What are the values of (a) Δf G^∘(O2, g, 298 K) (b) Δf G^0(O2, g, 450 K),(c) Δf H^∘(O2, g, 298 K

step 1 In this question, we will be covering the topic of Gibbs free energy. Gibbs free energy refers t

What are the values of (a) Δf G^∘(O2, g, 298 K) (b) Δf...

What are the values of (a) $\Delta_{\mathrm{f}} G^{\circ}\left(\mathrm{O}_{2}, \mathrm{g}, 298 \mathrm{K}\right)$ (b) $\Delta_{\mathrm{f}} G^{0}\left(\mathrm{O}_{2}, \mathrm{g}, 450 \mathrm{K}\right),(\mathrm{c}) \Delta_{\mathrm{f}} H^{\circ}\left(\mathrm{O}_{2}, \mathrm{g}, 298 \mathrm{K}\right)$ and (d) $\Delta_{f} H^{\circ}\left(\mathrm{O}_{2}, \mathrm{g}, 500 \mathrm{K}\right) ?$

What are the values of (a) $\Delta_{\mathrm{f}} G^{\circ}\left(\mathrm{O}_{2}, \mathrm{g}, 298 \mathrm{K}\right)$
(b) $\Delta_{\mathrm{f}} G^{0}\left(\mathrm{O}_{2}, \mathrm{g}, 450 \mathrm{K}\right),(\mathrm{c}) \Delta_{\mathrm{f}} H^{\circ}\left(\mathrm{O}_{2}, \mathrm{g}, 298 \mathrm{K}\right)$ and
(d) $\Delta_{f} H^{\circ}\left(\mathrm{O}_{2}, \mathrm{g}, 500 \mathrm{K}\right) ?$

Key Concepts

Standard State

The standard state is the defined reference condition for substances, usually chosen as 1 atm (or 1 bar) pressure and a specified temperature (commonly 298 K). In this state, the properties of elements and compounds are tabulated and used as baselines. For instance, elements in their most stable forms at 298 K (like O?(g)) are assigned standard formation values, which serve as reference points for thermodynamic calculations.

Standard Enthalpy of Formation

The standard enthalpy of formation (?fH°) is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states at a specified temperature (usually 298 K). For elements in their standard state, such as O?(g) at 298 K, this value is set to zero by convention. At other temperatures, however, the enthalpy may change due to temperature?dependent heat capacities, and corrections must be applied.

Standard Gibbs Free Energy of Formation

The standard Gibbs free energy of formation (?fG°) is defined as the free energy change for the formation of one mole of a compound from its elements in their standard states at a specified temperature. At 298 K, the formation free energy for an element in its standard form (e.g., O?(g)) is assigned a value of zero. However, at temperatures different from 298 K, the Gibbs free energy will vary because of the temperature dependence via the relationship ?G = ?H – T?S, and thus may differ from zero even for elements.

Temperature Dependence of Thermodynamic Quantities

Thermodynamic properties such as enthalpy and Gibbs free energy depend on temperature. Their values at temperatures other than the reference point (often 298 K) can be estimated using temperature corrections, typically by integrating the relevant heat capacities or using relations like ?G = ?H – T?S. This means that while an element’s formation values are defined as zero at 298 K, they must be adjusted when considering other temperatures.

Thermodynamic Conventions

Thermodynamic conventions standardize how properties are defined and reported. One key convention is assigning zero values for the standard enthalpy and, at 298 K, the standard Gibbs free energy of formation of elements in their most stable forms. This convention is critical to maintaining consistency across tabulated thermodynamic data and ensuring that calculated reaction energies and free energies are relative to common benchmark states.

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