Question

When 1 mol of a fuel burns at constant pressure, it produces 3452\(\mathrm { kJ }\) of heat and does 11\(\mathrm { kJ }\) of work. What are \(\Delta E\) and \(\Delta H\) for the combustion of the fuel?

Short answer

\(\Delta E = -3441 \mathrm{kJ}\) and \(\Delta H = -3452 \mathrm{kJ}\)

Step-by-step solution

Understand the definitions of \(\Delta E\) and \(\Delta H\)

\(\Delta E\), or the change in internal energy, is given by the first law of thermodynamics: \(\Delta E = q + w\), where \(q\) is the heat absorbed and \(w\) is the work done on the system. \(\Delta H\), or the enthalpy change, is defined at constant pressure as \(\Delta H = q_p\), where \(q_p\) is the heat absorbed or released at constant pressure.

Calculate \(\Delta E\) for the combustion

Use the first law of thermodynamics to find \(\Delta E\). Since the fuel is burning, it releases heat and does work on the surroundings; therefore, \(q\) is negative and \(w\) is positive from the perspective of the system: \(\Delta E = q + w = -3452\mathrm{kJ} + 11\mathrm{kJ}\).

Solve for \(\Delta E\)

Calculate the value of \(\Delta E\) by simple arithmetic: \(\Delta E = -3452\mathrm{kJ} + 11\mathrm{kJ} = -3441\mathrm{kJ}\).

Calculate \(\Delta H\) for the combustion

Since the process occurs at constant pressure, \(\Delta H = q_p\) and the work done \(w\) is not a factor in calculating \(\Delta H\). Therefore, \(\Delta H = -3452\mathrm{kJ}\) because all heat given off is equal to the enthalpy change at constant pressure.

Key concepts

First Law of Thermodynamics

Understanding the first law of thermodynamics is essential when analyzing energy changes during chemical reactions. This fundamental law states that energy cannot be created or destroyed in an isolated system; it can only be transferred or transformed. In the context of our exercise, the law can be applied to the combustion of fuel, a chemical process that converts chemical energy into heat and work. The formula for the first law is expressed as \(\Delta E = q + w\), where \(\Delta E\) represents the change in internal energy, \(q\) is the heat exchanged, and \(w\) is the work done by or on the system. Here, if heat is released and work is done by the system, both are considered negative values in the context of the system gaining or losing energy.

Change in Internal Energy

The change in internal energy, represented as \(\Delta E\), is a key concept in understanding chemical thermodynamics. It is the total energy change within a system, encompassing kinetic and potential energy of molecules. For the given exercise, \(\Delta E\) is calculated by adding the heat released (\(-3452 \mathrm{kJ}\)) and the work done (\(11 \mathrm{kJ}\)). It's important to note that the sign convention states energy entering the system is positive, while energy leaving the system is negative. Therefore, since the system (fuel) is releasing heat and doing work on the surroundings, \(\Delta E\) will be negative, indicating the system lost energy during this process.

Constant Pressure

Thermodynamic processes, such as combustion, often occur at a constant pressure, specially in open atmospheric conditions. In the exercise, the fuel combustion takes place at constant pressure, which simplifies the calculation of enthalpy change, \(\Delta H\). The enthalpy change at constant pressure is directly equivalent to the heat gained or lost (\(q_p\)) in a process. For processes occurring at constant pressure, if \(q_p\) is negative, it means the system released heat to the surroundings, characteristic of an exothermic reaction, such as in the burning of fuel.

Heat Transfer

Heat transfer is the process of thermal energy moving from a hotter object or region to a cooler one. It can be achieved via conduction, convection, or radiation. In the context of the exercise, the heat transfer pertains to the heat released when fuel burns, a form of energy flow out of the system. This heat release can be quantified and is critical to calculating both \(\Delta E\) and \(\Delta H\). In thermochemistry, tracking this energy flow is crucial for understanding reaction energetics and predicting reaction behavior under different conditions.

Thermochemistry

Finally, thermochemistry is the study of energy and heat associated with chemical reactions and physical transformations. In our exercise, thermochemistry allows us to examine the enthalpy change during the fuel's combustion, identifying it as an exothermic process due to the release of heat. We're able to calculate the enthalpy (\(\Delta H\)) and internal energy changes (\(\Delta E\)) using principles of thermochemistry. These calculations help us quantify the energy change in the system, improving our understanding of how energy is conserved in chemical processes following the first law of thermodynamics.