The overall reaction and equilibrium constant value for a...

The overall reaction and equilibrium constant value for a hydrogen-oxygen fuel cell at $298 \mathrm{~K}$ is $$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I) \quad K=1.28 \times 10^{83}$$ a. Calculate $\mathscr{C}^{\circ}$ and $\Delta G^{\circ}$ at $298 \mathrm{~K}$ for the fuel cell reaction. b. Predict the signs of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the fuel cell reaction. c. As temperature increases, does the maximum amount of work obtained from the fuel cell reaction increase, decrease, or remain the same? Explain.

The overall reaction and equilibrium constant value for a hydrogen-oxygen fuel cell at $298 \mathrm{~K}$ is
$$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I) \quad K=1.28 \times 10^{83}$$
a. Calculate $\mathscr{C}^{\circ}$ and $\Delta G^{\circ}$ at $298 \mathrm{~K}$ for the fuel cell reaction.
b. Predict the signs of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ for the fuel cell reaction.
c. As temperature increases, does the maximum amount of work obtained from the fuel cell reaction increase, decrease, or remain the same? Explain.

Key Concepts

Equilibrium Constant (K) and Standard States

The equilibrium constant is a key parameter in thermodynamics that quantifies the ratio of the product activities to the reactant activities at equilibrium. Its value is directly related to the standard state of the system, and when expressed in concentration units, it requires careful conversion to relate to the standard Gibbs free energy. Understanding standard state conditions serves as the baseline for all thermodynamic calculations and comparisons across different systems.

Gibbs Free Energy (?G°) and Its Relationship to K

Gibbs free energy is a fundamental thermodynamic function that indicates the spontaneity of a reaction under constant temperature and pressure. The relationship ?G° = -RT ln K connects the equilibrium constant to the free energy change, allowing one to predict whether a reaction is thermodynamically favorable. This connection is central in determining the maximum non-expansion work obtainable from a process, such as in electrochemical cells.

Standard Enthalpy (?H°) and Standard Entropy (?S°) Changes

The standard enthalpy change describes the heat absorbed or released during a reaction, providing insight into whether the reaction is exothermic or endothermic. The standard entropy change reflects the change in disorder or randomness accompanying the reaction. The interplay between these two quantities determines the temperature dependence of the free energy change via the relation ?G° = ?H° – T?S°, and is crucial for predicting the thermodynamic behavior of reactions.

Temperature Dependence of Maximum Work

The maximum work obtainable from a reaction is directly linked to the Gibbs free energy change and is influenced by temperature. As temperature increases, the balance between the enthalpic and entropic contributions shifts, altering the free energy available for work. This concept is important in designing and optimizing energy conversion systems, as it dictates how efficiently chemical energy can be converted into useful work at different temperatures.

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