In the realm of thermochemistry, determining the energy released or absorbed during a chemical reaction is a crucial task. One common method for measuring this energy change, particularly for combustion reactions, is using a bomb calorimeter. This device allows us to measure the heat released at constant volume (ΔU), providing valuable insights into the energy content of fuels and the thermodynamics of chemical processes. This article delves into the step-by-step process of calculating the energy released when a sample of propane (C3H8) is burned in a bomb calorimeter. We will explore the underlying principles, the necessary calculations, and the significance of the results.
A bomb calorimeter is a device designed to measure the heat of reaction at constant volume. It consists of a strong, sealed container (the "bomb") where the reaction takes place. The bomb is submerged in a known mass of water within an insulated container. When a reaction occurs inside the bomb, the heat released or absorbed causes a change in the water's temperature. By carefully measuring this temperature change and knowing the heat capacity of the calorimeter (including the bomb and the water), we can determine the heat of reaction. Bomb calorimeters are particularly useful for studying combustion reactions, where a substance reacts rapidly with oxygen, releasing a significant amount of heat. The key principle behind bomb calorimetry is the conservation of energy. The heat released by the reaction inside the bomb is equal to the heat absorbed by the calorimeter and its contents (mainly water and the bomb itself). This relationship allows us to quantify the energy released by the reaction.
Propane (C3H8) is a widely used fuel in various applications, from heating homes to powering vehicles. Its popularity stems from its relatively high energy content and clean-burning characteristics. The combustion of propane is an exothermic reaction, meaning it releases heat into the surroundings. The balanced chemical equation for the complete combustion of propane is:
C3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(g)
This equation tells us that one mole of propane reacts with five moles of oxygen to produce three moles of carbon dioxide and four moles of water. The heat released during this reaction, known as the heat of combustion, is a crucial parameter for understanding propane's energy potential. In a bomb calorimeter, the combustion of propane occurs under constant volume conditions. This means that no work is done by the system (since there is no change in volume), and the heat released is equal to the change in internal energy (ΔU) of the reaction. To accurately determine the heat of combustion of propane, we need to carefully control the experimental conditions and precisely measure the temperature change in the calorimeter.
Our specific problem involves a 0.47 g sample of propane (C3H8) burned in a bomb calorimeter. The calorimeter itself has a mass of 1.350 kg and a specific heat capacity of 5.82 J/(g·°C). Our goal is to calculate the amount of energy released during this combustion process. To solve this problem, we need to consider the following steps:
- Calculate the number of moles of propane burned.
- Determine the heat absorbed by the calorimeter.
- Calculate the energy released per mole of propane.
We will use the given information and the principles of calorimetry to systematically arrive at the solution. Understanding the relationship between heat, temperature change, mass, and specific heat capacity is crucial for accurate calculations. We will also need to pay attention to unit conversions to ensure consistency throughout the calculations.
1. Calculating Moles of Propane
The first step in determining the energy released is to calculate the number of moles of propane (C3H8) burned. To do this, we need to use the molar mass of propane. The molar mass of propane can be calculated by summing the atomic masses of its constituent elements:
- Carbon (C): 3 atoms × 12.01 g/mol = 36.03 g/mol
- Hydrogen (H): 8 atoms × 1.01 g/mol = 8.08 g/mol
Molar mass of C3H8 = 36.03 g/mol + 8.08 g/mol = 44.11 g/mol
Now, we can calculate the number of moles of propane using the formula:
Moles = Mass / Molar mass
Moles of C3H8 = 0.47 g / 44.11 g/mol = 0.01065 moles
This value represents the amount of propane that underwent combustion in the calorimeter. It is a crucial intermediate value that we will use later to calculate the energy released per mole of propane.
2. Calculating Heat Absorbed by the Calorimeter
Next, we need to determine the amount of heat absorbed by the calorimeter. The heat absorbed (q) can be calculated using the following formula:
q = m × c × ΔT
Where:
- m = mass of the calorimeter
- c = specific heat capacity of the calorimeter
- ΔT = change in temperature
However, the change in temperature (ΔT) is not directly given in the problem statement. Therefore, let's assume the change in temperature (ΔT) after the combustion process is 1°C for the sake of this sample calculation. This assumption allows us to demonstrate the calculation process. In a real experiment, ΔT would be measured directly.
Given:
- m = 1.350 kg = 1350 g (converted kilograms to grams)
- c = 5.82 J/(g·°C)
- ΔT = 1°C (assumed for demonstration)
Now, we can plug these values into the formula:
q = 1350 g × 5.82 J/(g·°C) × 1°C = 7857 J
This value represents the heat absorbed by the calorimeter when the temperature changes by 1°C. It is important to note that this is just an example calculation, and the actual heat absorbed would depend on the measured temperature change.
3. Calculating Energy Released per Mole of Propane
Finally, we can calculate the energy released per mole of propane. Since the heat released by the combustion of propane is equal to the heat absorbed by the calorimeter, we can use the value calculated in the previous step. However, we need to consider the number of moles of propane burned.
Energy released per mole = Heat absorbed / Moles of C3H8
Energy released per mole = 7857 J / 0.01065 moles = 737,746 J/mol
To express this value in kilojoules per mole (kJ/mol), we divide by 1000:
Energy released per mole = 737,746 J/mol / 1000 = 737.75 kJ/mol
This value represents the energy released when one mole of propane is burned in the bomb calorimeter, assuming a 1°C temperature change. In a real experiment, this value would be more precise due to the accurate measurement of the temperature change.
Based on our calculations, the energy released when 0.47 g of propane is burned in the bomb calorimeter, assuming a 1°C temperature change, is approximately 737.75 kJ/mol. This value is an example of how we can determine the heat of combustion using bomb calorimetry. In a real-world scenario, the temperature change would be measured experimentally, leading to a more accurate result. The steps involved in this calculation are crucial for understanding the thermochemistry of combustion reactions and the energy content of fuels.
In conclusion, determining the energy released during a chemical reaction, such as the combustion of propane, is a fundamental task in chemistry. Bomb calorimetry provides a reliable method for measuring the heat of reaction at constant volume. By carefully considering the principles of calorimetry, the balanced chemical equation, and the experimental data, we can accurately calculate the energy released per mole of reactant. The step-by-step approach outlined in this article provides a clear framework for solving similar thermochemical problems. Understanding these concepts is essential for various applications, including fuel design, industrial processes, and environmental studies. The heat of combustion is a critical parameter for assessing the energy potential of fuels and for designing efficient combustion systems. Further research and experimentation in this area will continue to contribute to advancements in energy technologies and sustainable practices.