new substance (ΔH_combustion_new): ΔH_combustion_new = ΔH_total_new / mass_new ΔH_combustion_new = 43.26 kJ / 1.440 g ≈ 30.04 kJ/g

Step 3: Part (c): Effect of water loss on calorimeter heat capacity

If a portion of the water in the calorimeter is lost, it could decrease the overall heat capacity of the calorimeter because the water generally has a higher specific heat capacity than the other components of the calorimeter. However, if the change is small, it might not have a significant effect on the results of the experiment. If the water loss is substantial, it might be necessary to recalibrate the calorimeter to find the new heat capacity before performing further experiments.

Key Concepts

Heat of Combustion

The term "heat of combustion" refers to the energy released when a compound undergoes complete combustion with oxygen. This happens under specified conditions, often measured at standard temperatures and pressures.
In calorimetry, knowing the heat of combustion for a substance is crucial because it helps quantify the total energy released during a reaction. For instance, benzoic acid has a known heat of combustion of 26.38 kJ/g. When we burn a sample, this value helps us calculate the total energy emitted.
In the exercise, by multiplying the heat of combustion of benzoic acid with the mass burned, we determine the total heat released. Understanding this concept allows one to evaluate the energetic efficiency and energy output of different materials.

Benzoic Acid

Benzoic acid (C₆H₅COOH) is a simple aromatic carboxylic acid commonly used in calorimetric measurements. Its well-documented heat of combustion makes it ideal as a reference substance in bomb calorimeter experiments.
This compound burns cleanly, meaning the chemical reaction primarily involves its combustion to carbon dioxide and water. By using benzoic acid, scientists can accurately establish the calorimeter's heat capacity, which is crucial for subsequent experiments.
These properties of benzoic acid help ensure accurate and repeatable results. That's why it is often chosen as a standard for determining the heat capacity of the calorimeter equipment. Being an easily available compound, benzoic acid continues to play a vital role in thermochemical studies.

Heat Capacity

The heat capacity of a calorimeter is a critical factor in calorimetry. It represents the amount of heat needed to change the calorimeter's temperature by one degree Celsius. This characteristic includes contributions from all parts of the calorimeter, such as the container, instruments, and any water present inside.
To find the calorimeter's heat capacity, one can use a reference compound like benzoic acid with a known heat of combustion. By measuring the temperature change in the calorimeter when a specific mass of the compound is burned, the heat capacity can be calculated by dividing the total heat released by the temperature change.
Heat capacity is essential not just for one-time measurements but also for comparing experiments. Accurate calculations and calibrations ensure reliable data when measuring other substances in the same calorimeter.

Temperature Change

Monitoring the temperature change during a reaction within a calorimeter is essential for calculating the energy changes in chemical reactions. The temperature change (\( \Delta T \)) is determined by subtracting the initial temperature from the final temperature at the end of the reaction.
This temperature change provides direct insight into the amount of heat absorbed or released by the system. With each reaction, it's essential to record accurate temperature changes as they are used alongside the calorimeter's heat capacity to calculate the total energy change.
In our example, the temperature change helped calculate the total heat energy released in burning both benzoic acid and the new substance, crucial for evaluating the calorimeter's efficiency in energy measurement. The temperature readings, hence, are fundamental to all calorimetric experiments in determining the heat dynamics of a system.