Question

Consider the reaction of methane with oxygen. Suppose that the reaction is carried out in a furnace used to heat a house. If \(q=-890 \mathrm{~kJ}\) and \(w=+5 \mathrm{~kJ}\), what is \(\Delta E ? \Delta H\) at \(25^{\circ} \mathrm{C} ?\)

Short answer

Question: Determine the change in internal energy (∆E) and enthalpy (∆H) for a reaction at 25°C given the heat (q) is -890 kJ and the work (w) is +5 kJ. Answer: The change in internal energy (∆E) for the reaction at 25°C is -885 kJ, and the change in enthalpy (∆H) for the reaction at 25°C is -890 kJ.

Step-by-step solution

Find the change in internal energy (∆E)

To find the change in internal energy (∆E) for the reaction, we can use the given values of heat (q) and work (w). The formula to calculate ∆E is: ∆E = q + w Substitute the given values into the equation: ∆E = (-890 kJ) + (+5 kJ) Now, perform the calculation to find ∆E: ∆E = -885 kJ

Find the change in enthalpy (∆H)

Since we assumed the reaction occurs at constant pressure, the change in enthalpy (∆H) can be calculated using the given heat value (q): ∆H = q Substitute the given value of heat (q) into the equation: ∆H = -890 kJ So, the change in enthalpy (∆H) for the reaction at 25°C is -890 kJ. To summarize: - The change in internal energy (∆E) for the reaction at 25°C is -885 kJ. - The change in enthalpy (∆H) for the reaction at 25°C is -890 kJ.

Key concepts

Thermochemistry

Thermochemistry is the branch of chemistry concerned with the quantities of heat evolved or absorbed during chemical reactions. It's a foundational concept for understanding how energy is transferred between a system and its surroundings. For instance, when a fuel like methane burns in a furnace, energy in the form of heat is released. This heat can be quantified and related to other properties such as temperature and work. In thermochemical calculations, we often use units like joules (J) or kilojoules (kJ) to express the amount of heat involved in a chemical process.

Key to these calculations is the understanding that energy cannot be created or destroyed (the first law of thermodynamics). It can only change from one form to another. In the case of methane combustion, chemical energy is converted into heat, which may be used to warm a house. The furnace example illustrates a practical application of thermochemistry in our daily lives.

Enthalpy Change

Enthalpy change (∆H) is a measure of the heat change at constant pressure during a chemical reaction. It is an extensive property, meaning it depends on the amount of substance involved. When a substance reacts, the energy change associated with the reaction includes not only the internal energy but also the work done to change the system's volume against the surrounding atmospheric pressure.

For example, the complete combustion of methane (CH_4) in oxygen to form carbon dioxide (CO_2) and water (H_2O) has an associated enthalpy change. This ∆H can be negative, indicating an exothermic reaction where heat is released to the surroundings, or positive, for an endothermic reaction where heat is absorbed. In our furnace scenario, the negative value of ∆H denotes that the combustion of methane is exothermic, and therefore useful for heating.

Internal Energy

Internal energy is the total energy contained within a chemical system. It includes not only kinetic and potential energy at the molecular level but also chemical energy stored in molecular bonds. The change in internal energy (∆E) of a system can be influenced by transferring heat to or from the system or by doing work on or by the system.

To determine the change in internal energy for a chemical reaction, one can use the formula ∆E = q + w, where q is the heat exchanged and w is the work done. Positive values of q and w mean that heat is absorbed by the system and work is done on the system, respectively. Conversely, negative values of q and w imply heat loss and work done by the system. This concept is integral to understanding the energy changes during a reaction, such as the heat (q) released and work (5 kJ) occurring during the combustion of methane in our example.

Heat and Work in Chemistry

Heat and work are the two primary ways that energy can enter or leave a chemical system, and both play a crucial role in chemical thermodynamics. Heat, denoted by q, is related to changes in temperature and phase of a substance, while work, represented by w, is associated with the force exerted over a distance—a common form being the work of expansion against external pressure.

In a chemical context, work often includes pressure-volume work during reactions that occur at constant pressure. The knowledge that heat absorbed or released (q) under constant pressure is equal to the enthalpy change (∆H) is a key concept in understanding the energy aspects of reactions. In the exercise we're discussing, the negative q value indicates the release of heat, while the positive w value suggests that the system has done work on its surroundings, illustrating a dynamic interplay between heat and work in chemistry.