For Equilibrium between $\mathrm{Al}$ and $\mathrm{Al} 2 \mathrm{O} 3$ at $1273 \circ \mathrm{oC}$, a) Determine the standard enthalpy, entropy and Gibbs free energy of formation of Al2O3 at $298 \mathrm{~K}$ from Ellingham diagram. Compare the results in 1.a. b) Read the equilibrium oxygen pressure $\mathrm{pO} 2(\mathrm{~g}), \mathrm{pH} 2(\mathrm{~g}) / \mathrm{pH} 2 \mathrm{O}(\mathrm{g})$ ratio, and $\mathrm{pCO}(\mathrm{g}) / \mathrm{pCO} 2(\mathrm{~g})$ ratio from the Ellingham diagram using correct scales! c) Write chemical reactions for $\mathrm{Al}(\mathrm{l})$ used for these three different scales. d) What must be the gas mixture for all to protect Al(I) from oxidation? Use equilibrium constants!!

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∻Solution∻ ‖ 1 ⋮ **Determine the standard enthalpy (∆H°), entropy (∆S°), and Gibbs free energy (∆G°) of formation**: To find these values, we use the Ellingham diagram, which plots the Gibbs free energy change for various reactions against temperature. The standard enthalpy and entropy can be derived from the slope and intercept of the line for the formation of $\mathrm{Al}_2\mathrm{O}_3$ from $\mathrm{Al}$ and $\mathrm{O}_2$. ‖ ‖ 2 ⋮ **Use the Ellingham diagram**: The slope of the line on the Ellingham diagram gives the entropy change (∆S°), and the intercept at 298 K gives the Gibbs free energy change (∆G°). The enthalpy change (∆H°) can be calculated using the Gibbs free energy equation $\Delta G = \Delta H - T\Delta S$. ‖ ‖ 3 ⋮ **Calculate the values**: Without the actual Ellingham diagram, we cannot provide numerical values. However, the student would read the slope and intercept at 298 K to find ∆S° and ∆G°, respectively, and then use the Gibbs free energy equation to solve for ∆H°. ‖ ∻1 Answer∻ ⚹ The standard enthalpy, entropy, and Gibbs free energy of formation of $\mathrm{Al}_2\mathrm{O}_3$ at 298 K can be determined from the Ellingham diagram by reading the slope and intercept at 298 K and using the Gibbs free energy equation. ⚹ ∻Key Concept∻ ⚹ The Ellingham diagram provides information about the temperature dependence of Gibbs free energy for the formation of compounds, from which standard enthalpy and entropy can be derived. ⚹ ∻Explanation∻ ⚹ The slope of the line on the Ellingham diagram corresponds to the entropy change, while the intercept at 298 K gives the Gibbs free energy change. The enthalpy change is calculated using the Gibbs free energy equation. ⚹ ‖ 4 ⋮ **Read the equilibrium oxygen pressure ratios**: The Ellingham diagram can also be used to determine the equilibrium partial pressures of gases involved in the reduction of $\mathrm{Al}_2\mathrm{O}_3$. The ratios $\mathrm{pO}_2$, $\mathrm{pH}_2/\mathrm{pH}_2\mathrm{O}$, and $\mathrm{pCO}/\mathrm{pCO}_2$ can be read directly from the diagram at the temperature of interest (1273 °C). ‖ ‖ 5 ⋮ **Write chemical reactions**: For each gas ratio, write the balanced chemical reaction involving $\mathrm{Al}(l)$ and the corresponding gas species. ‖ ∻2 Answer∻ ⚹ The equilibrium oxygen pressure ratios can be read from the Ellingham diagram, and the corresponding chemical reactions for $\mathrm{Al}(l)$ can be written as follows: 1. $\mathrm{Al}(l) + \frac{3}{2}\mathrm{O}_2(g) \rightleftharpoons \mathrm{Al}_2\mathrm{O}_3(s)$ 2. $\mathrm{Al}(l) + \frac{3}{2}\mathrm{H}_2\mathrm{O}(g) \rightleftharpoons \mathrm{Al}_2\mathrm{O}_3(s) + 3\mathrm{H}_2(g)$ 3. $\mathrm{Al}(l) + 3\mathrm{CO}_2(g) \rightleftharpoons \mathrm{Al}_2\mathrm{O}_3(s) + 3\mathrm{CO}(g)$ ⚹ ∻Key Concept∻ ⚹ The Ellingham diagram can be used to determine the equilibrium partial pressures of gases at a given temperature, which can then be used to write the corresponding chemical reactions. ⚹ ∻Explanation∻ ⚹ The equilibrium pressure ratios are determined from the diagram, and the reactions are written based on the stoichiometry of the reaction between $\mathrm{Al}(l)$ and the gas species. ⚹ ‖ 6 ⋮ **Determine the gas mixture to protect $\mathrm{Al}(l)$ from oxidation**: To prevent oxidation, the gas mixture must have a lower oxygen potential than that required for the formation of $\mathrm{Al}_2\mathrm{O}_3$. This can be achieved by maintaining the partial pressures of the reducing gases ($\mathrm{H}_2$, $\mathrm{CO}$) higher than the oxidizing gases ($\mathrm{O}_2$, $\mathrm{H}_2\mathrm{O}$, $\mathrm{CO}_2$) according to the equilibrium constants of the reactions. ‖ ∻3 Answer∻ ⚹ To protect $\mathrm{Al}(l)$ from oxidation, the gas mixture should have a high ratio of $\mathrm{H}_2$ to $\mathrm{H}_2\mathrm{O}$ and $\mathrm{CO}$ to $\mathrm{CO}_2$, maintaining a low oxygen potential and preventing the formation of $\mathrm{Al}_2\mathrm{O}_3$. ⚹ ∻Key Concept∻ ⚹ To protect a metal from oxidation, the gas mixture must have a lower oxygen potential than that required for the formation of the metal oxide. ⚹ ∻Explanation∻ ⚹ The gas mixture should favor the presence of reducing gases over oxidizing gases, which can be determined by the equilibrium constants of the relevant reactions. ⚹◊What is the general relationship between the standard enthalpy, entropy, and Gibbs free energy of formation for a compound at a given temperature?⍭ Generate me a similar question◊

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