QuestionApril 23, 2025

Consider the following reaction and the corresponding data: N_(2)(g)+3H_(2)(g)arrow 2NH_(3)(g) S^circ (N_(2))=192J/molK Delta H_(f)^circ (NH_(3))=-46kJ/mol S^circ (H_(2))=121J/molK S^circ (NH_(3))=193J/molK What is Delta G_(rxn) at 298 K?

Consider the following reaction and the corresponding data: N_(2)(g)+3H_(2)(g)arrow 2NH_(3)(g) S^circ (N_(2))=192J/molK Delta H_(f)^circ (NH_(3))=-46kJ/mol S^circ (H_(2))=121J/molK S^circ (NH_(3))=193J/molK What is Delta G_(rxn) at 298 K?
Consider the following reaction and the corresponding data: N_(2)(g)+3H_(2)(g)arrow 2NH_(3)(g) S^circ (N_(2))=192J/molK Delta H_(f)^circ (NH_(3))=-46kJ/mol S^circ (H_(2))=121J/molK S^circ (NH_(3))=193J/molK What is Delta G_(rxn) at 298 K?

Solution
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Answer

\Delta G^\circ_{rxn} = -41.64 \, \text{kJ/mol} Explanation 1. Calculate \Delta S^\circ_{rxn} Use the formula: \Delta S^\circ_{rxn} = \sum S^\circ_{products} - \sum S^\circ_{reactants} Substitute values: \Delta S^\circ_{rxn} = [2(193)] - [192 + 3(121)] \Delta S^\circ_{rxn} = 386 - (192 + 363) = 386 - 555 = -169 \, \text{J/mol·K} 2. Calculate \Delta H^\circ_{rxn} Use the formula: \Delta H^\circ_{rxn} = \sum \Delta H_f^\circ(products) - \sum \Delta H_f^\circ(reactants) Substitute values: \Delta H^\circ_{rxn} = [2(-46)] - [0 + 3(0)] \Delta H^\circ_{rxn} = -92 \, \text{kJ/mol} 3. Convert \Delta H^\circ_{rxn} to J/mol Since \Delta H^\circ_{rxn} is in kJ/mol, convert it to J/mol: \Delta H^\circ_{rxn} = -92 \times 1000 = -92000 \, \text{J/mol} 4. Calculate \Delta G^\circ_{rxn} Use the formula: \Delta G^\circ_{rxn} = \Delta H^\circ_{rxn} - T\Delta S^\circ_{rxn} Substitute values: \Delta G^\circ_{rxn} = -92000 - (298)(-169) \Delta G^\circ_{rxn} = -92000 + 50362 = -41638 \, \text{J/mol} 5. Convert \Delta G^\circ_{rxn} to kJ/mol Convert back to kJ/mol: \Delta G^\circ_{rxn} = -41638 / 1000 = -41.64 \, \text{kJ/mol}

Explanation

1. Calculate $\Delta S^\circ_{rxn}$<br /> Use the formula: <br />$\Delta S^\circ_{rxn} = \sum S^\circ_{products} - \sum S^\circ_{reactants}$ <br />Substitute values: <br />$\Delta S^\circ_{rxn} = [2(193)] - [192 + 3(121)]$ <br />$\Delta S^\circ_{rxn} = 386 - (192 + 363) = 386 - 555 = -169 \, \text{J/mol·K}$ <br /><br />2. Calculate $\Delta H^\circ_{rxn}$<br /> Use the formula: <br />$\Delta H^\circ_{rxn} = \sum \Delta H_f^\circ(products) - \sum \Delta H_f^\circ(reactants)$ <br />Substitute values: <br />$\Delta H^\circ_{rxn} = [2(-46)] - [0 + 3(0)]$ <br />$\Delta H^\circ_{rxn} = -92 \, \text{kJ/mol}$ <br /><br />3. Convert $\Delta H^\circ_{rxn}$ to J/mol<br /> Since $\Delta H^\circ_{rxn}$ is in kJ/mol, convert it to J/mol: <br />$\Delta H^\circ_{rxn} = -92 \times 1000 = -92000 \, \text{J/mol}$ <br /><br />4. Calculate $\Delta G^\circ_{rxn}$<br /> Use the formula: <br />$\Delta G^\circ_{rxn} = \Delta H^\circ_{rxn} - T\Delta S^\circ_{rxn}$ <br />Substitute values: <br />$\Delta G^\circ_{rxn} = -92000 - (298)(-169)$ <br />$\Delta G^\circ_{rxn} = -92000 + 50362 = -41638 \, \text{J/mol}$ <br /><br />5. Convert $\Delta G^\circ_{rxn}$ to kJ/mol<br /> Convert back to kJ/mol: <br />$\Delta G^\circ_{rxn} = -41638 / 1000 = -41.64 \, \text{kJ/mol}$
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