The corrosion (rusting) of iron in oxygen-free water includes the formation of iron(II) hydroxide from iron by the following reaction: Fe(s) + 2 H2O(l) → Fe(OH)2(s) + H2(g). If 1 mol of iron reacts at 298 K under 101.3 kPa pressure, the reaction performs 2.48 J of P-V work, pushing back the atmosphere as the gaseous H2 forms. At the same time, 11.73 kJ of heat is released to the environment. What are the values of _x001F_H and of _x001F_E for this reaction?

Verified step by step guidance

Step 1: Understand the problem and identify the given data. The reaction involves the formation of iron(II) hydroxide and hydrogen gas from iron and water. Given data includes: 1 mol of iron, 298 K temperature, 101.3 kPa pressure, 2.48 J of P-V work, and 11.73 kJ of heat released.

Step 2: Recall the relationship between enthalpy change (ΔH), internal energy change (ΔE), work (w), and heat (q). The first law of thermodynamics states: ΔE = q + w. Here, q is the heat exchanged, and w is the work done by the system.

Step 3: Convert all energy values to the same units for consistency. Since the heat released is given in kJ and the work done is in J, convert the work from J to kJ by dividing by 1000. Thus, 2.48 J = 0.00248 kJ.

Step 4: Calculate the change in internal energy (ΔE) using the formula: ΔE = q + w. Substitute the values: q = -11.73 kJ (since heat is released, it's negative), and w = -0.00248 kJ (work done by the system is also negative).

Step 5: Calculate the change in enthalpy (ΔH). For reactions at constant pressure, ΔH is approximately equal to q, the heat exchanged at constant pressure. Therefore, ΔH = q = -11.73 kJ.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Thermodynamics

Thermodynamics is the branch of physical chemistry that deals with the relationships between heat, work, and energy. It is essential for understanding how energy is transferred in chemical reactions, particularly in terms of enthalpy (ΔH) and internal energy (ΔE). In this context, the heat released during the reaction and the work done against the atmosphere are key factors in calculating these energy changes.

Enthalpy (ΔH)

Enthalpy (ΔH) is a thermodynamic quantity that represents the total heat content of a system at constant pressure. It accounts for the internal energy of the system plus the product of its pressure and volume. In the given reaction, the heat released (11.73 kJ) indicates that the reaction is exothermic, and this value directly contributes to determining ΔH for the process.

Internal Energy (ΔE)

Internal energy (ΔE) is the total energy contained within a system, including kinetic and potential energies of the particles. The relationship between ΔH and ΔE can be expressed as ΔH = ΔE + PΔV, where PΔV represents the work done by the system. In this case, the work done (2.48 J) must be considered to accurately calculate ΔE from the known ΔH value.

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