91Ó°ÊÓ

Enthalpy, denoted as \( \Delta H \), quantifies the total heat content of a system. It is especially useful in thermochemistry as it describes the heat change at constant pressure. The reaction provided has an enthalpy change of \( -483.6 \text{ kJ} \). This negative value indicates that the reaction releases energy to the surroundings, known as an exothermic reaction.

In chemical processes, enthalpy changes give us insight into whether energy is absorbed or released.

• Exothermic reactions have negative \( \Delta H \) values, releasing heat.
• Endothermic reactions have positive \( \Delta H \) values, absorbing heat.

For this specific reaction forming water vapor from hydrogen and oxygen, the enthalpy change implies that the system releases 483.6 kJ of energy. This energy release helps to drive the formation of the product and stabilize it energetically.

Internal energy change, represented as \( \Delta U \), varies differently from enthalpy as it includes all energy changes within a system, not just the heat at constant pressure. To find \( \Delta U \), we use the equation:\[\Delta U = \Delta H - w\]where \( w \) is the work done on or by the system.

In this case:

• \( \Delta H = -483.6 \text{ kJ} \)
• \( w = 2.27072 \text{ kJ} \)

Substituting these values, we get:\[\Delta U = -483.6 \text{ kJ} - 2.27072 \text{ kJ} = -485.87072 \text{ kJ}\]This calculation shows that the total internal energy of the system decreases. The energy leaving the system indicates that a greater amount of energy is being expended due to both heat loss and work being performed.

Work done on a system is represented by the work (\( w \)) formula:\[w = -P\Delta V\]where

• \( P \) stands for pressure, equivalent to 1 atm or 101.3 J/L under standard conditions
• \( \Delta V \) is the change in volume, equating to \(-22.4 \text{ L} \) for this reaction because the volume decreases.

Thus, calculating work gives us:\[w = -1 \text{ atm} \times (-22.4 \text{ L}) \times (101.3 \text{ J/L}) = 2270.72 \text{ J} = 2.27072 \text{ kJ}\]This calculation shows 2.27072 kJ of work is done on the system.

Total work is positive when it's done on the system and negative if work is done by the system. Through these calculations, we see that the surrounding pressure performs work on the chemical system as it contracts, contributing to the overall energy dynamics between the reactants and products.